VALUATION, DEPRECIATION AND THE RATE-BASE VALUATION, DEPRECIATION AND THE RATE-BASE CARL EWALD GRUNSKY, Exc. D. Member of the American Society of Civil Engineers Member of the American Institute of Consulting Engineers ASSISTED BY CARL EWALD GRUNSKY, Jr., E. M. Member of the American Society of Civil Engineers SECOND EDITION REVISED AND EXTENDED NEW YORK JOHN WILEY & SONS, Inc. Lonpon: CHAPMAN & HALL, LiMiTED BY 1927 COPYRIGHT, 1916, 1927, BY C. E. GRUNSKY Lo © TARE & Printed in the U. S. A. Stanbope Press TECHNICAL COMPOSITION COMPANY F. H. GILSON COMPANY BOSTON, MASS. UA ta ' A 3 . PREFACE TO SECOND EDITION In this revised edition of ““ Valuation, Depreciation and the Rate-Base,” several new chapters have been added and the tables at the end of the volume have been extended both in number and in the degree of accuracy to which values are therein given. One of the new chapters, appearing as Chapter XIV, deals with “ The Standard of Value;” another, Chapter XV, is devoted to some elements which deserve special consideration when rates of public utilities are to be fixed — such as obso- lescence, losses from fortuitous events, hazard, compensation for management, the relation of intangible elements of value to the volume of business and the like. In the introduction to Table 33 (old Table 27) attention is called to the error in the formulas as ordinarily used for the determination of present value and of ac- crued depreciation — this error resulting from the non-conformity of the actual life of individual articles of any group with the aver- age life thereof. In a new paragraph on page 31 the use of the term ““ Natural Rate-Base ” is suggested. The general accept- ance by valuation experts of the term ‘ Rate-Base ”’ has been noted with much satisfaction. C. E. GRUNSKY. San Francisco, CAL., May, 1926. PREFACE TO FIRST EDITION A thorough discussion of the principles which control the engineer, the economist, the assessor and the business man in making valuations will not be attempted in these pages. This book is the result of personal contact with the valuation problem. No apology need be made for the fact that, in pre- senting an original analysis of the problem, the arrangement of the material is not always as logical as might have been ex- pected if the present state of the art only had been brought under review. Special consideration has been given to a dis- cussion of the non-agreement of the actual life of articles which have a limited period of usefulness with their probable or normal life. The effect of this non-conformity has been studied by the author and the results have been thought worthy of a special chapter. These results show that there is great advantage in adopting, instead of ““ present value,” a rate-base without deduc- tion of depreciation, which will include but little, if anything, other than legitimate and properly estimated cost as the start- ing point when rates are to be fixed. He therefore recommends for the thoughtful consideration of the student, the method of procedure which he has named the Unlimited Life Method and which is herein fully explained. The author feels, too, that the owner of a public utility is, generally, entitled to larger earnings than will yield a bare interest return on the invested capital. Volume of business transacted and also the unearned increment should, sometimes, be taken into account when estimates are made of the earnings that may with propriety be allowed. Such matters as these have received attention and it is hoped that some of the ideas that are herein advanced may stimulate further thought along similar lines and may, here and there, prove helpful to those who have appraisals to make or . PREFACE rates for an output or for a service to establish. Careful at- tention has been given to the fundamental principles which should control when appraisals of public utilities are made for rate-fixing purposes and their practical application is explained. The tables which are presented in this volume are intended to meet the needs of valuation engineers, but will also be found useful by any one having problems of finance and bonding to solve. They are based throughout on original calculations. Those relating to replacement requirements and to expectancy are of a novel type not to be found elsewhere. Special care has been taken to secure accuracy and convenient arrangement. Acknowledgment is due to the office staff of the American Engineering Corporation the members of which have assisted in the preparation of the tables. C. E. GRUNSKY. San Francisco, CAL. February 1st, 1916. In the second thousand of this book there will be found a new paragraph on page 31, suggesting the use of the term ‘natural rate-base,’”’ and, at the end of the volume, a mathematical demon- stration of error when the depreciation of any article is deter- mined by ordinary methods. Some minor changes and correc- tions of a few typographical errors have also been made. C. E. GRUNSKY. San Francisco, CAL., April 30th, 1918. v1] Note ABBREVIATIONS AND NOTATION Amort. = Amortization. Ann. = Annual. Beg. = Beginning. Eq. = Equal. Payt. = Payment. A = the annual replacement requirement for each dollar of capital invested annually in a growing plant. Am = the accrued amortization in m years when the annual amortization in- stallment is @ and the interest rate is 7. A’ = the amount of $1.00 at compound interest at the end of the nth year at the interest rate 7. A” = the amount of an annuity of $1.00 paid at the end of each year at com- pound interest at the interest rate i. an = the amortization installment which must be invested annually, in order to amount at compound interest to $100 in n years. a,’ = the annual installment which at compound interest at the rate 7 will amount to $1.00 in 7 years. an!’ = same as an’ when annuity is applied at the beginning instead of at end of year. an'"’ = the annuity receivable at the end of each year which $1.00 will buy for n years. am = the current amortization in the mth year, i.e., the amortization incre- ment a plus interest on the amortization fund already accumulated. It is the amortization installment which in the remaining years of life will retire the remaining capital. C = cost of replacing a group of articles. ¢ = the annual renewal requirement for a group of articles whose cost of replacement is C. e = expectation, that is the probable remaining years of usefulness of any article whose probable life new was » years. ¢ = relative expectancy of an article whose probable life new is 10 years when compared with an article m years old whose probable life new is n years. g = the average annual investment in additions to a plant. i = the rate of interest per year expressed fractionally — thus for 6 per cent; 7 = 0.00. m = a number of years. m’ = relative age of an article whose probable life new is 10 years, when compared with an article m years old, whose probable life new is #n years. Note: Other symbols are explained in the notes which precede the several tables. 3 1 Vili : ABBREVIATIONS AND NOTATION n = the probable life term in years of any article; or the term of amorti- zation. P = the present value of $1.00 due at the end of » years. P’ = the present value of an annuity of $1.00 receivable at the end of each year during » years. R = amount in the replacement fund expressed in percentage of the original investment. S = the sum of all annual replacement requirements estimated for a number of articles of various ages. Sn = the sum of all annual replacement requirements during » years. CONTENTS CHAPTER 1 Page INTRODUCTION AND GENERAL NOTES + « + « ¢ es 00a sss sess easns I CHAPTER 11 DEFINITIONS « » «xs a a oe Tze ss sxsw vss suns: 10 CHAPTER III FUNDAMENTAL PRINCIPLESIE, eT es she sos cotit ss ssocesesisno 32 CHAPTER 1V ESSENTIALS OF VALUE: Cost of Physical Elements. . « « + + « «10s v.05 nm s.55s 820s 38 Overhead EXPenses, « . + acs sss v0 x a sien wis winin vinie uo oivie S42 Promotion EXpenses . . . «ccc «vv sions sinnsseneieniny sis Noy Intangible Elements of Value . .........c. oie Franchisesand Related Matters . . . . . « cc te ces ss svn n se "4 Appreciation and the Unearned Increment . . . . . «ovo v vv nn 73 CHAPTER V ELemeNTs WHICH REDUCE VALUE: Deductions from Value (|. . 0 alte ol a ial sieiie te xiiwiiol whale lice eeibenekic $70 The Overbuilt Plant and Property not Required for Immediate Use 80 Depreciation, Amortization, and the Replacement Requirement . . . 84 CHAPTER VI Tae Errect oF THE NON-AGREEMENT BETWEEN AcTUAL AND PROB- ABLE LIFE UroN THE DETERMINATION OF DEPRECIATION ... 1I04 CHAPTER VII Tae PURPOSE OF THE APPRAISAL: General Statement . « oo Vala ules sine 'n a einle xe et ul olin sle le W122 Valuation for Purchase or Sale . «vv ss vas a's din vvnisla sini 124 Appraisals as a Basis for Fixing Rates . ................ 127 Appraisals for Taxation Purposes . ........ 00000... 138 Appraisals for the Purpose of Capitalization ............. 139 CHAPTER VIII TeE FIxXing or RATES: Public Utilities and the Regulation of Public Service ........ 140 The Rato-Base . « « « « sino = + = wie ute ielntietetti) sie sisiwie visiv: i 150 1X CONTENTS CHAPTER IX AGE PossiBLE PrRocEDURES WHEN THE RATES FOR A PUBLIC SERVICE ARE OE RD ee et se =e el us CHAPTER X Notes oN THE DETERMINATION OF THE VALUE OF REAL ESTATE IN EMINENT DOMAIN PROCEEDINGS AND FOR RATE Fixing Pur- PORE oe I ae a eves =o re Ty CHAPTER XI THE VALUE OF A WATER-RIGHT AND OF RESERVOIR AND WATERSHED ARDS Ee 0 Se el le ets iy ak ip re a Vs ITO CHAPTER XII THE ACCOUNTING SYS Try Tr alles oo a, 229 CHAPTER XIII THE VALUATION oF MINES AND OIL PROPERTIES By CE, GRUNSRY, Jr, ee = = =o 237 CHAPTER XIV HE ANDAR OR ALE LE = = es as a oe a ee ul a3 CHAPTER XV ELEMENTS DESERVING SPECIAL CONSIDERATION WHEN RATES ARE TO BE orgy NE re Avy eve ERRATA TARR CHAPTER XVI A Few Recent Court DECISIONS rete 3 CHAPTER XVII SUPPLEMENT =="PABTES |. |, to luis ott a lo tie wo To” od ule Fal wal) ei Vm i fn (nln LE STO) INDEX TOMPARTERY fi a te te ole Tee eee ty ea hole Le ila lle il E308 TABLES: 10: Simple Tuterest, 360 Day Year . loo tl Al NS iia SL LS ia6 20, The Number of Fach Day in the Year .}, nilel olivia i, Lo ias8 21, Simple Interest, 365 and 366 Day Year. i. i a 0.88 SLE 320 22. Amount of One Dollar at Compound Interest . . . .......... 332 23. Amount of One Dollar at Compound Interest Compounded Every Sl amis a a a Re te Rhee U Medes! of olla eit fy ll SAE 24. Amount of One Dollar at Compound Interest Compounded Every Three Mantle ae Hie Lee cise a fu vv iar BR BAS 25. PresentiValue of One Dollar i 0 tat fl be ll i i 3 oY 26. Amount of an Annuity of One Dollar iat fia. 0 RE ILE. 5.8 BN 364 27. Annuity which will Amount toOneDellar .............. 377 28. Present Value of an AnnuityofOneDollar . . . . ... ....... 390 20. Annuity which One Dollar willlPurchase®. 0.0L REED, LL. 403 30. The Probable Useful Life of Machinery Structures and Appliances. . 415 31.) Expectancy and Remaining Value is flo BUR ELL LE0 L . e og 3D 32. Expectancy of Human Life... |. i iu it en hile o 0 Js S440 23. Amortization and Depreciation. i=. i= 0. 0.0.5. ff 0 0 LL Le 2 x P= z= 2I¢ VALUATION, DEPRECIATION AND THE RATE-BASE CHAPTER 1 INTRODUCTION AND GENERAL NOTES Conflicting Views Relating to Procedure. — The need of har- monizing the conflicting views relating to the best methods of dealing with the establishment of rates that are to be charged by public service corporations for the service which they render or for the commodity which they supply is recognized by econo- mists and engineers. This need is the more pressing in view of the fact that the public, in exercising control over the opera- tion of the utility through properly constituted authority, may and no doubt frequently has established onerous and burden- some regulations, resulting at times in the confiscation of prop- erty. At any rate the limitations relating to permissible charges have frequently been such that the question of the reasonable- ness and sufficiency of these charges has been taken into court and the courts have reached certain conclusions from which there is apparently no appeal but concerning some of which the wisdom of permanent enforcement may well be called in question. Rapid progress is being made in recognizing the fundamental principles which should control when an appraisal of public service properties is to be made as a basis for the establishment of rates for service rendered. This subject is, however, today still in a controversial stage. The assembling of facts relat- ing to such fundamental principles as will be of service to the appraisers of operating plants of any character, whether used 2 VALUATION, DEPRECIATION AND THE RATE-BASE in the public service or not, is the task which was set in under- taking the preparation of this volume. It is hoped that the same will fill the gap for a time until wider experience of the valuation experts shall have eliminated the involved and ofttimes useless procedures which are still in practice and explanations of which have, therefore, been included in the text. The Public and the Owner. — The question may well be asked whether the reformer, who has been seeking protection against the demands of the trusts and corporations which have frequently been guilty of over-capitalizing, has not in his turn gone too far in the endeavor to reduce the earnings of the cor- poration-owned public utilities. The public has demanded and, in some measure, has obtained, from various rate-fixing bodies, and from the courts, the introduction of methods of procedure that are not always equitable, but the baleful effects of which are slow in becoming manifest. There has, for example, been no little confusion in the matter of defining depreciation and not a few valuation experts have had difficulty in grasping the fact, which when once recognized seems fundamental, that the repayment of capital (amortization), is one thing and that the making of provisions for the replacement of worn-out or dis- carded parts at the end of their term is another thing. It is fundamental that the owner of a public utility should be allowed: a. To obtain, sooner or later, a reasonable return on his investment. b. To recover at some time the capital invested for the public good. ¢. To reap a suitable reward for establishing and managing the enterprise. It is the knowledge that these principles have obtained uni- versal recognition which prompts the capitalist to embark upon such ventures as those known as public utilities. Control of Public Utilities a Recent Innovation. — Until within the last few decades the control by the public of the operations of the public utility concern has generally been so loosely ex- INTRODUCTION AND GENERAL NOTES } ercised that the margin for a possible profit was large; regula- tion was more or less perfunctory and, very frequently, due to the imperfect knowledge of the problem, neither the owner of the utility nor the rate-payer knew whether the earnings were deficient, reasonable, or excessive. The recent tendency of the public to insist upon its right to control and the attempt to make a close study of what would in each case be reasonable earnings has stimulated the work of the economist and the valuation engineer and has led to a consideration of many new phases of an interesting subject. Prof. John H. Gray in an address before the Economic Club of San Francisco on July 28, 1914, in presenting a historical survey of public utilities said: “We have very recently entered upon the experiment of administrative control through central commissions. But we have failed entirely to grasp the significance of the problem, or the steps necessary to solve it, if we fail for a moment to re- member that until the establishment of the Board of Gas Com- missioners in Massachusetts, in 1885, no industries, save that of transportation, were classed as utilities, and that the other states have been very slow to follow the lead of Massachusetts in this matter. In fact, it is only within the last decade that the problem may be said to have been taken up seriously by the country as a whole. That is altogether too short a time to adjust the law, the theories, or the practices to the economic needs and conditions of the situation. Much more is it too brief a period in which to have modified to any considerable degree the pioneer philosophy that still dominates the private owners of these industries. “The scientific theory is that the utilities should render adequate, safe, and universal service, at just, reasonable, and fair prices to all, and that the sovereignty shall be the final judge in every case of these matters. This statement implies, of course, that the total gains or rewards of the owners shall be reasonable under all circumstances, including that of virtually guaranteed monopoly, and that they shall have just compen- sation in case of expropriation.” Fundamental Principles Apply to Industrial Establishments. — The work which has been done in studying the fundamental 4 VALUATION, DEPRECIATION AND THE RATE-BASE principles looking to the fair treatment of both the rate-payer and the owner has also been of benefit in a large way to the factory, and to all the great industrial establishments of the country, because it points the way to a closer approximation of the actual cost of production, thereby establishing a better basis for fixing the sale price of the output. The discussions in the following pages are necessarily directed mainly to the valuation of public service properties and to a discussion of the procedure to be followed in determining what are reasonable earnings, but the general fundamental principles are equally applicable to the private concern. Value must be ascertained when the ownership of property is to be transferred from one person to another as in the case of a sale; it must be ascertained when the property is capitalized as a basis for the issuance of securities, and, too, for taxation purposes. When rates or prices to be charged for service or commodity output are to be fixed, it is necessary to know the amount of capital which is properly invested — to know, in other words, what the amount is which should be taken into account as a ‘‘ rate-base.” Depreciation and Withdrawal of Capital. — The practice is altogether too common of treating every earned depreciation allowance as equivalent to a withdrawal of invested capital and of assuming that any of the various methods of estimating present value are equitable, regardless of the past history of the plant under investigation. So, too, there is sometimes a too rigid construction of the generally recognized requirement that only those parts of a property which are actually in use or which are useful elements are to be considered in valuing the property for rate-fixing purposes. This has occasionally worked a hardship upon the public service corporation and may there- fore be regarded as one of the factors which have caused a de- mand for large allowances for all kinds of intangible and more or less indefinite elements of value to offset losses and unpro- ductive investments. Every private industrial establishment, too, has its depreciation INTRODUCTION AND GENERAL NOTES 5 problem to deal with. Depreciation enters into the cost of pro- duction and must be covered in the sale price if there is to be any profit. The cost of the perishable parts of the plant which are consumed, just as fuel is consumed though at a slower rate, must be recovered sooner or later. Definition of Terms. — The definitions of terms, herein pre- sented, relate to the sense in which these terms are used in this volume. There is not yet any perfect agreement among en- gineers and accountants relating to all of these terms and, as time goes on, some modification of terms or of the definitions of terms is to be expected. These definitions are therefore offered with due appreciation of the fact that some of them may not survive and that others remain subject to modification. The Agency Theory. — Every owner of a public service prop- erty is in a certain sense the agent of the rate-payer. If re- garded as such agent he is under obligation to render the service which he has engaged to perform in a satisfactory manner; he is entitled to protection against unreasonable competition, and he is entitled to protection of his investment, provided, of course, that the investment is a proper and reasonable one. There may be some cases, however, where unwise investments have been made, and others where part compensation for making the in- vestment has been found in the increased value of real estate or other property, perhaps not connected with the utility but owned by the same individuals who own the utility, and in such cases the value of the service rendered to the public may bear an unusual relation to the investment. Thus an irrigation canal, which was constructed to develop a region of little or no value without water, when considered by itself, apart from the land which it irrigates, may have cost so much that the service charges cannot be made high enough to yield a revenue on its cost. And yet the canal was justified, though perhaps not as a separate venture. In such cases a transfer of the canal to the land owner would be appropriate in order that the question of a reasonable return on invested capital might be eliminated, or as an alternative a bonus charge 6 VALUATION, DEPRECIATION AND THE RATE-BASE against the land whether under this name or under the name of “water right,” or otherwise, might be agreed to, such that the capital remaining in the canal enterprise, as a proposition apart from the land, would be reduced to a reasonable amount. If neither of these alternatives are adopted the canal venture may be permanently unprofitable, from the standpoint of present owners. This will be the case when the rates that would yield interest on the investment are in excess of the value of the service rendered and cannot be supplemented by a participa- tion of the canal owner in the unearned increment which the construction of the canal has brought to the land owner. As another illustration a railroad may be considered which was primarily constructed for the development of a tract of land or for the development of mineral or timber resources. There can be no question that when considered from the broad standpoint of the advantage to society the construction of a railroad under such circumstances may be justified. When this railroad begins to serve the public and the freight tariff and passenger rates are to be fixed, these may have to be established on the basis of the fair value of the service rendered without any attempt to make the earnings yield interest on the capital invested in the road, or suitable consideration may have to be given to the fact that a part of the investment was made for the benefit of some special enterprise such as a rock quarry or a lumber business and should not have been charged to the road at all. These limitations upon the use of an appraisal as an element for consideration in fixing rates are fully recognized, but these and other limitations are not such as to detract from the de- sirability of referring to and using appraisals under ordinary circumstances. Basis for Sale Price — Business Enterprises. — Everyone who engages in a business enterprise must know: The cost of the article in which he deals at the time the article is sold. The cost of the plant such as buildings, roads and equipment INTRODUCTION AND GENERAL NOTES which are necessary to manufacture or to care for the article pending the time of sale. The operating costs of the business. The depreciation of the plant or the replacement require- ments thereof. The profit which it is desired to make. When these elements are known and a proper analysis of operating cost has been made the prudent business man will distribute his fixed elements of cost, such as management, de- preciation and the like with a view to making the price of the article or the charge for the service which he renders, attractive to his customers. In a large machine works where the charges for repair work appeared unusually high, it was found upon investigation that overhead expenses were unequally distributed to new and to the repair work. This was done in order that new work which had to be obtained in competition with other concerns could be taken at lower figures. While this is only an isolated example, it shows the importance of being in a position to analyze costs in order that charges may be fixed low enough to secure business and yet high enough to yield an adequate profit. Reference to the Tables in this Volume. — As an aid to the appraisers of industrial and public utility properties, this volume would fail in its purpose without tables containing information relating to the probable term of service and the expectancy of the articles in common use in such establishments or plants and also interest and annuity, amortization and depreciation tables. The amortization and depreciation table not only covers a range from 2-year life to 75-year life, but it has been so arranged that the remaining years of service, instead of age, can be made the starting point when it is desired to enter the table for present value and the so-called current rate of depreciation. While such tables and explanations as are furnished in this volume are generally applicable they have been prepared, as stated, with special reference to the requirements of appraisers and of the public service commissions and of other rate-fixing / 3 VALUATION, DEPRECIATION AND THE RATE-BASE bodies. They will meet, too, the requirements of the owners of industrial and other properties, who owing to lack of such in- formation occasionally allow over-capitalization and excessive dividends, coupled with inadequate earnings, to cripple their enterprises. The Panama Canal and Fundamental Principles. — The neces- sity for a clear understanding of the fundamental principles to be followed when rates are to be fixed may be illustrated by reference to the case of the Panama Canal. Here is a great work representing an investment by the United States of about $375,000,000. Itis a type of canal which involves large oper- ating expense. In connection with this canal the question arises: What should the earnings be? The problem of the canal tolls may be broadly considered along the following lines: First: Who is ultimately to pay for the canal? Is it to be the user of the canal? Second : Has the canal been built by the United States as a revenue-producing investment or is the canal to be regarded as worth what it has cost for military purposes and as an instru- ment of general benefit? Third : What shall be included in the operating expenses? The ordinary citizen is under the impression that the $375,- 000,000 which the canal has cost is an investment similar to those which the United States has made in constructing the Eads jetties at the mouth of the Mississippi river, in constructing the Ambrose channel for access to the New York harbor, and in building the San Pedro breakwater for the protection of the harbor of Los Angeles and the Columbia and Eureka bar jetties for the improvement of other Pacific Coast harbors of more or less local importance. If this is the fact, the investment in the canal has been made as a non-revenue-producing investment for all time and there will be no need of recovering the cost of the canal from those who use it nor even interest on this cost. If the United States plans to collect the cost of the canal in in- stallments from the users of the canal, no matter how small INTRODUCTION AND GENERAL NOTES these installments may be, the canal will ultimately be paid for, in part at least, by foreign people. And if interest only is covered by the toll charges, then this Nation will stand in the position of having made a loan to the commercial interests of the world of $375,000,000 for the construction of the canal. Once the fundamental principle has been adopted relating to the extent to which commerce shall recoup the United States for its outlay and the question has been settled as to whether the users of the canal shall pay interest on the investment, the question of operating expenses will have to be taken up. Salaries, wages, materials and supplies are readily determinable. All expenditures for repairs and upkeep will be included with per- haps no difficulty until the question of depreciation is to be con- sidered. Shall each element or class of elements be considered sepa- rately, according to probable useful life, and some sum be set aside which together with interest thereon will replace the worn- out parts, or shall the amount to be set apart for replacements be determined directly from the relation of probable life to the cost of replacement of each perishable part by setting apart an- nually such a fraction of the cost that these annual increments, without interest, added together will be equal to the cost, or finally shall provision be made from year to year for the re- placements that will probably have to be made in each year? It is hoped that what is presented in this volume may prove of some assistance in the solution of problems of this character. Unprofitable Expenditures and Early Losses. — Unprofitable and unproductive expenditures which may be the results of mistakes or of accidents and early losses in the business are elements which should not be regarded as adding value to a property. They belong in some measure to the hazards of the business. They are, nevertheless, to be taken into account when rates are to be fixed because they usually represent legiti- mate expenditures. They represent an outlay which in nearly every case would have been incurred under consent of the rate- payer, if the owner had been acting as the agent for the rate- 0 10 VALUATION, DEPRECIATION AND THE RATE-BASE payer and with his approval. Consequently the rates should be fixed with a view to amortize sooner or later such expenditures. In thus making provision for unproductive expenditures de- termined, perhaps, from actual expenditures legitimately in- curred in excess of cost of works in use, care must be taken not to go too far. Wasteful expenditure is not to be sanctioned and wise and prudent management is entitled to reward. Ex- perience alone can determine what allowance should be made for hazards of the business and for the cost of establishing the business and bringing it up to a paying basis. If it be found, for example, that a suburban electric road will not be on a pay- ing basis for a number of years, the losses (or deficient earnings) during these years may be added to the cost of the road not as elements of value but as a part of the investment on which an interest return is to be allowed or as the preferable alternative, net earnings in excess of interest on the cost of the road can be allowed in such amount that within a reasonable time the early losses will be amortized. Thereafter a continuation of some excess of earnings above the returns from ordinary safe invest- ments will be the owner’s reward for having engaged in the enterprise. Franchise and Water-right Values. — When the public through properly constituted authority grants a franchise or confers a privilege to enter upon a business which is in the nature of a public service, as, when it grants the use of water for power, for irrigation or for other purposes, the franchise or water-right is valuable only to the extent that the public pro- vides a market for the service rendered or commodity supplied. When the rates to be charged are subject to regulation and are not fixed in the franchise or water-right grant, no basis exists (except in the cases of strategic value) for determining fran- chise or water-right value. This value depends, as will be explained, upon earnings in excess of a fair return on the invest- ment and if earnings are not protected by franchise terms, it will lie in the power of the rate-fixing body to eliminate fran- chise and water-right value altogether. This is as it should INTRODUCTION AND GENERAL NOTES I: be. At the same time with due regard to the share in the general prosperity to which the owner of the utility is entitled, he should be allowed to earn more than ordinary interest on his investment and a capitalization of any such excess earnings when these are fairly assured will furnish him with a basis for approximating the sum of all intangible values of whatever nature. Amortization and Depreciation. — A clear distinction should be made between the amortization of capital that is invested in any enterprise and provision for depreciation or the replace- ment of perishable elements. The sinking fund for the retire- ment of bonds, or other debt, should not, in other words, be confounded with the fund usually referred to as the “ deprecia- tion ”’ fund which is intended to meet the replacement require- ments as they arise. Valuation for Purchase or Sale. — In appraising for a sale, various matters are to be taken into account which are of minor importance when rates are to be fixed. If the accrued de- preciation has actually been allowed in the earnings and has been permitted to accumulate in a fund, and if the accumulated fund properly represents the accrued depreciation, and is a part of the property to be transferred, then the appraisal in- cluding this fund should be in substantial agreement with the legitimate investment. If, on the other hand, there is no de- preciation fund, if the earned and collected adequate depre- ciation allowance in excess of the expenditures therefrom for replacements has been absorbed for other purposes by the owner, then a purchaser would make the depreciated value or the legitimate investment less depreciation his starting point in determining the amount which a plant is worth, because in purchasing the property he assumes an obligation to replace perishable parts as they go out of use. If the plan is followed of allowing earnings which will meet all replacement require- ments together with interest on the full investment, without deduction for depreciation, then a purchaser in view of the assured return will make the legitimately invested capital i) 12 VALUATION, DEPRECIATION AND THE RATE-BASE without deduction for depreciation his starting point in de- termining what he can afford to pay. This last case is in conformity with the requirements herein explained, that the investment in a public utility should remain, at all times, unimpaired. It is at variance with the plan ad- vocated by many and approved in various court decisions, that the appraisal for rate-fixing purposes shall fluctuate from year to year with the age and remaining service value of the perish- able elements that go to make up a public service plant. Present Value as a Starting Point. — Despite prevailing sen- timent and rulings of the public service commissions and de- cisions of the courts in favor of making ‘‘ present value’ the starting point when rates are to be regulated, it will be ap- parent to the student that what is estimated as ““ depreciation ” which may never have been earned and collected has not neces- sarily been a repayment of capital and that therefore “ present value ” is not always the best starting point. The wisdom of starting with present value ”” or with “ value ” in any form may well be questioned because value is a result of assured earnings and such values as are not covered by the invest- ment do not exist until the earnings create them. In appraising for rate-fixing purposes the aim should be to make the legitimate investment and not the depreciated value the rate-base. It is sometimes difficult to modify the “fair value” basis of rates as heretofore insisted upon by the courts so that it will fit local conditions as in the following illustrations: 1. Adjacent to the built-up section of a community which is being supplied with water at satisfactory and in every way equitable rates, a large subdivision of acre property is being made. Streets have been laid out and paved, sidewalks have been constructed, an adequate sewer system has been provided and a system of water mains has been constructed. These water mains conform in every respect to the requirements of the owner of the water-works to whom this system of mains is now offered on the sole condition that he supply prospective customers with water. INTRODUCTION AND GENERAL NOTES 33 Acceptance of this system of mains may bring no immediate increase of revenue. The development of the newly subdivided area may be slow. Some years may elapse before the sales of water in the district will be equal to the added burden of main- tenance, collection of rates, and depreciation. Shall part of the system thus acquired be included in the valuation on which the owner is to receive a return? Or shall such inclusion be deferred? And if deferred for how long a time? The inclusion of such property merely because it has “ value ” can perhaps be justified on the plea that it makes no difference what a plant has cost the owner and that according to the de- cision of the courts value alone should be considered. It will be held that it represents a necessary extension of the distribut- ing system that could best be made at the same time that other street improvements were made, and that it would be impracti- cable to attempt in the case of this considerable addition to the system to fix the time when the extent of the use of such new pipe and the addition of revenue resulting from such use would no longer add to the burden of the remaining, or rather, older rate-payers. But the fact remains that when considered as the agent of the public the water-works owner hasnot made the in- vestment. The investment has been temporarily made by the owner of the subdivided tract. He will be reimbursed by the purchaser of lots, for the outlay for this and all other improve- ments made on the tract will appear in some form in the selling price of the lots. If the municipality owned the water-works, in what situation would it now find itself? The same treatment should be ac- corded the owner as would be accorded to an agent of the mu- nicipality. Viewed from this standpoint, the owner, when he accepts the addition to his distributing pipe system as a gift, assumes at once also the obligation to keep this part of the system in repair and to replace the same when worn out or dis- carded for other reasons. The owner is therefore entitled (necessity for the extension of the system being admitted) to the A i + LR 14 VALUATION, DEPRECIATION AND THE RATE-BASE necessary allowance for operating expenses including a proper allowance for anticipated future replacements but should not always immediately be allowed interest on the full cost of this extension which, as already stated, together with other im- provements such as street grading, paving, sidewalk and sewer construction will be included in the price charged by the owner for the lots and will therefore represent a contribution by this new section of the municipality to the cost of the privately owned water-works. In some measure a donated extension to a water-works system, as here used for the purpose of illustration, bears a similar re- lation to the plant, as does property held for future use in excess of the capacity of the plant, with the difference that in the one case the public donates the property to the owner, in the other, the owner secured the same by investing his own capital. In the fixing of rates the increase of capital due to the receipt of gifts and donations should generally be considered separately from the actually invested capital. Individual cases will arise requiring special treatment. The owner in most cases will not be entitled to as large a return on this donated capital as on his actual investment. 2. The above case is not materially different from that of the municipality which needs water-works but cannot afford to make the necessary expenditures. To induce the investment of private capital in a water-works enterprise, the offer of a bonus is made. To avoid legal restrictions this has sometimes been done through the medium of extra large annual payments extending through a number of years for the water required for street sprinkling, for sewer flushing, for extinguishing fires and other municipal uses. Whenever a direct or an indirect con- tribution is thus made, the owner’s invested capital — the rate- base — is not necessarily represented by the cost of the repro- duction of the entire water-works. Fair Value as a Rate-Base. — In concluding this introductory chapter attention may be called to the accepted view of the courts in the matter of valuations for rate-fixing purposes. It INTRODUCTION AND GENERAL NOTES I§ appears from the various decisions of the courts which have been cited and from many others that might be referred to, that the majority of the courts are definitely committed to the idea of making the ‘fair ”” value of the property used for the con- venience of the public, that is to say the “ present value ” of this property the basis of all calculation as to the reasonableness of the rates to be charged by a public service corporation. If the general analysis of the fundamental principles, which must control when rates are to be fixed, as presented in this volume, contributes in any degree to the modification of this attitude of the courts, the author will feel repaid for having at- tempted the analysis. It seems to him illogical to make the earnings dependable on value which itself is the direct result of the earning capacity of the property for whose output rates are to be fixed. The real starting point is the properly invested capital and the volume of the business which is transacted. What consideration should be given to these elements and to other factors affecting a legitimate return to the owner of the public service property will be further discussed. CHAPTER II DEFINITIONS Value. — Value is the worth of anything measured by any standard of purchasing power. It is the exchange power which one commodity or service has in relation to another. The word value is used in this sense throughout this volume. The other meaning of the word relating to adaptability for a certain purpose has not been brought under discussion. It is only value in exchange and not utility which is of interest to the appraiser. A careful distinction must be drawn between the cost of an article and its value. The cost frequently determines the price at which an article is offered and taken in exchange and there may therefore be at times a close relation between cost and value. But the words are in no sense synonymous and cannot be used interchangeably. Value in the sense of worth estimated by any standard of purchasing power, is, in the case of such properties as public utilities, a result of the earning capacity. In the case of certain properties such as highly improved residence property a de- termination of value from earning capacity may not be imme- diately apparent but the rental value is nevertheless generally there and can be determined. In the case of such properties as works of art, however, which are not ordinarily revenue pro- ducing, but which are desired for the pleasure which they give and for educational purposes, the value in exchange cannot thus be measured, and consideration must be given to the more abstract question of supply and demand. The discussion in these pages will be restricted to the valuation of properties which have an earning capacity. Market Value. — In the sense in which used in this volume “ value ” is synonymous with market value. 16 DEFINITIONS ; Fair Value. — The term “fair value” is used so frequently in the valuations of public service properties for rate-fixing purposes, that it deserves more than passing notice. As a basis for the fixing of rates it is difficult to define. Apparently it is usually intended to mean market value, — the value which would be ascertained by a prudent purchaser making thorough inquiry relating to all circumstances affecting value. But in reality the value is a result and not a basis of earnings. It should not be made the rate-base.” The term ‘fair value ”’ has been used in a measure, no doubt, to rule out ““ book value ” or cost which may include items and amounts of doubtful propriety and to rule out estimates of value based on stock and bond issues and the market value of such securities. The term fair value as used by the courts has not yet been satisfactorily interpreted and no attempt will here be made to reconcile divergent views in relation thereto. But attention may be called to the difficulty which has been experienced by all who have attempted to make appraisals for rate-fixing purposes, in reconciling the value to a purchaser with the “fair value” which the courts wish to have considered when fixing rates. Why should there be one valuation for purchase and another for rate-fixing? The answer that has been given by the courts is practically to the effect that there should be no such difference, and experts have found difficulty in so appraising values that any such difference shall disappear. The value to an investor is unhesitatingly determined from the net earnings, with due regard to hazards of the business. The value for rate-fixing purposes as the courts say is to be that value on which, with the same regard for the hazards of the business, the owner is to be allowed to earn a fair interest return. Value should be the same whether determined by a rate-fixing body or whether determined for a purchaser. When the acquisition of the properties of the Maine Water Company by the Kennebec Water District was under consider- ation, the Supreme Judicial Court of Maine included in its in- structions to the appraisers (Dec. 27, 1902) the following: I 18 VALUATION, DEPRECIATION AND THE RATE-BASE “ The capitalization of income, even at reasonable rates, can- not be adopted as a sufficient or satisfactory test of present value. But while not a test, present and probable future earn- ings at reasonable rates are properly to be considered in de- termining the present value of the system.” In this case, ‘“ Kennebec Water District vs. City of Waterville et al” (97 Maine 185; 54 Atlantic 6), the district was authorized by law to acquire the entire plant property and franchise, rights and privileges of the Maine Water Co. and the instructions referred to were issued by the court upon a joint request. According to the decisions of the courts, as the matter stands today, that which is to be ascertained and made the starting point when rates are to be fixed, is the present value of the property devoted to the public use. In this connection the Supreme Court of the United States says in the Minnesota Rate Cases (230 U.S. 352): “ The basis of calculation is the fair value of the property used for the con- venience of the public.” In San Diego Land and Town Co. vs. National City the Court says, “ What the company is entitled to demand, in order that it may have just compensation, is a fair return upon the reasonable value of the property at the time it is being used for the public.” In the Minnesota Rate Cases the Court also quotes with its approval from Smyth zs. Ames (169 U.S. 466). “Tn order to ascertain that value, the original cost of con- struction, the amount expended in permanent improvements, the amount and market value of its bonds and stock, the present as compared with the original cost of construction, the probable earning capacity of the property under particular rates prescribed by statutes, and the sum required to meet operating expenses, are all matters for consideration and are to be given such weight as may be just and right in each case. We do not say that there may not be other matters to be re- garded in estimating the value of the property. What the com- pany is entitled to ask is a fair return upon the value of that which it employs for the public convenience. On the other hand, what the public is entitled to demand is, that no more be DEFINITIONS extracted from it for the use of a public highway than the services rendered by it are reasonably worth.” It is to be noted, too, that the U.S. Supreme Court holds to the view that the value as a basis for establishing rates is to be the present value. The Court uses the following language in Will- cox vs. Consolidated Gas Co. of N. Y. (212 U.S. 19, 52). “And we concur with the court below in holding that the value of a property is to be determined as of the time when the inquiry is made regarding the rates. If the property, which legally enters into the consideration of the question of rates, has increased in value since it was acquired, the company is entitled to the benefit of such increase. This is at any rate the general rule. We do not say there may not possibly be an exception to it, where the property may have increased so enormously in value as to render a rate permitting a reasonable return upon such increased value unjust to the public. How such facts should be treated is not a question now before us, as this case does not present it. We refer to the matter only for the purpose of stating that the decision herein does not prevent an inquiry into the question when, if ever, it should be necessarily presented.” The Court has apparently taken the view that the unearned increment may generally be allowed to go to the owner of the utility either as an offset in whole or in part to early losses or as a reward for having undertaken the enterprise. The fact should, however, not be lost sight of that any such increase in value is, strictly speaking, a part of the aggregate earnings and due consideration to this fact should be given in making appraisals. While these rulings of the highest tribunal in the country seem to compel the valuing of a public utility property accord- ing to accepted standards at present worth, when value is to be ascertained and made the starting point for fixing rates, we may nevertheless be permitted, and we consider it a duty, to point out the limitations of these rulings and the desirability of secur- ing some modification thereof. This matter will be further discussed in the chapter on depreciation. IQ 20 VALUATION, DEPRECIATION AND THE RATE-BASE Remaining Value. — The term ‘‘ remaining value ” is equiva- lent in its meaning to present value when applied to an article whose value lessens with age. It is generally dependent upon and to be computed from three elements; (a) the probable use- ful life term of the article new; (b) its expectancy or probable remaining term of usefulness; and (c) the cost of replacing it with some article of equivalent usefulness, which, when prices are not subject to change, is the original cost less the residual value of the article when it goes out of use. Residual Value. — The ¢ residual value” is the value which remains in any article after the same has ceased to be useful as an integral part of a public service or other property. The residual value may be only scrap value, or it may be the price at which it can be disposed of for use in connection with some other property. It is usually estimated as the value to an out- side purchaser, less the cost of delivery to such purchaser. Condition Per Cent. — The existing condition of any article can be expressed by comparison with the condition of the same article new. If the article when new is taken at 1oo per cent and present condition in comparison therewith is noted in per cent this is called the condition per cent. It is the present or remaining value in comparison with value new, based upon the condition of the article, expressed in percentage. Accrued Depreciation. — The accrued depreciation is the difference expressed in money between the original cost of an article and its remaining value. Probable Life. — The probable life term of an article is the time, usually expressed in years, during which it may reason- ably be expected to render useful service. The probable life term of any article is to be determined by the experience, the world over, with other articles of the same kind. It depends not alone upon the time required for an article to become value- less by use, by ordinary wear and tear, but also upon the time when by reason of accidental destruction, inadequacy or obso- lescence, the article must be replaced by a new one better adapted to fulfill its purpose. If the life of a large number of articles of DEFINITIONS the same kind, as for example telegraph poles, be recorded it will be found that a few fail almost immediately, being destroyed by storms, by fire or by accidents, that a larger number will fail within a few years due to inherent defects in the timber and other causes in addition to the causes of failure already named, that failures will multiply at some period such as 10 to 15 years according to the character of the timber of which the poles are constructed and that some will survive many years beyond the average life term of all. From such records the probable life term of a new pole is ascertained; but while this probable life, here synonymous with average life, is known or can be ascer- tained as explained, the actual life of individual poles will depart therefrom more or less. The total number of service years of the poles which fail early will fall short of the expected total number by as many service years as those of the poles which survive the probable term will exceed this number. Expectancy or Remaining Life. — The expectancy of any article is the probable time, usually expressed in years, during which it may reasonably be expected to render efficient service. For a new article the expectancy is its probable life. When the life of a candle which will burn for a number of hours is under consideration, the expectancy is ascertained by subtracting age from probable life new. But in all ordinary cases the expectancy cannot be ascertained by any such simple mathematical process. Every article which has been in service for some years, and has escaped the accidents which might have put it out of business in its early life, stands a better chance of being among those which will outlive the probable life term fixed for it when it was new, than it had when new to outlive this term. Consequently the expectancy is not to be determined by subtracting age from probable life. It is to be determined from the actual con- dition of the article and all local circumstances which may affect its continued usefulness. A high-duty pump, which originally had a probable life of 25 years, when it reaches the end of this term, may be in a con- dition almost as good as new. It has escaped the possible acci- 21 22 VALUATION, DEPRECIATION AND THE RATE-BASE dents of the early years of its life and by careful attention and replacements of its wearing parts is still rendering first-class service. The value of this pump is not to be written off the books, neither should it be regarded as good as new. Its value is ascertained by determining its probable additional years of use- fulness and the probable cost of replacing it at the end of this term. An irrigation canal usually improves with age. So far as wear and tear is concerned, it has unlimited life. But under the development of extensive areas, the small original canal may in the course of time be superseded. The probable life of this canal, and therefore, too, the annual replacement increment, is estimated on some assumption relating to the rate of this develop- ment. Finally the time comes when the project for a compre- hensive canal system has taken shape and it may reasonably be assumed that within a definite period, five or ten, or some other number of years, the original canal will be superseded; its di- verting dam and its headworks, and perhaps the canal itself, will then be abandoned. The remaining life or expectancy of the canal is at that time only five or ten or some other number of years, as the case may be, and within this time the remaining investment in the canal is the amount under consideration for replacement. Composite Life. — The composite life of a complex plant is that term of years within which the accruing depreciation of all items of which the plant is composed, on the assumption of no replacements, would amount to the cost of the plant. As in the case of articles in classes according to their probable life, so in the case of entire plants, the life thus determined for various types of plants is made an aid in estimating the current de- preciation. Without recourse to the more laborious method of dealing separately with each item of which the plant is made up, it becomes possible if composite life is known to approximate the current depreciation or replacement requirement. Composite Age. — The composite age of a complex plant is that age which it would have to acquire, if treated as a depre- cating unit, to make its accrued depreciation equal to the DEFINITIONS : aggregate accrued depreciation of the individual items of which the plant is made up. “Amortization.” — In the sense used in this paper the term amortization applies to the retirement of capital. When an article is to be permanently retired from connection with a busi- ness and not to be replaced, the annual depreciation increment or the annual replacement increment allowed in the earnings becomes an amortization increment. Ordinarily a discarded article is replaced by a new one which will render equivalent or better service. The amount to be provided during the life of the article and made available at the time it goes out of use is, for all practical purposes, its re- placement cost, being the cost of installing an equivalent new article, less the residual value of the original article. The amount thus provided may be treated as amortization, but there is no need of doing so as will be fully explained. Depreciation. — Depreciation is the lessening in worth of any perishable article which takes place from use and advancing age. It is not solely due to inherent deterioration or to wear and tear but results, too, from the fact that owing to progress in the arts and sciences and methods of manufacture, an article may become obsolete and that due to growth of communities or other causes, appliances or structures may become inadequate and have to be replaced in the course of time by new ones better adapted to the requirements. Every circumstance tending to limit the term of usefulness of an article should be taken into account when its probable life or expectation and consequent rate of depreciation are to be determined. Annual Depreciation. — The annual depreciation or the cur- rent depreciation is the annual theoretical lessening in worth, expressed in money. Appreciation. — Appreciation is the increase in worth ex- pressed in terms of money. It applies not alone to real estate but to any article, structure or thing which increases in value due to general prosperity or to the more obvious cause of higher wages and greater cost of materials. 272 24 VALUATION, DEPRECIATION AND THE RATE-BASE The Current or Annual Replacement Requirement. — The current or annual replacement requirement is that amount which should annually be covered by the earnings, to meet the renewals which must be made from time to time. The amount necessary to accomplish this may be estimated from the known character, number and cost of the articles which must annually be re- placed or in the case of large units, from the rate of depreciation. The Obligation to Replace. — The obligation which every owner of a public utility has assumed to continue in business for either a definite or an indefinite time period carries with it an obligation to replace the articles which are essential for the proper conduct of the business with equivalent new articles whenever the original articles cease to be useful. This obliga- tion to replace grows with the age of the article in service. When expressed in money, it is equivalent to the accrued theo- retical depreciation. This obligation to replace, together with deferred maintenance, must be taken into account by the ap- praiser of property which is to be purchased. Deferred Maintenance. — “ Deferred Maintenance ”’ is the neglect, expressed in dollars, which has resulted from failure to keep an article in good condition and repair. It is the sum which should at once be expended to restore the article to ordi- nary good service condition, and to protect it against causes of rapid destruction so that its deterioration will not be unduly rapid. Ordinarily there should be no “ deferred maintenance.” By proper attention to maintenance and repairs the service rendered should be kept at the standard which is expected of the plant. The plant in other words should, practically at all times, be at 1oo per cent efficiency. Wear and Tear. — “ Wear and tear ” is the term applied to the deterioration of an article from use. The article is kept in serviceable condition by the renewal of its worn-out parts and by suitable attention to its wearing parts. Maintenance and repair are to be included in operating expenses. The expendi- tures for repairs and maintenance are intended to keep the article at or near roo per cent efficiency. DEFINITIONS y It is sometimes difficult to draw a close distinction between repairs and replacements and between deferred maintenance and accrued depreciation. It is generally assumed that deferred maintenance results from neglect to make the lesser repairs and renewals such as are current from year to year and that depreciation comes into consideration when dealing with the more important items which when new have a probable life of at least a number of years. Replacement Cost. — The replacement cost is the cost of a new article with which a worn-out article is replaced, less the residual value of the original article. It is the cost of effecting a change from the worn-out part of the property to a new part of equivalent service value. Invested Capital or Investment. — The investment or the capital invested hardly needs a definition. It is the aggre- gate of the expenditures which have been made and which re- main in the business. It is the summation of the cost of the various items which make up the property in question and render the same efficient for the purpose for which it is intended, less such sums as may have been applied out of earnings for the retirement of the capital. In connection with the valuation of public utility properties it may be regarded as the aggre- gate of the reasonable and proper expenditures which have been incurred to make these properties serviceable. It may and generally does include such items as the cost of establishing the business. Wearing or Service Value. — When the fact is taken into account that an article after it has ceased to be useful in con- nection with one enterprise or property may still have value in connection with another, and usually does have some scrap value, it will be plain that the lessening of worth is not to be estimated from the original full cost of the article. It is the difference between the first cost and the residual value which is being consumed during the useful life of the article. This dif- ference is frequently referred to as the wearing or service value of the article. ZL 26 VALUATION, DEPRECIATION AND THE RATE-BASE Remaining Service Value. — The service value of an article which is no longer new is its remaining service value. It is determined from the original service value by deducting the accrued depreciation. Intangible Values. — The term intangible value is applied to any element of value other than elements of a physical na- ture. The value of a franchise is an intangible value, so too the “good-will” of a business; “going value;” rights of access; ” “ water-rights; 7 ¢ power-rights,” and the like. The cost of organizing and establishing a business is an element for consideration in making an appraisal of value just as legiti- mate as the cost of the physical elements of a property. Cost of Business Development or the Cost of Establishing the Business. — The cost of development or the cost of estab- lishing the business is a summation of the expenses not charge- able to construction which have been incurred in building up the business and bringing it upon a paying basis. Preliminary expenses, advertising, commissions and losses due to inade- quate revenue in the early years may all be brought under review in making up the cost of development. It is not always a simple matter to know where to stop in the matter of charg- ing up expenses to the cost of development and to the capital account. To a certain extent the losses due to deficient busi- ness in early years may be regarded as part of the capital reason- ably invested. The European practice is to do this to a far greater extent than is customary in the United States. When feasible, the better practice would be to recognize the early losses as a necessary incident to the business and to make pro- vision for their amortization as circumstances may justify. In general it may be said that any legitimate expense which it may be difficult to assign to construction or operating accounts can be regarded as development expense. Franchise. — A franchise is a privilege to do business granted by the public. A franchise may be limited to a specified period of time, it may be indeterminate or it may be perpetual. It may be, but is not necessarily, an exclusive privilege. It may DEFINITIONS be coupled with all sorts of conditions such as division of profits; the fulfilment of all kinds of obligations; the limitation of charges for the service rendered or the commodity furnished. It may be nothing more than a privilege to occupy the public highways with rails for transportation purposes or with pole or pipe lines for the transmission or delivery of electricity, water, oil or gas. It may be a grant without cost or may have to be paid for at a fixed price or subject to competitive bidding. It is one of the intangible elements which may represent value and frequently appears among the items of cost. Going Concern. — The term “ going concern ” is applied to such business enterprises as are in actual operation. If in suc- cessful operation, the value of the “ going concern ”’ should be somewhat greater than the sum of the value of the physical elements of which the property is made up. Going Value. — The increment of value which is due to the fact that a business has been established and brought upon a paying basis is its “ going value.” By some appraisers the cost of developing the business, measured by deficient earnings or estimated on the basis of prevailing conditions, is included in the rate-base under the designation ‘going value.” But going value cannot be measured by any specific items of cost. If the early losses have been treated in the accounts as operating loss and not as invested capital it may be found that early deficien- cies of earnings have been fully made good. There may be “going value” despite this fact but the relation between actual cost and this value is lost. It will, in other words, be difficult to establish any generally applicable relation between the going value of any utility and the actual cost of establishing its business. Good-Will. — The term good-will” is closely related to “ going value.” It represents the intangible element of value in an ordinary business and is applied generally in those cases where there is competition with other like business ventures. The courts hold that where there is no competition there can be no good-will. 27 28 VALUATION, DEPRECIATION AND THE RATE-BASE Overhead Expenses. — Certain expenditures in connection with the development and operation of any revenue-producing property are usually classed as overhead expenses. Econo- mists and engineers are not all agreed as to just what part of the cost of construction or operation should be classed as over- head. Ordinarily the cost of management is treated as the overhead. When work is done by contract, the amount paid to the contractor is the cost. An analysis of cost to the con- tractor when compared with what he has received may show a profit but this is no part of the overhead expense. The com- pensation of the general manager, on the other hand, and of the engineer and legal staff and the expense of the general office should be treated as overhead — so, too, interest during construction, taxes and insurance. Whether or not they are taken into account in making valuations for the purpose of establishing a “ rate-base ”” (it being no concern of the public how the funds for establishing an enterprise are raised), the commissions to brokers who sell bonds are a real item of ex- pense to the owner and will be classed by him either among the overhead expense or as a promotion expense. Promotion Expense. — The term ‘promotion expense” is used to designate certain expenditures, which cannot well be included in the “ overhead ” nor yet in the legitimate cost of establishing the business. To this class of expenditures belong a variety of expenditures usually incurred prior to the perma- nent organization of the business enterprise and may include commissions to real-estate agents, and the various expenditures that have been incurred apart from actual cost in acquiring the properties forming the nucleus of the enterprise. Adver- tising and discounts and commissions to bond brokers may also be at times properly classed as promotion expense. The cost of bringing together the various fundamental properties into one holding, representing the result of the promoter’s activities, except to the extent that the cost of promotion work appears in enhanced value, is generally accepted as being covered by the item ‘ promotion expense.” DEFINITIONS The amount of the promotion expense may vary within wide limits according to the character of the works, the difficulties to be overcome and the thoroughness with which preliminary investigations are made. Such expenditures are generally much less in connection with the additions to an established enter- prise than they would be in connection with an original plant of the same character and magnitude. Reproduction Cost New. — The ascertainment of what it would cost to construct an exactly equivalent property, iden- tical with that to be valued, is frequently an acceptable aid in determining value. Any article which forms a part of a revenue-producing property has a value in the service which may reasonably be measured by the cost of replacing it. Its value in the service may be estimated from the cost of installing a new article at the end of the expectancy term. Generally the value at some particular time is under consideration and it would be theoretically correct to apply the prices of material and labor which are current at that time in making the estimate of reproduction cost. But con- struction was a process requiring time and reconstruction would also require time. Furthermore the appraisal may have to serve for some time, perhaps for a term of years. It is reason- able and logical, therefore, to depart from the strictly theo- retical requirement and to adopt, in making such an estimate, unit prices which represent average conditions, preferably for a period of about 5 years. The instructions to appraisers by the Supreme Judicial Court of Maine, in the Kennebec Water District Case (1902), (97 Maine 185; 54 Atlantic 6), when the properties of the Maine Water Co. were to be valued contained the following reference to reproduction cost: “The appraisers may properly consider what the existing system can be reproduced for. But the cost of reproduction will not be conclusive. It will be evidence having some ten- dency to prove present value. The inquiry along the line of reproduction should be limited to the replacing of the present system by one substantially like it.” 20 30 VALUATION, DEPRECIATION AND THE RATE-BASE Public Utility. — A public utility is an enterprise which ren- ders a service or which supplies a commodity of general neces- sity or convenience to the public. There may be public owner- ship of the utility, or the privilege of serving the public may be delegated to a private person. When the private person is a corporation, we have the public service corporation. Rate-base. — The ‘‘rate-base” is the starting point, the basis of the calculation when earnings are to be determined to which the owner of a public utility is entitled. The owner is entitled to a fair return on the legitimate investment which he has made for the benefit of the public. He may also be en- titled to more than what would be considered a reasonable return on ordinary investments but this fact is to be deter- mined by the circumstances in each particular case. To know the legitimate investment, whether ascertained from book rec- ords or by estimating the cost of reproduction or otherwise, is fundamental. The rate-base which is the most satisfactory is the actual reasonable and proper investment or original cost new, includ- ing a proper allowance for the cost of establishing and develop- ing the business, undiminished by depreciation, though in some cases, perhaps, diminished by the bonus which may have been contributed by the public or by the rate-payer. The endeavor is made in these pages to show that the value of the service rendered and the earnings are independent of accrued depreciation and that for this reason the present or depreciated value of the physical elements is not the best cri- terion for a determination of the legitimate amount of the earnings. But the sacrifice which the owner has made, the amount of money which is in the business legitimately as of the date of construction, the original.cost, in other words, less the capital which has been contributed to the work as a bonus and not as amortization, is the essential element for con- sideration and should be made the starting point when rates are to be regulated. It is to be understood, as a matter of course, that special consideration may have to be given to the DEFINITIONS overbuilt plant and to property held for future use. If the owner has gone too far in the matter of providing capacity or in the matter of securing property not immediately required, the cost of such property may have to be omitted from the rate-base or the rate of return on the rate-base should be lower than would otherwise be allowed. The author suggests that the rate-base determined from the investment, undiminished by accrued depreciation, which he advocates and recommends as the logical basis of the calculation when rates are to be fixed, be called the ‘natural rate-base.” A clear distinction will thereby be made between this rate-base and the other so-called rating bases which involve a consideration of vale, 31 CHAPTER III FUNDAMENTAL PRINCIPLES WHICH CONTROL WHEN APPRAISALS OF PUBLIC SERVICE PROPERTIES ARE TO SERVE AS A BASIS FOR: FIXING RATES 1. The earnings of the public service property should be such that, within the life of the property, there will be returned to the owner, the capital which he has properly invested in it, and in addition thereto, interest at a reasonable rate upon such amount of capital as from time to time actually and prop- erly remains as an investment in the property. 2. The reasonable cost of each item which goes to make up a property may be returned to the owner during the probable or during the actual life of that item or it may be returned to him in a lump sum when that item ceases to be useful. In the case of items which are of sufficient importance to be individu- alized the amortization of cost may be progressive during a fixed term which is generally determined by the probable life of the item. In the case of numerous articles the amortization, with equal propriety, may be deferred to the end of the term of usefulness of each article. 3. During the early years of most public utilities the oper- ating costs will exceed the revenue. The business is conducted at a loss. When such losses are legitimate, they may be regarded as the cost of establishing the business and may be added to the invested capital. They may, as an alternative, be regarded as temporary advances which are then to be amortized within a reasonable time. 4. The owner of the public service property is entitled to proper compensation for assuming the hazards of the business and for establishing and operating the utility. 2s FUNDAMENTAL PRINCIPLES 5. The owner of a public utility is entitled to a reasonable share in the general prosperity of the community which he serves. For this reason he should be allowed a share in the increase of value which results from population growth. If present value is made the rate-base, he will get the apprecia- tion of real estate (if such increase be not excessive). If the public utility has but little or no property which appreciates then some other factor may be brought into consideration in determining the fair return. It would be sound doctrine to exclude appreciation from the rate-base thus avoiding uncer- tain and accidental reward and to allow the unearned incre- ment to appear in the net earnings. 6. Where the invested capital is small and the volume of business large, the owner of the utility is entitled to have the volume of business considered as well as the invested capital when rates are to be fixed. It would generally be good prac- tice to take the volume of business into account as well as the rate-base when rates are to be regulated, but this is not yet an established practice. 7. The depreciation of an item used in the public service does not reduce the value of the service or commodity which the public utility supplies to the consumer. The value of the service is ordinarily unaffected by depreciation. Depreciation is a lessening of worth which may result from any cause. Wear and tear suggest themselves as the prime cause of the deprecia- tion of articles in use, but it is sometimes difficult to establish a connection between the rate at which an article is consumed in service by wear and tear and its lessening worth. The accrued depreciation of any article is ascertainable from the probable life new of the article, the cost of replacing it at the end of its life, its probable remaining term of usefulness, and its original cost. In practice the accrued depreciation is usually computed from the cost of the article or rather from its wearing value, its prob- able life new and its expectancy. The cost affords a convenient basis for approximation. (This does not apply to certain articles which are readily replaced such as automobiles when 33 34 VALUATION, DEPRECIATION AND THE RATE-BASE considered apart from a complex property. Treated by itself the automobile shows a marked drop in value as soon as it goes into service and thereafter may be considered as decreasing at a fairly uniform rate per year.) 8. Whenever the rates to be charged for the service rendered by a public utility are to be fixed the current depreciation or the current replacement requirement must be estimated. This is usually done by compound interest annuity methods or by the so-called Straight Line Method. According to the procedure under which the necessary amount of earnings are determined, either the current depreciation or the current replacement re- quirement are then made a part of the necessary earnings. 9. According to the procedure which is adopted for treat- ing the replacement requirement, depreciation and amortization in the accounting system, the computation of earnings that are necessary from year to year will vary. Any one of a number of methods of procedure may be adopted with due regard to the following: a. Is it desirable to keep the required earnings in the early years relatively low? b. Is any portion of the invested capital to be amortized or is there to be any amortization of expenditures for unproduc- tive work? c. Has there been any amortization of capital in the past? d. What hasbeen the relation of earnings to operating expenses? e. What amount of prospective business is to be taken into account? 10. An earned depreciation allowance may be regarded as an amortization increment. The depreciation allowance is then for all practical purposes a repayment to the owner of a part of his invested capital. It will, in that event, make no difference in the ultimate result, at what rate the repayment of capital is made. Ordinarily capital is retired as follows: a. In equal annual amounts which without interest will in the life of the article whose cost is to be amortized amount to that cost. (The Straight Line Method.) FUNDAMENTAL PRINCIPLES ) b. In amounts which increase from year to year, figured on the compound interest basis. (Equal Annual Payment Method.) ¢. In equal annual amounts which together with compound interest thereon will in the life of an article amount to its cost. (Sinking Fund Method.) 11. A public service property may be regarded as having an unlimited life. Taken as a whole when rates are to be fixed the accrued depreciation may then be disregarded; but provision must be made for the renewal of those parts which for any reason become useless. In this event there need be no repay- ment of capital, except only those portions thereof which may be regarded as temporarily invested. 12. In so far as this may be practicable, the earnings of the public utilities should be adjusted to the ability of the rate- payer to pay. Ordinarily, therefore, the aggregate earnings should be kept relatively low in the early years when the number of rate-payers is small. 13. The owner of a public utility has the right to do what he pleases with any portion of his capital which is paid back to him, which is, in other words, eliminated from the rate-base. 14. The owner of a public utility should be held accountable for all sums collected from the rate-payers for the specific purpose of making repairs and renewals. A diversion to other uses of any fund intended for this purpose is equivalent to a repayment of capital. 15. The basis of calculation, the starting point when rates are to be fixed for a public utility, is the amount of capital whose in- vestment was necessary to build the plant and develop its busi- ness and on which there should be a proper interest return to the owner. This may be either the legitimate original cost new, or it may be the properly invested capital reduced by the accom- plished amortization. This basic amount is for convenience called the “ rate-base.” 16. As a general proposition the earnings present and pro- spective should be such that they will give the property a value in excess of the capital actually (and properly) invested — the 35 36 VALUATION, DEPRECIATION AND THE RATE-BASE excess of value being the amount of the reward (including per- haps some unearned increment) to which the owner is entitled for having established and for managing the business. 17. Strategic value, resulting from a combination of circum- stances such as low operating cost and ample market for the output at prices fixed by or for competing concerns which have not the same advantage of low operating cost, is a part of the reward to which the owner of a public utility may be legitimately entitled. 18. The various procedures for estimating the required earn- ings of public service properties are usually based on the assump- tion that the same procedure has been used from the beginning of operations. A procedure which may be correct if consistently and continuously applied, may be unfair to either the owner or the rate-payer, if introduced at a later period. Consequently it should be regarded as imperative that consideration be given to past history when the rates of an operating concern are to be fixed. 10. Franchises and water-rights and in general the privilege to do business are not to be made a part of the rate-base except in certain cases in which such rights and privileges have defi- nitely ascertainable strategic value or have had to be purchased as, for example, when a city sells the right to construct and main- tain a street car system or when the acquisition of a water- right involves the purchase of adverse riparian or other rights. 20. The net earnings of a public service property should in some measure exceed the return from ordinary safe investments. 21. The prospective business must be taken into account when the rates are to be fixed particularly in the case of a new enterprise, where the rate-payers are too few at the outset to produce, at a reasonable charge for the service, the revenue which would yield a proper current return on the investment. 22. The replacement requirement is to be determined from the expectancy (remaining years of usefulness), the probable life when new of similar articles and the estimated cost of effecting the replacement. It is not dependent on original cost nor age, FUNDAMENTAL PRINCIPLES 37 although original cost and age may frequently be valuable aids in making an estimate thereof. 23. Whenever the current replacement requirement or de- preciation are to be estimated, due consideration must be given to the fact that the actual period of usefulness of perishable articles rarely coincides with their probable term of life. = CHAPTER IV ESSENTIALS OF VALUE Cost of Physical Elements Supply and Demand. — The value of any property is usually determined by the law of supply and demand. This is perhaps best illustrated by reference to perishable property such as articles of food which can be preserved in marketable condition for a limited time only. According to information that may be available relating to the world’s supply of wheat and of coffee the value of the wheat or coffee will be high or low. The harvest prospect in the case of such perishable elements has a direct effect upon the market value. Or as an additional illustration take the limited output of a great sculptor or artist. The de- mand, particularly after the sculptor or artist has ceased to produce, may greatly exceed the supply and in such case the market value may rise far in excess of what would otherwise be the value. The popular actor, or vocalist, the skillful musician, the poet and the author have something to offer in the world’s market which is unique and may be in great demand, and therefore may command a return out of all proportion to the compensation for ordinary individual effort. Cost of Physical Elements in Relation to Value. — Productions of this type which have value are not here under consideration. It is the revenue producing property which is to be discussed and to which the chapters of this volume are addressed. Nearly every such property is made up of both physical and intangible elements. Taken in the aggregate this combination of physical and intangible elements has value” based upon earning capacity. This is a fundamental fact which if lost sight of may 28 ESSENTIALS OF VALUE : lead into confusion when the term “ value ”’ is used. Both the physical and the intangible elements which make up the entire property may have been acquired by the outlay of money or in exchange for other valuable property. Consequently the question of cost deserves consideration and may at times be found a fair guide in determining value. Usually the physical elements of any property in successful use are worth at least as much as it would cost to reproduce them in the condition in which they are found at the time of the valuation. At any rate a prudent purchaser would desire to know what this cost would be and he would be very apt to make it his starting point in determining what he could afford to pay for the property. The first step therefore in practically every valuation is the determination of the cost of the physical elements which go to make up the property. In making the valuation of the physical properties account must be taken: 1. Of the cost of replacing each inventoried item with a new equivalent article. 2. Of the probable remaining term of usefulness of the item. 3. Of the probable term of usefulness of the same or an equiv- alent new article. 4. Of the cost of replacing the article with an equivalent article at the time when the article will probably be discarded. 5- In the case of valuation for purchase or sale account should also be taken of the accrued depreciation, which will aid in determining the present value. The Determination of Cost. — The appraiser will therefore begin with an inventory of the property which should be in sufficient detail to facilitate a cost estimate such as an engineer would make who is called upon to construct a duplicate of the property to be valued. He will call to aid in making this in- ventory the records of the owner and he may find that he need only verify or amplify a list of items already enumerated. He will then estimate the cost of reproduction and here again he should call to aid, if it is available, the record of the cost of con- 3G 40 VALUATION, DEPRECIATION AND THE RATE-BASE struction. The actual cost, intelligent direction and super- vision being assumed, is generally a better guide to the cost of accomplishing a result, than the estimate of the expert who, no matter how much he knows about present cost, must make certain assumptions relating to the past or the future which will always brand his conclusions as approximations, even though the approximations are in some cases to be accepted as being quite as dependable and as acceptable as though they were of absolute accuracy. It is not proposed to introduce into this volume sample sheets enumerating all the various items that may be encountered in valuing the various classes of public utilities and industrial establishments. The blanks in use for these purposes are ob- tainable, at least for the utilities, from any of the public service commissions and will be found an excellent guide in listing and appraising the physical elements of value. The Relation of Present Worth to the Cost of Replacement. — After the cost of reproduction has been determined the time must be estimated during which — everything considered — the article to be valued may reasonably be assumed to continue in service. With this time and the probable life new of articles of the same class it will, as elsewhere explained, be possible to estimate the relation which the present worth of the article bears to the cost of replacing it at the time it will probably be discarded. If now the cost of reproduction be so modified that it will represent the cost of replacing the article at the end of its period of usefulness and the present worth or condition factor is applied to this cost of replacement the result will be the present worth. When the property to be valued includes land, rights-of-way or water-rights, regard should be had to the principles dis- cussed in the chapters on the “ Valuation of Land in Eminent Domain Proceedings ” and the “ Value of a Water-Right and of Reservoir Lands.” Extent of Detail Required. — It has become a common prac- tice in valuing property for rate-fixing purposes to approximate ESSENTIALS OF VALUE ? the legitimate investment or the present value of physical properties by means of a close estimate of the cost of repro- duction. Such estimates are a check upon the records of actual cost and are valuable even when used for no other purpose than as a check. The fashion is growing of making the estimates of the cost of reproduction with attention to the minutest detail. These esti- mates are frequently made with more care and with more care- ful enumeration of items, of specials, fixtures and incidentals and of labor and overhead, than would satisfy a contractor bidding on the work. And when this is done, when the sleeves and elbows of the pipe lines have all been counted and weighed and fence posts have been pulled to determine their length, unit prices are applied — sometimes as they prevail at the date of the valuation but more frequently as they have pre- vailed throughout a series of years 2, 3, 5 or 10, in order to give weight in a measure to the conditions under which the plant came into being. An approximation results. Then, perhaps, the accrued depreciation and deferred maintenance are esti- mated by some method of approximation and are deducted and finally appreciation of value may be allowed and an addition is made for the “cost of establishing the business” for going value ” or for other intangible elements such as * franchise or “water-rights.” To the original approximation other ap- proximations are added with a result not always entirely satis- factory. Where this is the case, one may well pause to consider how far into detail the appraisal of the physical elements should go, and whether there are not many cases where actual cost, with such checks as may be necessary to determine whether the cost is strictly reasonable and legitimate, would serve as the best starting point when a rate-base is to be determined. The expense of making an appraisal with strict attention to every possible detail is not always justified and it may, more- over, defeat its own purpose, because by the time that a first valuation is completed, as in the case of the railroad systems of a3 42 VALUATION, DEPRECIATION AND THE RATE-BASE the country, a revaluation may be necessary if the same stand- ard of approximation to reconstruction cost is to be continuously maintained. At any rate, the public utility commissions of the country should see to it that useless work on these lines be not demanded. It is their province to fix the standard in this matter. When rates are to be fixed, they are based on a forecast of what the earnings should be. The exact result of charging for the service rendered at any fixed rates cannot be known until the rates have been in effect for a time. A deficiency in the earnings is discouraging to the owner and makes him prone to give inferior service. He may be forced into the courts and will then incur legal and other expenses which in the end will be paid by the consumer. An accumulating surplus, on the other hand, should insure high-class service and can be used to safe- guard the property against unforeseen accident and to make sure of its proper upkeep without giving to the owner, in the long run, any larger amount in dividends than he is legitimately entitled to receive. If there be error, it should be on the side of the adequate return, provided always that a limit is set to the rate of return on the investment and to the compensation for managing the business, and that the charge for the service rendered be a reasonable charge. Overhead Expenses Cost Includes Overhead Expenses. — Overhead expenses have already been defined. They include primarily the cost of management, engineering, interest during construction, taxes and insurance. In the determination of “cost” whether the actual cost or the estimated cost of reproduction, whether at present day prices or at prices applying to a selected period or to a par- ticular time, it will be essential to have due regard to the over- head expense. It is not enough to be able to state item for item what it would cost to reproduce each in its exact present condition of serviceability, but proper account should be taken ESSENTIALS OF VALUE 3 of the amount of general expense, of the cost of management, engineering and supervision of the expenditures due to unforeseen conditions, of unprofitable expenditures, and of losses by acci- dent, that would ordinarily be anticipated in the execution of similar work under the same general conditions. The finished plant if constructed under better than average conditions is entitled to a credit due to this favorable circumstance, and if constructed under adverse conditions, may not be entitled to an appraisal at full actual cost. The determination of the allowance which should be made for overhead expense is therefore a matter of considerable im- portance as will be seen from the quotations presented here at some length, which will give a fair idea, based upon experience, of the actual overhead expense connected with many public enterprises. The Special Committee of the Am. Soc. C. E. on the Valuation of Public Utilities is Cited on Overhead. — In reference to en- gineering as an overhead expense the Special Committee of the American Society of Civil Engineers on the Valuation of Public Utilities in the progress report which it submitted in January, 1014, Says: Am. Soc. C. E. Committee, Engineering. — “ Under the head Engineering are usually included not only strictly engineering expenses, but those of other technical employes and of inspec- tors. It is difficult to draw the line between the preliminary engineering and that during construction, and it is probably best in most cases to include the part of the preliminary engineering expenses connected with the preparation of the final design of the works with those incurred during their con- struction. “The percentage of the cost of the work represented by engi- neering differs with the character of the works and with the amount of care and skill exercised in their design and con- struction. On railroads it is commonly estimated that the engineering cost will amount to 5 per cent of the physical valu- ation of the property, exclusive of overhead charges. Statistics of the cost of engineering are available in connection with several municipal and other works as follows: 4% 9, 44 VALUATION, DEPRECIATION AND THE RATE-BASE “ Metropolitan Water-Works, Massachusetts. This property, costing to the end of 1912, $42,036,000, is to the extent of $15,- 300,000 made up of old works purchased from the City of Boston and others, on which the engineering charge is not known, leaving $26,736,000, of which the engineering charge was $2,077,- ooo, equal to 7.77 per cent. Based on the total cost, exclusive of engineering, the percentage is 8.42. These amounts include both the preliminary engineering and that during construction. « New York Water-Works, now in process of construction. The disbursements upon this work to the end of September, 1913, amounted to $103,178,000. The engineering expense directly attributable to the work under construction amounting to $10,050,000, equal to 9.73 per cent of the total disbursements for this work. In addition, there were engineering expenses re- lating to investigations of other drainage areas, which are only indirectly attributable to the work under construction, amounting to $304,000 or 0.38 per cent of the total disbursements, making the total for engineering 10.16 per cent. It is to be noted, however, that there is included in this case under the head * en- gineering ”’ the cost of unusually extensive borings and investi- gations which were not included as an engineering charge upon the Metropolitan Water-Works. There is not included, how- ever, the cost of expensive investigations by sinking shafts at the Hudson River, which, although originally charged to the engineering account, has been deducted because the shafts afterward became a part of the final construction. « Boston Subways. The following table has been compiled from official reports: ESSENTIALS OF VALUE ‘““ BOSTON TRANSIT COMMISSION (1895-1912) Percentage Percentage feo Total cost. of total siructio Subway: Engineering....................... $407,475.48 9.88 11.34 General expense (inc. commission). . 131,681.87 3.19 3.68 Construction. . .. (i eee 3,586,002.33 86.93 100.00 Total...... ceee.. $4,125,159.68 100.00 East Boston Tunnel: Engineering. ...... vii viveds orion ys $191,466.57 5.90 6.62 General Expense... uv. av sisi 161,134.78 4.96 5.57 CONSIIRCtiOn. iis x wns nik sn sd rns 2,894,595.01 89.14 100.00 Total...." se rie 'ali a sei RSS, 24. 7,100 300 TOO .00 Boston Tunnel and Subway: Engineering... 0 sain ii dy od wn $417,866.25 5.05% 5.48 General expense. «. vu. uivvs nan snes 226,441.57 2.73 3.58 Construction. . . 0. sha oh 7,623,206.56 92.22 100.00 Total...............0.50. 00. SS, 267,514 . 33 100.00 Cambridge Connection: Engineering. oi. dv es sete vy $96,575.46 7.10 8.05 General expense.......... vue eui.. 62,355.20 4.59 5.20 Construction. . « . vc... EN 1,199,904.39 88.31 100.00 Total..........0e sve savy ss oR 9T,358,535. 05 100.00 ‘““ CHARLES RIVER BASIN COMMISSION, BOSTON Dam, Lock, Embankments, Marginal Conduits, Etc., Completed 1909 Percentage Percentage f COM Total cost. of total struction Administration. . ....s:cszs:sicasnsesss $04,011.97 Engineering........... J vars 446,006.03 . .. . Construction: Preliminary... $10,783.86 OH «5.05 sik iw asmnlll wii viv nF Selaie isl Contracts. .... 2,620,671.95 . 73.10 sass snusisinindlls + «vee BN . Additional..... 237,433.22 6.6 TL SIE, , 2,877,889.03 8.0 = Real estate. ........ SELL. 170,730.77 0 so $3,597,727.80 100.00 45 46 VALUATION, DEPRECIATION AND THE RATE-BASE “ Pennsylvania Railroad Tunnels. — The cost of engineering for the East River Division of the Pennsylvania Railroad tun- nels amounted to 5.8 per cent of the total cost of the work, including excavation, retaining walls around the station area in New York, the tunnels eastward under the streets and East River to the surface in Long Island, terminal yard in Long Island, and engineering. This is equivalent to 6.1 per cent of the cost, exclusive of engineering. “ KENNEBEC WATER DISTRICT, MAINE New Gravity Water Supply, with Auxiliary Steam Pumping Plant, 1906 Percentage Percentage fon Total cost. of ott struction AAMINTS ERA TOT es erates ois shetiso a =i sn ue $6,161.20 2.30 2.53 Engineerimgiil hate suid elk 17:972-35, 6.69 735 Construction: Richisof way... hl oui 926.97 0.36 Pumping station.) CLL 20,833.39 7.80 [Cvo6 oo Stearniplantl on ha Se, 6,275.59 2.34 : ChinaLake pipe line. 0 LLL LE, 215,302.93 80.51) _ Ol eet ers es aerate CH Eo BY ACBL AS 100.00 “ LOUISVILLE, KY., SEWERAGE WORKS, 1906 TO 1912 This Work Consisted of Intercepting Sewers, Trunk Sewers, and a Small Proportion of Lateral Sewers Percentage P Total cost. or re ip 0 penditures. contractors. Administration’, ian rE he, $78,025.03 2.09 2.37 Engineering tL Lode doable l oie de 336,544.87 9.00 10.23 Rights of way... tot uu ails LLL LL 12,319.36 ©.33 | 0.37 Castings and other metal work. ...... 15,461.29 0.41 0.47 Damage suits (exc. of rights of way). . 8,307.52 0.22 0.25 Amounts of payments to contractors 3,289,330.89 87.95 100.00 $3,739,988.96 100.00 The above total is exclusive of the cost of preliminary en- gineering, which involved an expense of approximately $57,000, equivalent to 1.7 per cent of the construction cost ($3,289,330.89) shown above. ESSENTIALS OF VALUE ay ¢“ Watertown. — Mechanical filters built in 1903; cost, $97,065; engineering cost, 5.9 per cent. “ Ogdensburg. — Sand filters built in 1910; cost of work $167,604; engineering charges, 7 per cent, excluding cost of preliminary report, which amounted to $500. “ Hudson River State Hospital. — Sand filter plant built in 1904; cost $36,000; total cost of engineering, 103 per cent. “ Peekskill. — Sand filters built in 1908; total cost, $63,304; cost of engineering, 7.1 per cent. “ Yonkers. — Open sand filters, built 1903; total cost, $50,165; total cost of engineering, 7.3 per cent. Covered sand filters, built in 1907; total cost, $106,708; cost of engineering, 8.7 per cent. “ Ithaca, N.Y.— Filters built in 1903 on a percentage basis under rush conditions; cost, $192,114; engineering cost, 7 per cent. “Springfield, Mass. — Water-works built 1910; construction of additional supply from Little River, including diversion works, reservoir, filters, and pipe lines; cost $1,465,393; cost of engineering, 10 per cent. The basis of computation does not include the sum of $268,000 paid for land, legal and other expenses. “ Springfield, Mass. — Ludlow filters; built in 1906 at a cost of $43,306, to meet an emergency, and requiring very rigid in- spection to secure proper grade of sand and proper sanitary conditions during construction; cost of engineering, including board, livery, cots, bedding, and provisions for inspectors on work, 17 per cent. “It is obvious that the cost of engineering varies with the character of the work. For instance, the construction of an important dam or aqueduct, built in place and requiring skill in designing and a careful inspection of every part of the work as it is built, requires a larger expenditure for engineering than a large cast-iron pipe line where the cost of laying the pipes in a trench is but a small percentage of the total cost of the line, and the work progresses so rapidly that the inspection cost is small in proportion to the total cost. “The cost of engineering varies not only with the class of work but with the character of the design and execution. For instance, works may be built with very little inspection, from crude designs prepared by unskilled engineers, with the result that the cost of works may be large although the percentage paid for engineering may be small. Works skilfully designed - pr 48 VALUATION, DEPRECIATION AND THE RATE-BASE and efficiently constructed necessarily involve a larger cost for engineering, which should be recognized in any valuation when the works give evidence of such skill and efficiency. “The cost of engineering for additions and extensions of a property may be as large, or even a larger percentage of the total cost than for the original plant, but under a continuous system of regulation engineering for additions and extensions, if charged to current expense, should not be included in the valua- tion. “It is sometimes suggested that no engineering charge should be made in the acquisition of real estate, and there may be some cases where such a view would be substantially correct. It is frequently the case, however, especially where strips of land are to be acquired, that the engineering cost is as great as for other portions of the work. “The record of the cost of the Wachusett Reservoir, where the engineers had little to do with the acquisition of land other than to prepare the plans of the lands and to make appraisals of the mill property and water-rights, amounted to about 3 per cent of the total cost of the property acquired. The per- centage would have been considerably larger if nearly all of the property had not been acquired by purchase and very little by condemnation proceedings. “The records of the New York Water-Works show that the engineering connected with the acquisition of land to the end of September, 1913, amounted to 1.87 per cent of the total expendi- tures on land account.” Am. Soc. C. E. Committee, General Expense. — The same committee in referring to general expenses says that these include: ‘ All administrative, legal and other general expenses during the period of construction. Such expenses include general office rent, the salaries of the officers of the corporation and of the secretary, treasurer, legal advisers, clerks and others. Statistics showing the amount of such expenses in the case of corporations are not available to the Committee. The statistics of munic- ipal public service properties throw some light upon the sub- ject, although generally defective in that the offices are fre- quently in public buildings where no rent is charged and the financial and legal duties are performed to a large extent by those who receive salaries paid out of general funds. ESSENTIALS OF VALUE 5 “On the Massachusetts Metropolitan Water-Works, the ad- ministrative and expert services, with a small portion of the legal services, amounted to 1.43 per cent of the cost of the work, an unusually low figure, as there was very little litigation in connection with the work. “On the New York Water-Works the strictly administrative expenses to the end of September, 1913, were 1.12 per cent of the total disbursements to that date, but in addition, adver- tising and the fees of special counsel and commissioners of appraisal to the end of 1912, all in connection with the acqui- sition of land, amounted to $2,966,000, equivalent to 3.39 per cent of the total disbursements to that date, making the total for general expenses, exclusive of police services, 4.51 per cent. “On the Boston subways the general expenses, as given by accounts, have amounted to 3.42 per cent of the total, but some items usually classed as general expenses were charged directly to the various sections of the work. “It should be remembered that in all cases above cited, a part of the general expenses have been paid out of general funds and are not included in the above percentages. “ In modern works in populated sections of the country there is a strong tendency toward an increase in general expenses, owing to the greater attention paid to policing and sanitation where large bodies of men are employed. “On the Metropolitan Water-Works the charge for police services amounted to $211,000 for works costing $26,737,000, equal to 0.79 per cent. “On the New York Water-Works to the end of 1912, the total disbursements amounted to $87,551,000, of which $1,369,000 was for police, equal to 1.56 per cent of the total. “ The Committee believes that original conditions should be considered in determining the proper percentage for general ex- penses and that the allowance above suggested for police and sanitation should be included only when similar expenditures were actually made in the creation of the property under con- sideration.” Am. Soc. C. E. Committee, Contingencies. — “In making an estimate of the cost of a projected undertaking, the ex- perienced engineer adopts a policy of liberality with the inten- tion of reaching the probable actual cost of the proposed work, and even under such circumstances the actual cost is as likely to exceed as to run below the estimate. “This policy of liberality includes an addition to the com- 4G 50 VALUATION, DEPRECIATION AND THE RATE-BASE puted theoretical or geometrical quantities in all cases where the actual quantities are likely to be greater, the adoption of liberal rather than minimum prices for the various items of work, and a further allowance for contingencies. If the plans are in- complete, so that many minor features are omitted, he properly adds more for omissions and contingencies than where the plans are in greater detail. “In the valuation of a public service property, the same ideas should be kept in view and the percentage or sum to be allowed for contingencies should be governed, to a considerable extent, by the completeness of the inventory and the amount already allowed for omissions, by the extent to which additions have been made to the computed theoretical quantities and by the degree of liberality of the prices affixed to the various items of the inventory, but in no case should the contingencies be omitted or reduced to a small figure. Large contingent expenses are necessarily incurred in practically all important public works. They may occur from very many causes, among which may be enumerated the failure of contractors and the cost and legal expenses incident thereto; to the delay of certain parts of the work caused by such failure; to injunctions or to the inability to obtain possession of the land in due season, thereby necessi- tating the execution of such portions of the work under winter conditions or other adverse circumstances; to stringencies in the money market, causing a temporary shortage of funds, and a consequent disorganization of the forces employed on the work; to protracted strikes; to the necessity of rebuilding parts of the work which have failed because of improper design or unfore- seen causes; to making alterations found to be necessary or de- sirable after the work is built; to the slipping of earth or rock; and to making changes in plans which increase the cost of the work. “ Such contingent expenses as those above enumerated, with the exception of the last two, should be included as contingent expenses in any valuation of an existing property because the existence of the property does not give any clew to the amount of most of the contingent expenses involved in its creation.” Am. Soc. C. E. Committee, Insurance and Risk. — “There is an- other subject closely related to contingencies which may be classed as insurance or risk. For instance, if an owner of property is constructing a building he runs the risk that it may be burned. If a fire occurs when a building is nearly finished and the owner has to rebuild it, the cost of the completed structure, if he has ESSENTIALS OF VALUE i no insurance, will be nearly that of two buildings. In esti- mating the reproduction cost of the building, only one building would appear on the inventory, but in estimating its value, there should be added to the reproduction cost of the single building as otherwise determined, the sum necessary to insure its whole value against fire, and this sum should be added whether the owner actually paid it to an insurance company for carrying the risk or whether he assumed the risk himself. Similarly any other property which involves risk during its construction and testing should have added a contingent sum representing what the cost of insurance would be were there insurance companies to insure against such risks. “It is seldom that a large public service property is examined that there is not a disclosure of some large expenditure for works which have been destroyed, reconstructed, or not used because of faulty design or construction. In some cases this is dis- tinctly the result of negligence, but in a majority of cases such expenditures have taken place where the owners were not negligent in that they have taken due care in the selection of engineers to design and contractors to construct the work. They are the result of human fallibility. “ Many examples of failures have been furnished by masonry dams. A considerable portion of the Quebec bridge failed while in process of construction; there was a great slip in the Necaxa Dam, one of the highest earth dams ever built, when it was far advanced toward completion; the Loetschberg tunnel in Switz- erland encountered bad ground, which required the abandoning of the tunnel for about a mile and its relocation through another portion of the mountain; the change in plan of the new Croton Dam of the New York Water-Works involved an additional ex- pense of more than $1,000,000 for construction and interest. These are only a few instances of many which might be cited. Such disastrous occurrences are not contemplated by engineers when they make a provision for contingencies in preliminary estimates of the cost of works, but it seems proper in the valu- ation of an existing property which has been completed and successfully tested to recognize that the owner has been re- quired to assume the risk of accident and failure and should be compensated therefor by at least the amount which insurance companies would charge for taking such risks were they doing this kind of business. This feature may properly be included in the valuation by increasing the amount allowed for con- tingencies and risks.” 8] 52 VALUATION, DEPRECIATION AND THE RATE-BASE Am. Soc. C. E. Committee, Interest and Taxes. — Referring to interest and taxes the Committee says: “ Interest upon the capital invested in the plant up to the time when it is first operated and begins to have earning capacity is an unavoidable expense. “ Under the most favorable conditions it is necessary to raise the money required for the construction of the work months in advance of its expenditure and in many cases the whole amount must be raised before beginning the work in order to insure against a suspension of operations with the large loss neces- sarily incident thereto. “ The rate allowed for interest during the construction should be the prevailing rate at the time of the valuation, having re- gard, however, to the variations in rate in different localities and the character of the property. The rate of interest on money required for the original plant will generally be larger than on that required for extensions and betterments as the corporation naturally has a stronger financial standing after it possesses a successful operating plant. “ The amount to be allowed for taxes during construction must be determined largely on the basis of local tax rates and other local conditions and in this case, as in others relating to over- head charges, the original plant and subsequent additions should be treated separately.” Overhead in Railroad Construction. — While as in the case of other items of cost the records of expenditures may be the best guide when overhead charges of an operating property are to be determined, they are not always to be accepted without ques- tion; the appraiser must know whether they are reasonable or not. It is for this reason that such data as above presented are of interest to the appraiser. Following this matter further it may be noted that in valuing the railroads of the State of Wash- ington Mr. H. P. Gillette ascertained from their records of cost that their overhead costs were as shown in the following table: ESSENTIALS OF VALUE TABLE 1. OVERHEAD COST ITEMS Railroads in the State of Washington. By H. P. Gillette W.and F.&S.[S.& N.| N.P. | O.R. CrLN.JGuN GR Rr | Rr | RE | & N. giz M., a " 8 M., 32M, 132 Whe, 1654 M.,, 501 M., cent. {_cent. = nh et. os. ots Engineering. ............ | 2.50 | 3-23 1 4.40 ' 3.56 3.50 | 5.51 | 2.83 General expense. .........1 0.28 | 0.26 0.08 .... 1.00! 1.22 0.48 Legal expense.............| APN CB, en | 3.550... ..lifo.01lifo.02 Insavance. od lei Soils | 0.01 0Lob I wii TE TR. Interest on advances......l 0.93 1.23 3.250 xix Di. l EE Bond interest during con- struction. .............. 002.240 3 .84 fo. i. s.25 1123.60) 2.61 Bond expense............ Mo. 1olo. 18%... CIF TH TAT TER Taxes... liv asiiig l 0.17 sewn lil Sl AE]F Wait folios Undistributed accounts... .... .... eo va. |... 80.01 | 2.64 Totals....... ... 0... 6 27 5.74 | 7-91 | 7.17 | 9.75 l21.25 | 8.63 i" Gt. N. = Great Northern. W. & Gt. N. = Washington & Great Northern. F. & S. = Fairhaven & Southern. S. & N. = Spokane Falls & Northern. N. P. = Northern Pacific. O. R. & N. = Oregon Railway & Navigation Co. In valuing the railroads of Michigan, Prof. M. E. Cooley who had charge of this work adopted the following percentages in estimating the reasonable allowance for overhead costs: Per cent. EE INORIINg or Ve ener ees tse re nena 4.00 Lema) EXPENSE 1s J hl aise se tee cate vee aed n. 50 Organization expense i. | ves ants nv sbos ob dav sn barat 56 Interest during construction .......... 0. 0) Lins Tr 00 .00 The Wisconsin Railroad Commission on Overhead Allowances The following information is found in the records of the Wisconsin Railroad Commission: In Hill et al vs. Antigo Water Co. (decided Aug. 3, 1900). Overhead charges in the case of water companies are usually 10 to 18 per cent. The staff engineers estimated in this case at 10 per cent or the minimum (engineering, 5 per cent; interest during construction, 3 per cent; and contingencies, 2 per cent). 53 54 VALUATION, DEPRECIATION AND THE RATE-BASE In City of Ripon »s. Ripon Light and Water Co. (decided March 28, 1910) the staff allowed 12 per cent (5 per cent being for engineering and superintendence, 4 per cent interest during construction and 3 per cent legal expenses, organization expense and casualties). The respondent claimed 6 per cent interest during construction. In Dick et al vs. Madison Water Commission (decided Nov. 11, 1910) the staff allowed 1o per cent instead of the usual 12 per cent because the plant is a municipal plant. In State Journal Printing Co. vs. Madison Gas and Electric Co. (decided March 8, 1910), engineering was estimated at s per cent on the cost of the original physical plant, but not on additions to the plant. The staff of the Commission assumed that construction extended throughout one year and allowed 3 per cent for interest but subsequently changed to 4 per cent as the construction period may have been underestimated. The respondent contended for 6 per cent interest during construction, claiming a 2-year period of construction. In the tentative valuation the staff had allowed 2 per cent for various items including contingencies, omissions, casualties, legal and organization expenses but on revision allowed 3 per cent. The respondent claimed through various experts 4 to 7 per cent, the larger amount being based on 2 per cent for omissions and contingencies, 3 per cent for legal and organization expenses and 2 per cent for casualty liability. The Commission in this case says it is fair “ that rates charged for the service rendered be fixed at a level that is high enough to cover all reasonable costs.” In City of Racine zs. Racine Gas Light Co. (decided Jan. 21, 1911) the staff allowed 12 per cent for interest during construc- tion, engineering contingencies, etc. In the application of the LaCrosse Gas and Electric Co. the staff allowed 12 per cent while the petitioner claimed 15 per cent for interest during construction, engineering and contingencies. In City of Milwaukee vs. Milwaukee Electric Railway and Lighting Co. (decided Aug. 23, 1912) 3 Cent Fare Case, the ESSENTIALS OF VALUE 55 respondent contended that 22 per cent for overhead is not ex- cessive and that there are cases in which such additions have been as high as 51 per cent. Mr. W. D. Pence of the engineering staff of the Commission testifying to an appraisal of the property made in 19o7 says the basis was: Four per cent for engineering and superintendence. Two per cent for organization and legal expense. Three per cent for contingencies. Three per cent for interest during construction. Mr. Beggs, the manager of the Company, stated that con- tractor’s profit would be at least 15 per cent of cost of labor and materials. (The Commission included contractor's profit in unit prices.) Mr. Beggs also claimed that interest during construction could not be less than 5 to 73 per cent and engineering from 5 to 63 per cent. Prof. M. E. Cooley in revising the staff’s figures allowed 5 per cent for contingencies during construction on all items except land, furniture, etc., besides 5 per cent for contingent omissions on the investment not including land, cars and car equipment; 4 per cent for engineering, 3 per cent for insurance, 23 per cent for organization and legal expense, and 6 per cent interest; total 22 per cent. Mr. M. G. Starrett on behalf of the Company claimed 4 per cent for engineering and superintendence, 2 per cent for organi- zation and legal expense, 3 per cent for interest, 5 per cent for contingencies of construction, g per cent discount on bonds and I per cent for working capital; total 24 per cent. The Commission as the result of a study of 30 cases of actual expenditures finds a range of 4.5 to 23.43 per cent and an aver- age of 10.13 per cent for engineering, superintendence, organi- zation and legal expense and interest during construction. This does not include contingencies. Some of the individual per- centages were low because a portion of the cost of supervising extensions was charged to construction. 56 VALUATION, DEPRECIATION AND THE RATE-BASE In re Purchase of the Oshkosh Water-Works plant (Sept. 17, 1913) the City estimated 1o per cent for engineering, superin- tendence, interest during construction, contingencies, etc., this on the physical plant not including general equipment. The Commission allowed 15 per cent and said: “ Tt will be noted that the valuation recently placed on the Oshkosh Water-Works property contained an item of 15 per cent for engineering, superintendence, interest, organization, etc. It will also be noted that the report of the previous valuation only contained 12 per cent to cover these items. It should be stated that this change from 12 to 15 per cent represents the results of an extended study of the costs of such work and it is my opinion that where the actual costs are not known for such a property as the Oshkosh Water-Works, 15 per cent of the cost of specific construction represents about a fair amount! for these overhead charges.” In re Application Manitowoc Gas Co. (Dec. 4, 1913) the Commission allowed 15 per cent exclusive of contractor’s profits which should be included in the separate cost items. In re Investigation Ashland Water Co. (July 10, 1914) the Commission allowed 15 per cent. Promotion Expenses Promotion Expenses. — There is an additional class of ex- penditures incurred in connection with many of the public service and some private enterprises which has a more remote connection with the cost of these enterprises than the overhead or the cost of developing the business. Capital is timid and needs guidance. Preceding nearly every investment of capital in the development of an enterprise of any magnitude the same has been in the hands of the promoter whose investigations and efforts are supposed to have been directed to a unification or combination of properties that will make them available as the basis for the enterprise. The reward to the promoter should ap- pear in the enhanced value of the unified property when com- pared with the cost of the individual items that go to make it up. But this is not all that there is to promotion expense. ESSENTIALS OF VALUE &7 Advertising may be necessary to find a market for the securities whose sale is to furnish the money with which construction will be undertaken. A commission may have to be paid to the agent who buys the properties or who markets the securities. The securities may have to be sold at a discount so that the in- debtedness on which interest is paid may exceed the sum that was actually required to construct and acquire all the essential property. Promotion expense of this character does not usually appear in any valuation, nor in the estimate of the investment, though it may nevertheless have been an essential element of cost. The necessity which may have compelled the incurrence of a promotion expense may be deplored and yet it must be ad- mitted that, on the whole, society has benefitted by the pro- moters’ activity and by the carrying out of many enterprises which were not at the outset so attractive that bonds based thereon would sell at par or command a premium. In this connection it may be noted that the Wisconsin R. R. Commission holds that the cost of marketing bonds should be taken into account as a promotion expense but that all discounts do not necessarily become proper additions to physical value. The appraiser whether of value or of the investment will rarely be required to make a close estimate of the promotion ex- pense, but the fact that under the prevailing conditions there has generally been some legitimate promotion expense which may not appear in the valuation, should not be overlooked when rates are fixed. Intangible Elements of Value The Total Intangible Value. — Whenever the net return ex- ceeds a fair interest rate on the capital invested in the physical elements of any enterprise, there will be other elements of value in the same, not represented by the cost of any physical portion thereof. These values being apart from the actual investment in physical properties are usually regarded as intangible values. Ordinarily the sum of all intangible values will be the capitalized net annual earnings, less the investment in the physical proper- Ld 58 VALUATION, DEPRECIATION AND THE RATE-BASE ties (if the accounting system throughout has been proper and the enterprise has met with no untoward experiences) or what may generally be a safer approximation, the capitalized net earnings, less the cost of reproducing the physical properties. A taxicab concern, for example, has invested in the business $100,000. The net annual earnings after allowing for depre- ciation are $30,000. If it be assumed that 1o per cent per annum is a reasonable return on an investment of this character and permanency of the business may be assumed the capitaliza- tion of the concern might be at $300,000. The good-will of this taxicab business appears at $200,000. That is to say, if there were no fear of a reduction of income through competition or other causes, a valuation three times as great as the actual in- vestment might be justified. In such a case the sum of all in- tangible values connected with the business which may include besides what is strictly good-will, advantageous leases on de- sirable space for the taxi stands and contracts with railroads or other transportation companies, is the capitalization of the net earnings of $30,000 per year, or $300,000, less the value of the physical properties assumed as above stated to be $100.000. Ordinarily, however, in a business of this character, the earn- ings may at any time be cut down by competition. Any in- tending purchaser taking this into account as a hazard of the business will conclude that, while earnings of 10 per cent a year on the value of the tangible property may be adequate, the re- turn on the value of uncertain intangible elements should be very much greater. He may find circumstances that will justify him in concluding that the return on any allowance for good-will should be 20 per cent and in this event he will find: Total annual net earnings. « . . is «ves rvs eee oii .. $ 30,000 Ten per cent of value of physical properties. .......... 10,000 Net annual return on intangible values............... » 20,000 Capitalization of $20,000 per year at 20 per cent............ $100,000 Consequently, the amount which he, as a prudent purchaser, would be willing to pay for the business would be only $200,000 ESSENTIALS OF VALUE = instead of $300,000. In other words, $300,000 would be an over- capitalization in view of the risks of the business, and an adequate annual net return from a business of this character should exceed 10 per cent on the total value thereof. As another illustration of relatively high intangible value, a newspaper route may be cited. A thousand subscribers, at $4 each, would make the value of this route $4000. The invest- ment in physical elements such as a cart and horse may be in- significant. There are, no doubt, many such routes where the bicycles and hand carts in use by the delivery boys are furnished by these boys and not by the owner of the route. Practically the entire value of such a route is represented by good-will. Intangible Value Under a Restricted Franchise. — When public utilities are under consideration, the problem may be- come quite complex and each case will have to be considered by itself. A restricted or limited franchise, for example, may make a monopoly of the enterprise, and its terms may be such that charges for service cannot be reduced by any rate-fixing body during the life of the franchise. Under such circumstances, when the volume of business is determinable, it is possible to forecast with some degree of certainty, on the basis of past ex- perience, the annual net earnings and a capitalization of these at a fair rate of interest leads directly to a determination of value. A comparison between value thus ascertained and the cost of reproduction of the physical elements establishes the aggregate value of all intangible elements of whatever nature connected with the utility. Of course, the capitalization of earnings, as here set forth, may not in all cases be a simple matter, because many factors are to be taken into account: The allowance for replacements must be correctly determined. The hazards of the business must not be overlooked. The value of the properties remaining on hand subject to sale at the termination of the franchise may be a factor of some moment in determining how much of the investment is to be amortized within the life of the franchise. Nevertheless, the fact remains that the restricted, exclusive 5Q 60 VALUATION, DEPRECIATION AND THE RATE-BASE franchise usually affords a definite basis for estimating its value. When the rates for service rendered or for commodity furnished are subject to regulation by public service commissions or other similar rate-fixing bodies, this is not so, at least not until rates thus regulated become dependable for a number of years and the policy to be pursued by such bodies in the discharge of their duties can be forecast with confidence. Over-capitalization. — The cases have been so frequent where exorbitant earnings, real or in some measure fictitious, have been made the basis of enormous over-capitalization of enterprises both private and quasi-public in character, that the general public leans strongly toward extreme restriction of earnings whenever the law and circumstances and the power of the rate- fixing bodies will permit of such restriction. Why allow any public utility to earn more than is ordinarily earned by a safe investment? Why allow anything for unprofitable investments even though made under good expert advice? Why take into account any lean years of the past? If the utility was not profitable or is not profitable, why should not the loss fall upon those whose poor business judgment led them into a losing venture? Such questions and others of similar character de- serve serious consideration when rates are to be established, which are to be fair alike to the owner and to the rate-payer. Kansas City Water-Works Case and Intangible Value.— Justice Brewer, in stating the conclusions of the Court in the Kansas City Water-Works Case (Circuit Court of Appeals, Eighth Cir- cuit, July 2, 1894, 62 Feb. Rep. 853), says: “ A completed system of waterworks, such as the company has, without a single connection between the pipes in the streets and the buildings of the city, would be a property of much less value than that system connected, as it is, with so many build- ings, and earning, in consequence thereof, the money which it does earn. The fact that it is a system in operation, not only with a capacity to supply the city, but actually supplying many buildings in the city — not only with a capacity to earn but actually earning — makes it true that ‘the fair and equitable value ’ is something in excess of the cost of reproduction. The ESSENTIALS OF VALUE fact that the company does not own the connections between the pipes in the streets and the buildings — such connections being the property of the individual property owners — does not militate against the proposition last stated, for who would care to buy, or at least give a large price for a waterworks system without a single connection between the pipes in the streets and the buildings adjacent. . . . It (the city) should pay there- fore not merely the value of a system which might be made to earn, but that of a system which does earn.” According to this view of the court there is no question about the inclusion of intangible elements among the properties which have value. The Supreme Judicial Court of Maine in its in- structions to the appraisers of the properties of the Maine Water Co. (1902) in the Kennebec Water District Case (97 Maine 185; 54 Atlantic 6) said: “In addition to structure values, the appraisers should allow just compensation for all the franchises, rights, and privileges to be taken.” Here, too, the court recognizes the fact that franchises and privileges may have value. Intangibles as a Protection to the Owner. — The courts and the public service commissions must protect the investor whose enterprise is developing the latent resources of the country and who is, therefore, to be encouraged, and they must at the same time prevent as far as may be the robbing of the public by over- capitalization and over-bonding with consequent over-charging for the service rendered. But in protecting the public they should not lose sight of the fact that the owner of the utility is entitled to fair compensation for his time and his business ability, and for the risks which he assumed in embarking upon a venture for general benefit. To do this adequately, in conformity with the rulings of public service commissions and the decisions of the courts, the appraiser has frequently had recourse to intangible elements of value under such names as “ unification of properties,” “ going value,” “solidification of road-bed,” ‘appreciation of land ” 61 62 VALUATION, DEPRECIATION AND THE RATE-BASE or of “conduit values due to paving,” “cost of establishing business ”’ or under some other designation. Such an addition of intangible value under the name of “ going value ” based on the losses during the early years of operation has been seriously advocated. If regard should be had in this connection to the exact amount in each case of early operating losses, of unprofitable investments, such as tunnels or wells for water which turned out to be unproductive; destruction by fire or earthquake and the like, then the allowance for unprofitable expenditures might be greatest in the case of the least worthy enterprise, which would be an absurdity. Nevertheless, some allowance for unproductive expenditures and for early losses is fre- quently justified and these may be taken care of either in the appraisal of the rate-base or they may be taken care of in the rate of return which when fixed somewhat higher than the return on ordinary safe investments will in the course of time amortize a part or all of the expenditures which do not appear in the rate- base. Under such a procedure there is a recognition of the fact that early losses may have been unavoidable, that no blame may attach for having made certain unprofitable expenditures and that the owner who has invested wisely and under more fortu- nate circumstances is entitled to the reward which will be brought to him either by giving suitable consideration to * going value ” or by allowing him to earn more than ordinary interest on his actual investment. Example of Intangible Value Created by Earnings. — Take as an illustration the case of a property operated at a loss for 5 years and thereafter at a profit. Suppose that the investment in the property was $1,000,000 before operation commenced; that cost of operation exceeded the earnings in the first five years of operation by $100,000 and that money for the entire investment had been borrowed at 6 per cent. During the five years the interest payments, compounded at 6 per cent, amounted to $338,220, which, together with the operating loss, makes $438,220 as the actual outlay by the owner at the close of the fifth year in addition to the original investment of $1,000,000. ESSENTIALS OF VALUE . No compensation for hazard or management is included in the foregoing figures. The property as assumed will yield more than operating expenses after the first five years. Unless the excess over operating expenses is more than 6 per cent on the total outlay of $1,438,220 the owner will still be conducting business at a loss and unless it is sufficiently in excess of 6 per cent to compensate him adequately for management and risk he will not realize all that he had a right to expect. By reason of increase of population increased demand for his output, or for the service which is rendered by the utility it may be possible after the first five years to reproduce the utility or to construct a substitutional plant with established business at a less cost than $1,438,220. The question is how to determine what will be fair earnings. Two procedures are open: a. The actual cost of developing the business may be added to the cost of reproducing the physical plant and the sum ap- proximating $1,438,220 may be introduced into the calculation as the rate-base. b. The cost of reproducing the physical plant together with actual cost of franchises, water-rights or rights-of-way or about $1,000,000 is made the rate-base, and the cost of developing the business, in this case approximately $438,220, is estimated and treated as a business loss subject to amortization in a reasonable number of years. Any allowance less than will result from these procedures would be confiscation of a part of the investment and therefore unfair to the owner, who is in this illustration assumed to have used good judgment in undertaking and developing the enter- prise. Kennebec Water District Case on “ Going Concern.” — In this connection, too, the instructions issued by the court in the Kennebec Water District Case to the appraisers of the Maine Water Co. (97 Main 185; 54 Altantic 6) may be cited: “In estimating even the structure value of the plant, allow- ance should be made for the fact, if proved, that the company’s 67 64 VALUATION, DEPRECIATION AND THE RATE-BASE water system is a going concern, with a profitable business established, and with a present income assured and now being earned.” “ Going Value ” and ‘ the Going Concern.” — A distinction is to be made between the ‘ value of the going concern” and “ going value.” The value of the going concern is the total value of the entire property, its market value. “ Going value ” is the increment of value due to the fact that the business is established and in successful operation. It should be at least equal to the reasonable cost of establishing the business, includ- ing a reasonable allowance for losses in early, lean business years. If assured earnings are large when compared with the operating cost it may greatly exceed early losses just as value may exceed cost. In the case of unprofitable business, as when a company’s properties are in a receiver’s hand, going value will be only nominal. It sometimes happens that the public is responsible in some measure for inadequate earnings as in the case of competing utilities. By permitting the competition and a duplication of works, the cost of bringing the business up to a profitable basis is increased and may be the cause of increased losses. Going Value in the Decisions of the Wisconsin R. R. Com- mission. — On the subject of ““ going value ”’ the Wisconsin Rail- road Commission in the Cashton Light and Power Co. case (Wis. R. C. R., Vol. 3, p. 85) declares this to be an element of value which must be taken into account. The Commission after stating that it is akin to “ good-will ” refers to Justice Brewer's views in National Waterworks Co. vs. Kansas City (62 Fed. Rep. 853) and then cites the opinion in Cedar Rapids Water Co. vs. Cedar Rapids (118 Towa, 234) to the effect that “ going value ” is “that value which arises from having an established going busi- ness . . . and attaches to the business rather than the property employed in such business.” The Commission takes a sound view when it says in the Antigo Water Co. case (Wis. R. C. R., Vol. 3, p. 707) that the ques- tion as to whether deficits resulting from operation, or due to ESSENTIALS OF VALUE 3 other causes, should be regarded as investment, will depend upon the circumstances of each case. The Commission discusses methods of ascertaining the ‘ cost of establishing the business ”” and “ going value ”’ in Green Bay vs. Green Bay Water Co. (Wis. R. C. R,, Vol. 11, p. 243-252), and in this case says: “The method which is generally followed by the Commis- sion aims to determine, as far as possible, what the actual cost of developing the business in question has been, and to what extent, if at all, such losses have been recovered in later years of operation. There are a number of difficulties in determining, by this method, what the cost of building up a business has been, among which may be mentioned: “1. Entire or partial lack of records covering the develop- ment period. “2. Difficulty of finding original cost of physical plant. “3. Difficulty of eliminating from reported operating expenses amounts which are the results of extravagance, inefficiency, or other causes which tended to keep the costs above a nominal figure. “. .. This method, where it can be applied to its full ex- tent, enables the investigator to determine what it has actually cost the utility in question to build up its business. This sum, added to the actual investment in the physical plant, gives the total amount which the plant and the business have actually cost. . . . Where it is impracticable to determine what the actual cost of the physical property has been the only method of arriving at the value of that property is to ascertain the cost of reproduction. “ The method of determining going value as followed by Mr. Alvord, and which, for the sake of convenience we will refer to as Alvord’s method, is an attempt to fix the amount which it would cost to reconstruct the business of the utility, somewhat as a physical valuation reveals the cost of reconstructing the physical plant. There are two assumptions vital to this method: “1. A city similar in all respects to the one under considera- tion, except that there is no public water supply system but in which the people are in a general way cognizant of the advan- tages of such a water supply. “2. Capital seeking investment which may be either used to construct a plant and business in the city with no water supply or to purchase the existing plant and business. 6¢ 66 VALUATION, DEPRECIATION AND THE RATE-BASE “In a computation of going value according to Alvord’s method the going value is the present worth of the amounts by which the net earnings of the comparative plant are less than the net earnings of the existing plant during the entire period from the date of the first preliminary work until the earnings of both plants are equal. . . . The loss to capital invested in the comparative plant is not to be measured by the extent to which its earnings during the construction period fall short of the net revenues of the existing plant, but rather by the amount by which they are less than the returns which have been foregone in order to enter the new field of investment. . . . The detailed computation of the cost of developing the amount of business necessary to yield a reasonable return upon the property in- volves a number of further assumptions which make the ac- curacy of the result very questionable.” Franchises and Related Matters The Franchise Value. — Any privilege or right granted by legislative authority to engage in a particular business is a fran- chise. Whenever the franchise or privilege to do business is an ex- clusive privilege and grants some latitude in the matter of the charges which may be made for the service rendered thereunder, it is an element that can be valued. It is well stated by the Supreme Judicial Court of Kennebec County, Maine, in in- structions to appraisers that its value ‘“ depends upon its net earning power present and prospective, developed and capable of development, at reasonable rates, and the value to be assessed is the value to the seller and not to the buyer.” When the value of a franchise is in question, all circum- stances that affect the earning powers of a property must be taken into account and by an analysis thereof the excess of the carnings over a fair return on the capital invested in physical properties must be determined. This excess of earnings when capitalized will give some idea of the total value of all intangible elements and may lead to the determination of the franchise value. Frequently, the only stipulation in the franchise in the matter ESSENTIALS OF VALUE 67 of rates is that these shall be fair and subject to regulation. In such cases the franchise value should not be made a part of a rate-base, determined by investment, except only to the extent that its acquisition has actually required legitimate investment, as is the case, for instance, when a city sells to a Street Railway Corporation the right to operate cars on certain streets for a certain period of time. The franchise value together with the value of other intangible elements is independent of the actual cost of these elements; but a franchise value may result from the establishment of rates which produce earnings in excess of reasonable interest return on the capital invested in the physical properties. The ascertainment of franchise value and value of all other intangible elements connected with public utilities is similar to the ascertainment of the value of the good-will of a private business but with this difference. . . . In the case of the public utility there is usually protection against competition, while in the case of the good-will of a private business, competition or the possibility of competition is to be assumed and such com- petition may materially affect the value. A franchise is sought for and operations thereunder are un- dertaken for profit. Sometimes, of course, the profit to the party who accepts the franchise and operates thereunder is an indirect one, as in the case of the railroads which make large land holdings valuable. While the privilege to do business is granted in order that certain property may be used for the benefit of the public, the person or corporation undertaking the business must be assumed to be doing so in the hope of reaping an adequate reward. The Franchise Term.— In many of the states perpetual franchises have been granted. Rights to use water-powers, wharf and water-front privileges, the privilege to supply gas or water and the right to occupy streets for various purposes when thus granted without time limit may acquire relatively high value and may prove a serious obstacle to the ultimate rational development of natural resources. The perpetual franchise 2. = 68 VALUATION, DEPRECIATION AND THE RATE-BASE has, however, one feature in its favor. The operator thereunder can look with some confidence into the future and if circum- stances justify, will find it to his interest and may be expected to make suitable provision for the growth and future demands of the community. Knowing that the prospective earnings justify this course, he can build far ahead of the immediate requirements. But this advantage is not of sufficient impor- tance to justify the grant of perpetual privileges and such privi- leges are now rarely, if at all, granted by any of the states. The term of a franchise should not be too short. When the evils of the perpetual franchise began to be fully realized, the next step was to the other extreme and terms were in some of the states restricted to 25 years. Usually several years are consumed in the construction of works, 5 to 10 years or more in the development of the business and thereafter there should be ample time left within which to make some profit. A term of 40 to go years would seem to be about right, not alone to en- courage reasonable development under a franchise, but also to give the public opportunity to renew, at not too great inter- vals, the conditions subject to which the privilege is granted. Amortization During the Life of the Franchise. —In any event suitable provision should always be made to amortize the capital invested either by a purchase on an agreed basis at the end of the franchise term or by the amortization of a part or all of the investment during the life of the franchise with a view to an acquisition of the property by the public. If the latter plan is followed, there may be danger of neglect in the last years of service, as it will be to the advantage of the owner to expend as little as possible in upkeep, provided only that he can continue rendering the service. The provision which must be made in such a case to amortize the investment may cover the entire term or only a portion of the franchise term. The Indeterminate Franchise. — The indeterminate franchise is fast finding favor. No definite term of life is fixed but pro- vision is made that at any time after a specified number of years, the community may take over the property either at an agreed ESSENTIALS OF VALUE r) price or at an appraised value. Usually the method of making the valuation is agreed upon in advance in order that there may be as few points of disagreement as possible. The in- determinate franchise may be granted subject to various con- ditions such, for example, as an allowance of 10 per cent or some other amount on the actual investment if the property is taken over within 10 years; or that after a certain number of years a part of the earnings will be turned over to the community; or that certain requirements relating to the character and quality of the service will be complied with. The indeterminate franchise has not yet been fully tried out, but in those states in which suitable provision has been made for the regulation of rates, there is good reason to believe that it will prove satisfactory. Capitalization of the Franchise. — The tendency has been to capitalize the value of the franchise, in other words, to use the franchise as a basis for the issuance of securities. Perhaps there is some reason for this in the case of a perpetual privilege, when thereunder the assured earnings exceed the ordinary fair inter- est return on other similar investments; but the capitalization of the franchise, except the actual cost thereof, is now quite generally prohibited by the laws which provide for the control and regulation of the public service corporations, and the de- cisions of the courts are adverse to such capitalization. The Wisconsin Railroad Commission says on this subject in the Antigo Water Case (Aug. 3, 1909), “ That if the municipality required the payment of money or its equivalent, or there was necessary legitimate payment made for the franchise, then the sum which may be reasonably said to have been paid for the franchise may be included in the valuation, the same as money necessarily invested in physical property. But the Commission refuses to consider the claim of some experts and corporations that franchises for which no money was paid may have ‘in- tangible ’ values which should be considered in the making of rates.” The Public Service Commission Law of New York provides: “ The Commission shall have no power to authorize the capitali- zation of any franchise to be a corporation or to authorize the Ec 70 VALUATION, DEPRECIATION AND THE RATE-BASE capitalization of any franchise or the right to own, operate or enjoy any franchise whatsoever in excess of the amount (ex- clusive of any tax or annual charge) actually paid to the State or to a political subdivision thereof as the consideration for the grant of such franchise.” Appreciation and the Unearned Increment Earnings Affect Value. — The earning power of a property determines its value. As its net earnings increase, its value in- creases. The earning power of public utilities, as a general rule, if rates remain undisturbed, increases as population density in- creases although not in the same ratio. The appreciation or increase of value which results when net earnings, in their rela- tion to the investment, are increasing is the reverse of depre- ciation, but it follows no definite law and it cannot be forecast with that degree of certainty which can, with some reason, be claimed for depreciation. The Unearned Increment. — Appreciation or increase of value without increase of investment is the unearned increment which results from the changing conditions of environment. Usefulness in service does not always decrease, but may increase with age. This may be the case with a dam or with a railway embankment, and this increase of usefulness when it can be ex- pressed in terms of money, or value in exchange, represents appreciation. Increase in the price of labor and materials, or a change in the conditions under which an enterprise was first established, may add to or may take from its value according to whether it would be more or less expensive to construct and establish the same enterprise under the altered conditions. As a general proposition, it may be stated that values as ex- pressed in terms of money are increasing. It is also true that, as a general rule, public utilities are to be included among the principal factors which are responsible for the growth of the community, and that, when viewed in this light, the owner of the utility is entitled to participate in the unearned increment ESSENTIALS OF VALUE ; 1 just as the owner of land participates. He does so, of course, in a measure as his business increases, but if held down to earn- ings which will barely yield the ordinary interest rates on safe investments, the extent of doing this may fall far short of the advance in property value shared in by practically all the owners of the realty in the community. Application to Public Utilities. — Such considerations as this, although not thus expressed, have led the U.S. Supreme Court to hold that the owner of a public utility is entitled, in most cases at any rate, to have the present value of his property made the basis of the computation when rates are to be fixed. In the Consolidated Gas Co. case (Wm. R. Willcox et al. vs. Consoli- dated Gas Co. of N. Y., 212 U.S. 19, 29 Sup. Ct. Rep. 192) as already quoted the court says: “And we concur with the court below in holding that the value of the property is to be determined as of the time when the inquiry is made regarding the rates. If the property which legally enters into the consideration of the question of rates has increased in value since it was acquired, the company is entitled to the benefit of such increase. This is at any rate the general rule. We do not say that there may not possibly be an ex- ception to it where the property may have increased so enor- mously in value as to render a rate permitting a reasonable return upon such value unjust to the public.” The court has, perhaps, overlooked the fact that unearned increments are earnings and can be allowed without adding them to the investment. It may have been perfectly fair to make the valuation allowance to the full extent of the unearned increment in the Consolidated Gas Co. case and this allowance is not here made the subject of criticism. It is only the practical applica- tion of the ruling which is brought into question. It is believed that as these matters are better understood there will be a general acceptance of the view that appreciation had better not be included in the rate-base. In the case of farm lands the situation may obtain of a greater supply thereof than can be made use of by the inhabitants of 7 72 VALUATION, DEPRECIATION AND THE RATE-BASE the country. The rental value is then low and the value is fixed rather by the supply of the desirable tracts of land than by the revenue which can be produced by cultivation. The unimproved farm and the unimproved town lot may be a source of expense instead of a source of income. The owner of such property expects appreciation to bring him a reward for having acquired and for hold ng the property. If he analyses his investment in such property after he has held it for a number of years, he may find that the first cost at compound interest, at savings bank rates, plus annual taxes amounts to more than other equally desirable property can be obtained for. His investment under such circumstances was not a judicious one, provided, of course, that the property while thus held was not income producing. But when real estate is held and is in use by the owner of a public utility, the intent is, whether always realized or not, to allow him to recover in the earnings at least interest on what this real estate has cost him. He is not in the position of the person who owns an unproductive piece of property. Never- theless, as already stated, in order to share in the unearned in- crement which he has helped to create for the community he should be allowed, if the prosperity of the community justifies this course, to earn more than ordinary interest on his invest- ment. In the Kennebec Water District Case, already cited, the court instructed the appraisers of the Maine Water Com- pany’s properties that “ subject to all the foregoing limitations, the owner is entitled to any appreciation due to natural causes.” If, in any measure, appreciation goes to the owner of a public utility which includes among its properties land holdings, then in the case of other utilities which include no appreciating property there should be a like opportunity for profit. In the case of these other utilities the unearned increment cannot be measured by the appreciation of land. Appreciation does not increase the invested capital. It is not essential that appre- ciation of land or of any other property be added to the rate- base; but the owner of the utility is, nevertheless, entitled to a reasonable share in the general prosperity which he helps to ESSENTIALS OF VALUE 5 create. This can best be allowed him, not in estimating actual appreciation, which is more or less uncertain and irregular, and, therefore, not always dependable, but in a suitable interest return on the original investment. Interstate Commerce Commission Comments on U. S. Supreme Court Decision. — The difficulty of conforming to the decision of the United States Supreme Court in the matter of allowing the appreciation of real estate was felt by the Interstate Commerce Commission of the United States which says in its opinion in the Western Advanced Rate Case (20 I. C. C. Rep. 344, decided Feb. 22, 1911): “ Certainly if the Supreme Court may decline to lay down the absolute rule that ‘in every case failure to produce some profit to those who have invested their money in the building of a road is conclusive that the tariff is unjust and unreasonable’ (Reagan vs. Farmer Loan and Trust Co. 154 U. S. 412), itis a conservative statement of the law to hold that a railroad may not increase the rates upon a number of commodities solely be- cause its real estate has risen in value.” “ While it is evident, therefore, that each case must be decided upon the facts peculiar to it, the Commission believes it proper in this case to follow the general rule, as stated by Judge Hough of the United States Circuit Court (Consolidated Gas Co. vs. City of New York et al., 157 Fed. Rep. 849, 855), ‘ Upon reason, it seems clear that in solving this equation the plus and minus quantities should be equally considered, and appreciation and depreciation treated alike.’ . . . Thus land has been taken at its fair value and not at its original cost, and the annual ap- preciation of land has been treated as a profit. By this method all property is treated absolutely alike, as Judge Hough sug- gests. No difference is made, except that as depreciation represents a decrease in assets, it is placed as a debit against operation, while appreciation is placed as a credit because it is an increase in assets.” Treatment of Appreciation and Depreciation. — The real difference between the way in which depreciation and appre- ciation should be treated has apparently been overlooked by the courts but recognized by the Interstate Commerce Com- 72 74 VALUATION, DEPRECIATION AND THE RATE-BASE mission. The lessening of worth is offset, or at any rate is in- tended to be offset, by an increase of the earnings. Depreciation then appears on both sides of the account. The owner of the property if fairly treated is no better nor worse off in consequence of deteriorating articles because they are made good to him as they deteriorate. But appreciation is usually not estimated from year to year and is not therefore entered with the annual revenue. When the occasional appraisal discloses appreciation, it appears as a profit. The Interstate Commerce Commission regards it as income. The United States Supreme Court holds that the owner of the public utility is entitled to the appreciation unless the same is excessive in amount in addition to a fair re- turn upon what would, without the inclusion of appreciation, be the reasonable amount of capital invested. How much simpler it would be to grant to the utility some reasonable share in the gen- eral prosperity not measured solely by the increase in the value of the real estate which it happens to own and use in the public service. The Secretary of the Treasury of the United States in decisions relating to the income tax says: « Profits realized on the sale of real estate during the year, also increase of value of unsold property, if taken up on the books of the corporation, (are) to be included in income.” Appreciation and the Rate-Base. — In weighing the question whether or not appreciation is to be added to the rate-base, con- sideration may be given to the alternative of the rental value of equivalent property. Suppose for example that among the properties owned by a public utility there is a large tract of land located in a region in which real estate values are advancing normally. If instead of acquiring this land the owner of the utility had entered into a lease thereof based upon an agreement that the rent from year to year should be commensurate with a proper valuation of the land, the amount of the rent increasing from year to year would be included in the cost of operation and rates would be fixed as though, in the case of actual ownership, the rate-base had included appreciation. ESSENTIALS OF VALUE 73 While this circumstance may justify the inclusion of appre- ciation in the appraisal of the rate-base in some cases, there will be others where the appreciation is out of all proportion to the original investment. Furthermore, a strict analysis will show that such inclusion would deprive the rate-payer of any share in the unearned increment to which he, too, is a contributor. It is, moreover, as already stated, difficult and oftentimes Impos- sible to ascertain the rate of appreciation which might fairly be taken into account and finally, if appreciation is included in the appraisal of land, it should also be included in the appraisal of all other kinds of property. Such inclusion would greatly and unnecessarily complicate every calculation relating to rates and would introduce an element of much uncertainty. It will be much simpler and yet fair to all concerned to exclude appre- ciation from the rate-base but, as already suggested, to allow the owner of every utility to participate in the general prosperity by allowing the rate of return on the rate-base to be higher than it would otherwise be estimated. If this practice coupled with the Unlimited Life Method of procedure could be made general there would be no revision of a rate-base, once established, except as made necessary by ad- ditions to the utility properties or changes therein, nor would there be any need of determining present value, and yet the unearned increment would not be ignored. It would appear in the earnings and not in the rate-base, and the equitable appor- tionment of the unearned increment to the utility owner and to the rate-payer would be facilitated. If the unearned increment (appreciation) is estimated from time to time and is treated as income and the total net return on the rate-base does not exceed ordinary interest rates on safe investments, the estimated appreciation should be added to the rate-base in fairness to the owner of the utility. If appreciation is estimated from time to time and added to the rate-base but is not treated as income, the rate-payer will be denied any share thereof. If appreciation is ignored, and a rate-base, once determined, — Tr 76 VALUATION, DEPRECIATION AND THE RATE-BASE is allowed to remain uninfluenced by appreciation, the owner of the public utility should be allowed a higher rate of return than if appreciation were included in the appraisal of the rate- base. The endeavor should be to secure a general recognition of the latter principle and thereby secure the same liberal treatment for those utilities which do not include among their properties land holdings, as is now accorded with approval of the courts, to those which do include large amounts of real estate. If treated in this way the owner will never be in a position to capitalize appreciation, unless the use of the property in the public service be abandoned. This is as it would be if the owner were acting as agent, and is equitable. In the Minnesota Rate Cases, the United States Supreme Court apparently recognizes the broad principle that the public service property should earn a return upon the increasing value of its properties, provided the appreciation be properly ascer- tained. The Court in these cases says: « Assuming that the company is entitled to a reasonable share in the general prosperity of the communities which it serves, and thus to attribute to its property an increase in value, still the increase so allowed, apart from any improvements it may make, can not properly extend beyond the fair average of the normal market value of the land in the vicinity having a similar character.” It would be much better to let this principle, recognized gen- erally by the courts when they say that present value is to be the basis of the calculations when rates are to be fixed, be ap- plied, as already suggested, without reference to or without being dependent upon and restricted to the present value of land, <0 that the same share in the general prosperity would come to the owner of the utility which owns no real estate as to the other utility which owns broad acres. Cost to Reproduce New Includes Appreciation. — When re- production cost is used as a means of approximating the in- vestment or the rate-base,” the basis of the calculation may ESSENTIALS OF VALUE 77 be current or comparatively recent prices and the general con- ditions as they exist at the time of the appraisal. Such repro- duction cost will include appreciation whether the same be enhanced value of real estate or increased cost of construction due to higher wages and higher prices of materials, or due to other conditions at variance with those which prevailed when the work was first done. Such appreciation comes up for con- sideration in the case of a pipe line which was laid before the street was paved but which is to be appraised after the street has been paved. The cost of reproduction in this case includes the cost of cutting through and replacing the pavement. This cost of reproduction may be some indication of present value but it is not a good measure of the investment, and at its best will be more or less unsatisfactory as a method of approximating the amount on which interest should be earned. Or a pipe which is to be valued may have been laid along an ungraded street. It may have been laid in a temporary trench to be deepened when the street was graded or it may have been placed in a deep trench. The cost of reproduction, if estimated after the street has been graded, will again fail to indicate correctly the amount invested in the pipe and is not entirely satisfactory be- cause the first cost of a deep trench or the lowering of the pipe during the work of grading were legitimate expenditures which the owner of the public utility, if he had been an agent of the rate-payer, would have been justified in incurring. Such con- siderations as these show how unsatisfactory any close adherence to the cost of reproduction may be and they show, too, that a wide latitude is sometimes allowable when the legitimate invest- ment is approximated by estimating the cost of reproduction. Furthermore, this method can hardly be applied satisfactorily without adopting some definite rule in the matter of valuing real estate. Suppose the rule to be that real estate and all other property be appraised on the assumption of present day cost of acquisition and construction, disregarding low original cost, dona- tions and all other factors and conditions that may have pre- vailed at the time of construction and that may have kept cost 78 VALUATION, DEPRECIATION AND THE RATE-BASE down. Under such a rule all relation between the capital legiti- mately invested and the cost of reproduction may be lost. In a private enterprise the former and not the latter would be used as the guide in determining what the earnings should be. But the cost of reproduction is generally held to deserve special con- sideration when the “fair value,” required by the courts, is to be appraised and it is frequently accepted as the starting point. When the courts shall have accepted the view that “ fair value is not the proper starting point, then the importance of close estimates of the cost of reproduction, which includes both de- preciation and appreciation, will fall away. CHAPTER V ELEMENTS WHICH REDUCE VALUE Deductions from Value The Lessening of Worth. — The value of a property may in- crease or decrease with age. Having in the preceding chapter called attention to the essentials of value and to certain elements which add value, there will be considered briefly in this chapter some of the factors which reduce value. In the case of any operating plant there will be parts which deteriorate or wear out under the effect of continued use. By ordinary care the rate at which the perishable parts of a plant are consumed in rendering useful service is held at or near the average rate which experience teaches should be regarded as inevitable. If ordinary care is not exercised and a plant by reason of neglect gets into a condition which requires special attention to restore it to an average condition, all circumstances of use and age being considered, the prospective outlay to ac- complish this rehabilitation is called deferred maintenance. But even when there is no deferred maintenance there may have been a lessening of worth due to the fact that on account of wear and tear, or by reason of obsolescence, or inadequacy, or from any other cause, the time of probable serviceability of any article in question is being continually lessened. Loss of value from such cause is depreciation. Or again, if cost is made a starting point, it may be found that there is included unused property perhaps held to meet a future demand, but which, when valuations as a basis for rates are under consideration, may have to be omitted or deducted from the aggregate of the listed properties. And, finally, the property under considera- tion may include items designed of a capacity to meet future 79 4S 8o VALUATION, DEPRECIATION AND THE RATE-BASE requirements and so far in excess of a reasonable allowance for growth in the near future that it must be regarded as overbuilt and not, therefore, entitled to be taken into account at its full cost. Without attempting a full discussion of all of these factors which must be brought under review by an appraiser, particularly when the establishment of a rate-base is involved, attention will be given briefly to property not required for immediate use, and this will be followed by a discussion of depreciation includ- ing some matter relating to amortization and the replacement requirement, here conveniently considered though not all strictly pertaining to reduction of value. The Overbuilt Plant and Property not Required for Immediate Use Plant Capacity in Relation to Requirement. — Ordinarily, and with good reason, public utilities are constructed of a capacity for service somewhat in excess of immediate requirements. It is customary in anticipation of the increased demand for service which comes with the growth of the community to give the utility ample capacity. A part of the utility plant is built, in other words, to meet the demands of the future rate-payer. The question may well be asked to what extent this is justified and to what extent the rate-payer of today should be made to bear a burden for the benefit of the rate-payer of tomorrow. Prudent foresight in such matters is always commendable. It should be exercised by the private owner just as it would be exercised by wisely managed municipal public utility depart- ments. Future requirements should be foreseen and provision should be made for expansion of works. This may sometimes require the acquisition of lands, of rights of way, of water- rights, of reservoir sites, and the construction of works beyond immediate requirements. Outlays in this direction, within limits, are generally more economical than deferred acquisition or deferred construction, at the advanced value of land and the higher cost of construction of the future. ELEMENTS WHICH REDUCE VALUE Bt While not endeavoring to set up a rule for the determination of the extent to which it may be proper to take future require- ments into account in planning any installation, attention is called to the fact that any such provision for anticipated future service adds to the investment of capital and thereby makes higher earnings necessary than would be required, if, at all times, the plant capacity could be kept exactly at the momen- tary requirement. Here then is an additional call upon the rate-payers, which, naturally, will fall heaviest upon those of the early years, at which time the disparity between actual demand and the provided capacity is generally greatest. There lies herein a further reason why the rate-payer in the early years of the life of any public utility should be relieved, as elsewhere suggested, of the requirement to meet amortization of capital. These rate-payers will ordinarily have done their full share if they contribute operating expenses, interest on the investment, and whatever may be necessary to anticipate and to meet re- placements of discarded parts as such replacements become necessary. Property not in Use. — Guided by the decisions of the courts and by the rulings of public service boards and commissions, it has become customary to discriminate with care between the property of a public utility which is in use and the property which may not strictly be regarded as in use. Property which is in no way related to the service rendered and which is of no prospective necessity will be left out of consideration in this discussion. But there is another type of property owned, but not in use, as for example a reservoir site, acquired by a water works owner at a favorable moment but not likely to be made a part of the system for an indefinite period, or a terminal right of way for a railroad, or an undeveloped water-power which according to sound judgment must be regarded as necessary for future expansion though not in active use as a part of the present system. The wisdom of early acquisition of such prop- erties at opportune moments can hardly be questioned. How to deal with them in making an appraisal for rate-fixing purposes 8. 82 VALUATION, DEPRECIATION AND THE RATE-BASE is the question. If such properties are included in the valuation of the rate-base as of date when purchased, the rate-payer is taxed for the benefit of the future. If, on the other hand, they are not included in valuations until they are actually put into use, then they must ultimately be included at original cost plus interest, or as seems to be a more general practice, at their value at the time they go into use. Sometimes by such pro- cedure a large unearned increment represented by increase of value goes to the public utility owner and generally he is entitled thereto as a reward for his foresight. As a general principle the holding of a reasonable amount of property which will at an early day be in use, should be con- sidered legitimate and in conformity with the practice that would be followed by any prudent management, and it will be proper to place such property in the same category as property in actual use. This, in its essence, is no different from allow- ing full value of the pumping plant which has twice the capacity immediately required, but which was planned with due regard to future demand upon it. When any property which is thus held to meet prospective requirements is not included in the appraisal, the burden of holding the same available for future use falls on the owner of the property. When he thus acquires rights, lands or other elements which are of value to his system of works, but are perhaps of a character from which no return can be expected, he puts the community under obligation to suitably recompense him for his foresight and for the material service which he thereby renders. By judicious investment from time to time in property which a prudent agent under like circumstances would acquire, the public utility owner not only provides for the expansion of his system of works, but he hopes to profit by the increased value that comes to all property located in prosperous sections that are well served by public utilities. The ideal arrangement would be to have all acquisitions of property of whatever nature that appertain to future service ELEMENTS WHICH REDUCE VALUE 83 made subject to the approval of competent representatives of those who are ultimately to pay the bills, and, in that case, there would be no question as to the propriety of including property held for future use. The only question would be whether the present rates should yield interest on the full in- vestment in such property or whether the owner should be required to carry the same, in whole or in part, for the benefit of the community until such time as the greater demand for the service and consequent greater earnings will justify the in- clusion of the property at cost, plus interest, plus such addi- tional amount as may be thought a fair profit allowance to the owner in each particular case. Approval of this character in the past has been out of the question. To a large extent it will be impractical, too, in the future. It frequently happens that the purpose of the acquisition of property must be kept under cover, because, if disclosed, the prices would become prohibitive. For this reason the publicity incidental to a pre- liminary approval by representatives of the public would often prove embarrassing. It will no doubt be suggested that con- demnation proceedings should be resorted to whenever prop- erty is to be acquired for the use of a public utility. No one who is familiar with the conduct and results of such proceedings in the courts of this country would be willing to admit the ad- visability of this procedure in all cases. The jury which is re- quired to base its findings on the evidence submitted in such proceedings frequently reaches conclusions that are not fair. Not until value of the property taken, and the amount of dam- age to remaining property, is made determinable by impartial experts, not selected by the litigants but appointed by the courts, will there be any hope of securing through court pro- ceedings, at a reasonable cost, the rights and properties that may be required by public utilities. Discussion of Overbuilt Plants by the Wisconsin R. R. Com- mission. — In the discussion of the value of the LaCrosse Gas and Electric Co. properties the Wisconsin R. R. Commission says (Wis. R. C. R,, Vol. 2, p. 5): 84 VALUATION, DEPRECIATION AND THE RATE-BASE “ Duplication of such plants is a waste of capital whenever service can be adequately furnished by one plant. . . . Com- petition in this service therefore usually means a bitter struggle and low rates, until one of the contestants is forced out of the field, when the rates are raised to the old level, if not above it, or to a combination of some kind between them which also ultimately results in higher rates.” The Commission in the case of the City of Racine vs. Racine Gas Light Co. (Wis. R. C. R., Vol. 6, p. 286) calls attention to the fact that the investment in physical properties is some- what greater than the amount ordinarily needed. The invest- ment was made to meet anticipated needs. Latitude must be given in such cases to owners but it is questioned whether the return allowed on the investment should be at such high rates as prevail in other cities of the same size. Referring to non-operating property the Commission in the LaCrosse Gas and Electric Co. case (Wis. R. C. R,, Vol. 8, p. 164) expresses the view that the value of such property can be made a part of the value used in fixing rates only when the income therefrom is added to actual income or deducted from operating expenses, even though future use of the same is an- ticipated. Discarded Property. — In Wisconsin it is required by law that discarded property must be left out of consideration in making appraisals of value as a basis for fixing rates. However there are nevertheless cases in which equipment, not actively a part of the plant, but held in reserve for emergency use, may properly be included in the base value (Wis. R. C. R,, Vol. 5, p. 24). Depreciation, Amortization and the Replacement Requirement Depreciation. — Depreciation is a lessening of worth with age which deserves special consideration in any discussion of rate regulation. The matter of amortization and the making of provision for renewals or replacements is so intimately inter- ELEMENTS WHICH REDUCE VALUE woven with the depreciation question, as ordinarily handled, that no attempt will be made to restrict the discussion to depre- ciation. Information bearing upon amortization and the re- placement requirement will here be found intermingled with the general discussion of the depreciation question. Assumptions Made in the Discussion. — The general presen- tation of the problems involved in determining what should be the fair earnings of a public utility will be simplified by assuming that the actual useful life or term of service of each of its parts will conform with the probable life term predicted for these parts. This is not in reality the case. In the preliminary presentation of the subject, however, this assumption has been strictly adhered to. How the departure of the actual term of usefulness from the probable term will affect the computation of the annual replacement requirement will be considered later. It has been found convenient to use an interest rate of 6 per cent throughout this volume for purposes of illustration and this rate is to be understood when no other rate is mentioned. Hypothetical Case; 20 Year Life, 10 Years Old. — Take the case of a plant, all parts of which have a life of 20 years, all constructed at one time and owned by a prudent owner who sets apart at 6 per cent interest, as an amortization fund, each year $0.027185 for every dollar invested therein. If the plant is one which will actually net 6 per cent on the invested capital, then the apparent excess of the annual earnings, over expenses, should be $6 + $2.72 = $8.72 continuously during the life of the plant, and the owner, in estimating the price at which he can sell it without loss at the end of any period, as, for example, at the end of 10 years, would figure as follows (for each $100 of original investment): Investment (original).......... +... $100.00 In the amortization fund: being the amount of a 10-year an- nuity of $2.7185 at 6 per cent interest................... _ 35.83 Remaining value. ....... cersanessrnsseee. $64.17 A prospective purchaser would figure that the plant should be worth at least as much as the present value of $8.72 per 8¢ 86 VALUATION, DEPRECIATION AND THE RATE-BASE annum treated as an annuity for the remaining 10 years, which, at 6 per cent per annum, is $64.17. At the end of 10 years, the original owner, keeping for his own use the money in the replacement fund, will be satisfied to sell at $64.17. The purchaser, content in this case with the assumed rate of interest of 6 per cent, will be willing to pay $64.17, be- cause at the end of the plant’s useful life, he will have recovered his investment with 6 per cent interest compounded annually. He will then be under the same necessity of replacing the plant, making a new investment of $100, as the original owner would have been if he had remained in possession. During the entire 20 years of usefulness the plant has been rendering adequate service. The efficiency of the service is inde- pendent of, and bears no relation to, the useful life of the plant, nor to the fact that some or all of its parts were gradually dete- riorating. Interchange of Terms — Depreciation, Amortization and Re- placement. — It cannot be known just how, nor at what rate, the actual deterioration of a plant takes place. This may be rapid at some period of its life, and slow at another, but, as the plant is supposed, at all times during its life, to be adequately performing the service expected of it, variations in this rate of deterioration are immaterial. In other words, the amortiza- tion of capital is a question which may be considered without regard to the physical condition of a plant at any period of its life. Nevertheless many engineers and economists have found it convenient to consider the actual, or the theoretical accumu- lation in an amortization fund as the measure of plant deprecia- tion with a consequent interchange of terms. The term “ de- preciation” is frequently used when the term amortization” would be more appropriate. There is a clear distinction between amortization and replace- ment. The amortization deals with the retirement of the in- vested capital. This may be in installments in uniform or in unequal annual amounts, or in a lump sum at the end of useful life. The replacement may mean the substitution of a new ELEMENTS WHICH REDUCE VALUE &7 identical plant, but at a cost dependent on new conditions, new prices of labor and material, or it may mean the substitution of new devices rendering equivalent service. In either event the replacement may be at a greater or less cost than the original cost, with, therefore, a corresponding increase or decrease of capital invested. Expenditures for new parts of a plant, which take the place of old parts which are retired for any cause, should be charged to replacement only to the extent of capital repre- sented by the part of the plant thus retired. Any excess of the expenditure for replacement over the cost of the discarded part of a plant should be treated as an addition to, and any less cost as a deduction from, the invested capital. The term “ replace- ment ” should not be used in the sense of retirement of invested capital, which deals with the cost of the replaced part and not with the cost of the new equivalent installation. Theoretically, the amount which should go into an amortization fund should be estimated on the basis of invested capital, or cost, and not on the cost of replacement. In the case of the supposed valuation by a seller and by a purchaser of a plant with a 20-year useful life, at the end of a 10-year period, there is no need of assuming that an amortiza- tion fund has actually been created. The amortization annuity, instead of actually appearing in a fund, may be otherwise invested. Example of Insufficient Amortization. — When the owner of a steamboat which has a limited life and which is yielding 6 per cent per annum of its cost and nothing for amortization, sets apart, out of the 6 per cent, an annual amount, also bearing interest at 6 per cent, to meet its replacement at the end of the steamboat’s life, he will have invested not only the original cost of the steam- boat, no part of which comes back to him in the annual 6 per cent return, but also a gradually increasing sum which in the life of the steamboat will become adequate to replace it. At the end of the steamboat’s usefulness, after replacing it with a new one, the total original investment will be doubled without any increase of earning capacity, and the owner will have, in effect, lost his original investment. 2» “a, 88 VALUATION, DEPRECIATION AND THE RATE-BASE It follows from this that a return of 6 per cent per annum, without anything for amortization, or for replacement, on an investment in a perishable article, when money is worth 6 per cent, is inadequate. The excess of earnings over expenditures must be at least equal to the current interest rate on safe money investments plus an increment depending on the useful life of the plant. This increment must be such that, within the life of the plant, it will either return to the owner his original invest- ment or will be adequate to replace the article in service with a new one. Had the owner borrowed money for the acquisition of the article, and were he paying interest on the borrowed money at 6 per cent, this fact would be seli-evident. ‘The 6 per cent earnings would then be required to meet interest payments, and, at the time when the article has reached the end of its life and must be replaced with a new one, he would find himself, not only in debt for the original article but would have to dupli- cate the indebtedness to make the replacement. Amortization and the Value of Stock. — The amortization increment is ordinarily expected to appear in the earnings as that sum which, at compound interest during the life of the article, will be adequate to retire the original investment. To illustrate these points further, let it be supposed that ownership is represented by capital stock of a corporation. If a plant owned by the corporation and built with funds contrib- uted by the stockholders earns just enough to net 6 per cent without any allowance for amortization, the stock which at the outset may have been worth zoo per cent will gradually decrease in value until, at the end of the plant’s usefulness, it will be worth nothing. The situation is quite different when the earnings net 6 per cent plus an annual amortization increment here supposed to be paid into a special fund. In this case, the stockholder re- ceives 6 per cent each year, and the amortization grows while the plant depreciates in value. The stock, if fully paid up, will be at par from the beginning to the end of the plant’s usefulness, ELEMENTS WHICH REDUCE VALUE 89 and the money in the fund at the end of the period is available either for distribution to the stockholders, being a return of the money advanced by them or it is available for reinvestment in a new plant to replace the original one. Should a sale be made at any time while the plant is in service, with due allowance for its depreciation (offset by the amortization fund) and, this value being recognized by a purchaser and the price paid, there would again be 100 per cent available for distribution to the stock- holders, the deficiency of the selling price being made up by the accumulation in the amortization fund. In the case of net earnings amounting to less than interest on the invested capital plus current depreciation, the valuation of the plant by a purchaser would be at all times less than the value determined by deducting accrued depreciation from cost. In the case of earnings amounting to a proper interest return on the investment plus an adequate allowance for amortization or for replacement the valuation would be, as already explained, capital invested (or the replacement cost) less depreciation. The Use of an Amortization Fund. — Theoretically, then, a part of the earnings each year may be placed in an amortiza- tion fund as a repayment of capital invested, and this fund may be used for the replacement of the parts of the plant as they go out of service or of the entire plant when it has reached the end of its life. The accumulation of an amortization fund for such use, how- ever, while theoretically sound policy, is a measure not always adopted in actual practice, particularly when the properties owned are of a complex character — when they are made up of numerous parts of various periods of probable usefulness. Muni- cipalities, State and National Governments, do not set apart funds for the replacement of worn-out or antiquated buildings, parts of water-works, street pavements, sewers, and the like, until the replacement is necessary. They do not maintain funds at interest representing accrued depreciation out of which to reconstruct their public works. The sinking fund required to retire bonds which may have been issued to construct these 00 VALUATION, DEPRECIATION AND THE RATE-BASE works originally must not be confounded with a replacement fund. The one may be necessary to pay for the works in the first instance, the other to maintain them for all time. T he annual contribution to the sinking fund is a partial payment for the original work. The contribution to a replacement fund, in the case of a plant which is to serve without time limit, is for the purpose of perpetuating the work, because in that case the replacement fund, as far as it will go or as far as it is required, will be used for making replacements. The Wisconsin R. R. Commission in the case of the Superior Commercial Club vs. Duluth Street Railway Co. (Wis. R. C. R., Vol. 11, pp. I to 21) elsewhere quoted makes clear the distinction between depreciation and amortization. Referring to depreciation the Commission in the matter of the Fennimore Mutual Water & Light Plant, in 1913 (Wis. R. C. R., Vol. 12, p. 209), warns against the confusion of the depreciation fund with the depreciation reserve. The “fund ” is actually created by setting a part of the income aside. The “reserve ” is merely a book account which designates the amount and character of various transactions bearing upon depreciation and replacement expenditures. Though it may be difficult to make satisfactory forecasts with reference to necessary reinvestments to replace discarded parts of a plant, the requirements for amortization, being based on cost, are usually readily determinable with some degree of precision. Application to Complex Plants. — Thus far, the plant is as- sumed to have been constructed and put into use all at once, and is of such a character that all its parts have the same life. The same principles will apply when a plant is made up of many elements or parts having various periods of usefulness. The amortization or the replacement annuity is, in such case, de- termined for each part and from the sum of the annuities thus ascertained the minimum earnings which will prevent loss are determined. Mathematical Determination of the Replacement Fund. — The following problem presents itself: In the case of a plant or or ELEMENTS WHICH REDUCE VALUE of gradual development but of full growth and mature age, com- posed of numerous units, the useful life of all the units or parts of which is # years, it is desired to know what amount is in the replacement fund at any time, that fund being assumed to re- ceive such an increment at the end of each year that, during the life of each unit, this annuity, with interest, will amount to the original cost of this unit. Being composed of a large number of elements — each year having added new ones — the addition to it per year will be taken for the purpose of this illustration at one-nth of the total plant as it stands at the end of the nth year. For each dollar invested on this assumption in the first year, there will be $1 invested in each succeeding year, and for each dollar thus invested there will be # dollars of total investment. Let a represent the annual contribution to the replacement fund for each dollar invested. Assume this contribution to be available at the end of each year. Then after n years, na will be the annual contribution to the amortization fund for each dollar of the annual investment. Let m represent any number of years greater than 7. Let ¢ represent the interest rate expressed in hundredths, i.e., for 6 per cent, 2 = 0.06. During the first # years, after beginning the construction of the plant, there will be no replacements, and the replacement fund continues to grow. At the end of the nth year the re- placement requirement, assuming permanency in character and cost, will be $1 for each dollar of annual investment, and this replacement requirement will continue at this rate thereafter. At the end of the nth year the replacement fund will contain: For each dollar invested the first year: a(x +2)" +a(xr +4924 «+. + adollars HC + 2)» — 1] dollars. Q2 VALUATION, DEPRECIATION AND THE RATE-BASE For each dollar invested the second year: a(x+d2+a(z+é)3+ --- + adollars | HE + 2)» — 1] dollars. For each dollar invested the nth year: a dollars. Therefore the total amount S, in the replacement fund at the end of the nth year, after deducting the $1 replacement requirement of that year: S. = Zatti (14+) t—14+---+(@+13) —1]—1 (1) S,= 42a = Dl —nf x (2) So =2l@ +a — @ +4) — mi] — 1. (3) There will be in the replacement fund for each dollar annually invested: At the end of the (# + 1)st year: Spi1 = Sn (1 +1) + na — 1. 4) At the end of the (n + 2)d year: Sez = S, (1 +12)2 + (ma — 1) (1 +14) + na — 1. (5) At the end of the (# + 3)d year: Seis =S, (1 +128 + (na — 1) (1 +7) + (na —1) (1414) +na—1, (6) and so on; and at the end of the mth year: Sm =S, (1 +3) + (na — 1) (1 +2)! + ma —1)(@ +24 os +e —1. (7) Substituting the value of S, and summarizing the series: a ; Nis ; Rossin Sr =5[( + dyn — (1 + Om — i (1 + 5)" — +d + Ea +r — dma — 1), ©) or \ <i ELEMENTS WHICH REDUCE VALUE which may be reduced to a : TW Sm = al + )mtl al (1 + 7)m +) ~<a +m tna — 1). (9) For the interest rate of 6 per cent: 7 = 0.06 and p= ET irae — Fla otr=n +na—1). (10) Form =n and i = 0.06 S, = er (1.067 — 1.06) — = (0.06 + na) (11) = en whl — al — 3. ar (1.06 1.06) ol Tb (12) If now the total amount in the replacement fund be com- pared with the total investment which, on the assumption made, will be 7 dollars for each dollar of annual investment, the rela- tion between the replacement and the investment expressed in percentage and called R will be found to be: = 1904 J ym+l __ yym—n+1 RR. = [(1 +14) (1 +19) ] == 2a +d" tna —1] (13) and for the interest rate of 6 per cent or i = 0.00, R, = 2%. (1.06™*1 — 1.06m—n+1) 0.00367 - Joo m—n+1 wo = (1.06 +na —1) (14) and for m = n and 7 = 0.06, 100 @ 100¢ 100 = —— (1,06"*] — 1.06) — == 22 Rn 0.0036 =i 250) 0.06 n (135) R,= 27,778 (1.06"" — 1.06) — 1667 a — i (16) 93 or or 04 VALUATION, DEPRECIATION AND THE RATE-BASE Table 2 is based on the foregoing formule. For comparison two rates of interest 6 per cent and 4 per cent per annum have been used in estimating the amount which should be in the replacement fund. TABLE 2. THE REPLACEMENT FUND For plants made up of numerous parts, all having the same probable life new, all serving their full probable term of usefulness and no longer. The plants are assumed to have an age equal to or greater than the num- ber of years in the probable life term of their parts. The total invested capital in each case will be # dollars for each dollar of annual investment, when 7 represents the number of years in the probable life term. Amount in the replacement fund expressed in percentage of the total investment. Shipesnd Prob. life 5 years. ' Prob. life To years. Prob. life 20 years. | Prob. life 40 years. 6 6 ren | Som age | op az om gm | ae a —_— — — —— 5 38.2 onal REE AE 10 3% 6 3 | HE a HR ashe a A 15 38.4 3, 2 | 41.8 40.2 lle ve ellis 20 38.4 | 37.8 | 41.8 40.0 41.1 38.0] .....01..... 30 Ln 230 lB i UAT ZZ oy MIE TE 40 A | ome BE ao. sl 47 ol 27 oJ 436.7 IRs .3 GOBER oo YF 38.0| 36.0 30.9 Sol. Rl IRL AT TE 36.1 30.9 In the foregoing mathematical analysis, a plant has been assumed which has reached its full growth and which has an age equal to or greater than the number of years in the useful life term of its parts. Moreover it has been assumed that all of its parts have the same probable life when new. The same formule will apply to any number of articles of the same probable life installed at a uniform rate per year, even when the plant of which they form a part is still being extended, because in this case the articles may be separated into two groups, one being composed of all articles » years of age and less, which have not yet been replaced and the other group of those articles which have replaced discarded articles. To each of these groups taken separately the above formule apply. ELEMENTS WHICH REDUCE VALUE ) It is noteworthy in the assumed case of a plant which has attained full growth and is made up of numerous parts that, when the replacement requirement is computed from the begin- ning by the compound interest method, the amount in the re- placement fund should theoretically vary between comparatively narrow limits; at 6 per cent interest from 31 to 40 per cent for life terms ranging from 5 to 40 years. But in reality there can never be absolute agreement between the actual useful life and the probable life of all parts of the plant. The formule noted in this chapter are not therefore strictly applicable. They are nevertheless valuable in illustrating a principle. Application of Earnings to Replacement and Amortization. — The demands upon the replacement fund usually begin long before the end of the probable life term is reached and may be quite irregular in amount. The non-existence of a replacement fund in the full amount indicated by mathematical and theo- retical consideration does not, therefore, prove that the defi- ciency has been distributed as profit, nor yet that there has been any waiver of the right to have the earnings cover a fair replace- ment increment. Furthermore, if the earned annual replacement increment be treated as amortization of capital and be immediately applied for this purpose, it will thereby be removed from all further consideration. The interest on any increment thus applied is not available to retire more capital. Treated as an annuity and remaining in the business, interest may be compounded so long as the fund is held for its intended purpose, that is, for retirement of capital at the end of the useful life of the item which is being retired. Interest ceases to accumulate the mo- ment the fund is applied to retire the investment in whole or in part. Consequently, if a uniform annual amortization incre- ment bearing interest compounded annually be determined from amortization tables based on the probable life of a new article and if it be covered by the earnings from year to year, even though the amortization increment as earned be reinvested in the property, it cannot rightfully be classed as a repayment of 05 96 VALUATION, DEPRECIATION AND THE RATE-BASE invested capital until the end of the probable life term. If the fund resulting from the accumulation of such increments be applied at any earlier date, a new amortization annuity, based on the remaining value and the remaining life, must be com- puted. Incomplete Amortization. — It will be seen that if an amor- tization annuity thus determined from probable life when an article goes into service be deducted from the investment from year to year, the result will be incomplete amortization. In the case of an article with a probable life of forty years, the amortization rate thus computed at 6 per cent interest would be 0.6462 per cent per annum. The amount of capital returned in forty years would be $25.85 on each $100 of capital invested and there would remain $74.15 still to be made good at that time. These facts make clear the point that, whenever amortiza- tion in lieu of replacement is accomplished by annuities bearing compound interest, the appraisal for rate-fixing purposes must be of the entire investment without deduction of accrued depre- ciation. Second Mathematical Determination of the Replacement Fund. — The foregoing mathematical demonstration that the accumulation in a replacement fund for a plant of mature age, when computed by the compound interest sinking fund method, and actually earned should amount to a considerable sum, con- firms a conclusion which can be reached in a more direct way. In the assumed case of a plant which has a life of » years, and of which one-nth has been constructed each year, after » years there will have to be replaced one-nth thereof each year. Because the annual investment in the installation has been uniform there will be, for each dollar invested per year, a total investment of # dollars. The annual replacement after # years, for each dollar annually invested, will be $1. If now the annuity to replace the several parts of the plant in # years is a dollars for each dollar of the annual investment, then after » years the annual amount re- ELEMENTS WHICH REDUCE VALUE ceived as annuity will be 7a, and this will fall short of meeting the actual expenditures by an amount expressed by (1 — na) which, at 6 per cent per annum, is the interest on — bo) 2 (1 — dollars; or, expressed in percentage of the cost, is Ice 2 7a) per cent of the total investment in the plant. For a plant not subject to further growth, with a uniform useful life of all its parts, and constructed progressively, there should be, at 6 per cent interest, an unexpended interest-bearing balance in the replacement fund as follows: When the useful life is five years: 2 (1 — EG Sa 0) 37.7 per cent of the total investment. When the useful life is ten years: 2 (1 — ml ost) = 40.2 per cent of the total investment. When the useful life is twenty years: 201 ioe role opty) = 38.0 per cent of the total investment. When the useful life is forty years: 2 (1 — tect lr = 0.2585) = 30.9 per cent of the total investment. If earnings have been adequate to provide an interest-bearing replacement fund, then these percentages represent the probable accumulation in such a fund. Some amount such as shown by these figures, depending on the expectancy, represents the accumulation of replacement annuities during that period of the plant’s life during which the actual replacement expenditures were less than the annuity. If the annual allowance for maintenance in the past has been based on the requirements of operation and repair without surplus to meet future replacements and if there has been no spe- cial allowance for amortization, the current allowance for amor- 97 08 VALUATION, DEPRECIATION AND THE RATE-BASE tization and replacements should not be determined by the interest bearing sinking fund method based on original probable life but should be otherwise determined, as hereafter shown. When, in other words, opportunity is not given to accumu- late the 40 per cent of the invested capital (approximately), which, for ordinary periods of useful life of perishable properties, should in the course of time be in a replacement, depreciation or amor- tization fund, any amount estimated from amortization tables on the original full period of useful life will fall short of the real replacement requirement. Illustration of the Replacement Requirements. — Let it be assumed that a conduit, such as a cast-iron pipe, used for any purpose, has a length of 40 miles. Let it be also assumed that the pipe is not being further extended, that the life of this pipe is 40 years, no more and no less, and that it was constructed progressively, one mile each year. It took 4o years to install the pipe, and at the end of this time the first mile of pipe laid was ready for replacement —it had served its time. Each year thereafter, one mile of pipe has to be replaced, and the replacement at this rate will continue indefinitely. The annual replacement expenditure during the first 40 years is nothing, but, thereafter, it is the cost of installing one mile of pipe. If prices of labor and material have remained constant, and if conditions have otherwise remained as they were when the first mile of pipe was laid, then the annual replacement expenditure will be one-fortieth of the total amount invested in the pipe line. Provision for this replacement must be made if the pipe is to continue in service. If, now, the extension of the pipe pro- gresses beyond the go-year period at the same rate, before assumed, of one mile per year, there will be no changes in the annual replacement requirement during a second period of 40 years, but at the end of this second period — at the end of 8o years — there will be 80 miles of pipe in service, and thereafter during the third go-year period there will have to be replaced annually 2 miles of pipe, or one-fortieth of 80 miles, or twice the amount of pipe extension per annum. ELEMENTS WHICH REDUCE VALUE J Determination of the Replacement Requirement. — It is pos- sible, by such analysis, when a plant is growing at a fixed rate and has attained an age exceeding the life of its perishable parts, to prescribe a rule for determining the replacement re- quirement; but it must be remembered that a rule thus deter- mined can be strictly correct only for the impossible hypothetical case of service in exact conformity with the assumed probable life, and that for practical application a rule thus determined may require some modification as explained in Chapter VI. For each group of parts having the same length of life, there is to be determined: first, the average annual capital invested, using, however, replacement cost instead of the actual invest- ment; and second, the full number of times that the age of the plant is greater than the useful life of the particular group of parts under consideration. The replacement requirement (for the hypothetical case, in which actual service conforms through- out with the assumed probable life) is then ascertained by multiplication. A pipe line may again serve as an illustration: Suppose it is desired to know the replacement requirement for a pipe line 300 miles long, which has been extended 2 miles each year, the age of the oldest portion of which, therefore, is 1 50 years. The life of the pipe being taken at 40 years, the full number of times this is contained in 150 years is three. The annual replacement requirement will be three times two, or 6 miles of pipe. The 6 miles of pipe requiring replacement were constructed 40 years ago, and the conditions under which this was done may have been materially at variance with those prevailing at the time of their replacement. Consequently, in the deter- mination of the replacement requirement, expressed in dollars instead of in miles of pipe, the replacement cost of the system and not the original cost of capital invested should be taken into account. Expressed as a percentage of the total length of pipe in service, or of the total cost of replacing the entire pipe line, this would be 2 per cent. QC 100 VALUATION, DEPRECIATION AND THE RATE-BASE By the compound interest annuity method of computation, in the selected illustration at 6 per cent interest, the allowance for replacement would be 0.646 per cent of the cost of the sys- tem, which is only one-third of the actual requirement, and this allowance, as already explained, would only then be justified if amortization had covered the entire period in the life of each part of the pipe during which there was no expenditure for re- placements, so that the inadequate annual allowance could be supplemented by the earnings of an accumulated replacement fund. In a plant which is made up of a multiplicity of parts of various periods of usefulness, those which have the same expect- ancy should, as before stated, be grouped together. For each group, the replacement requirement can then be estimated separately, and from the several amounts thus ascertained the total requirement is determined. The rule previously laid down for a hypothetical case is not strictly applicable under the conditions as they actually present themselves. There can be no absolute conformity between the assumed period of usefulness of the various parts of a plant and the time during which they actually prove useful. The probable useful life or expectancy is merely the average life, which is often not reached and is just as often exceeded. Thus, again referring to the pipe line, it is to be assumed that while some of it may serve beyond the average period of useful- ness of such pipe, other parts thereof, from one cause or another, will require replacement early in its life. Consequently, any rule such as that previously laid down, which indicates a uni- form replacement requirement in successive periods, with a sudden rise in the requirement at the beginning of each new period, if the plant be one that is steadily growing, will require some modification. The simplest modification of the foregoing rule is to assume gradual changes in the annual replacement requirement as the age of the plant increases, instead of the sudden changes, and then to call this requirement at all times inversely proportional ELEMENTS WHICH REDUCE VALUE to the useful life of any group of parts. This is sometimes re- ferred to as the “Straight Line Method.” It might with equal propriety be called a direct percentage method, as the inverse ratio is usually expressed in percentage. Under this direct percentage method, there would be allowed 2.5 per cent per annum of the replacement cost of all parts of a plant having a go-year life; 3.33 per cent per annum of the re- placement cost of all parts having a 3o-year life; 35 per cent per annum of the replacement cost of all parts having a 20-year life, and so on. This method, applied to the hypothetical case of a pipe line, constructed and extended one mile per year, and each mile thereof having a useful life of exactly forty years, would, at the end of the fortieth year, make the replacement requirement 2.5 per cent per annum, or one mile of pipe. At the end of the sixtieth year, the requirement thus determined would be 2.5 per cent of the 6o miles of pipe then in service, or r. 5 miles of pipe. This would be 50 per cent in excess of the amount actu- ally replaced, which at that time would be only one mile. This would also apply for any time before the pipe first laid has reached the limit of its usefulness, as at 20 years. In the assumed case there is no replacement requirement at 20 years; yet the straight percentage method indicates 2.5 per cent of 20 miles of pipe, or o.5 mile of pipe. It follows from this illustration that the Straight Line Method would give results somewhat too high. By further analysis of this problem, the following formulae have resulted, which are free from this objection and fulfill every ordinary requirement. In devising these formule, the fact was taken into account that there may be some replace- ment requirement in the early years of a plant’s life, and that this requirement gradually increases. These formulae apply only to plants which have been developed gradually and are being extended at a uniform annual rate. Using the notation already introduced, and designating with C the total cost of replacing the group of items, the probable I07 102 VALUATION, DEPRECIATION AND THE RATE-BASE useful life of which, when new, was » years, with ¢ the annual renewal requirement, and with g the average annual investment in extensions, the formulae are: For m less than #, c=" (17) anion For m greater than #, c= gos (-8) Rilia For very large values of m in relation to »# (n being the years of probable usefulness), the value of this expression approaches E which is the mathematical equivalent of the Straight Line Method. However desirable it might otherwise appear to introduce a method of computing the replacement requirement by recourse to amortization tables, to do this satisfactorily, in the case of a complex plant, is usually out of the question, when past earn- ings have been inadequate to accomplish the desired amortiza- tion. In such cases the use of some formula, as above noted, for estimating the probable replacement requirement is to be recommended and its application would be equitable from the standpoints of both the owner and the rate-payer. The Interest Bearing Annuity and the Replacement Require- ment. — When an annuity, bearing interest compounded annu- ally, is allowed to accumulate in a fund to retire invested capital, the demand upon the rate-payer is in annual installments. It would be equally proper to make the demand upon the rate- payer for the replacement of each individualized article, at the full cost of replacement, at the time when the article is discarded. In this case the lump sum cost of replacement, equivalent to the amount of the annuity, will take the place of the installments. If the annuity installments are forthcoming as they are due, then the annuity method is adequate. If the owner of the property does not get them, recourse should be had to the lump (1. ELEMENTS WHICH REDUCE VALUE sum allowance due at the time of failure if capital is to be kept unimpaired. It is perfectly reasonable, moreover, to assume, unless there is evidence to the contrary, that the method of estimating and providing for replacement requirements, which prevails in any case, has been introduced deliberately. The owner of the pub- lic service property may be perfectly willing to waive collection of the annuity installments if he knows that what they will amount to, that is, the actual annual replacement, will be cov- ered by the gross earnings when the time comes for discarding parts of his plant. In other words, he may be willing to accept the amount of an annuity in lieu of the annuity itself; and the rate-payer may desire such an arrangement, because, in the early days of the plant’s life, he may be unable to pay a sufficient amount for the service to cover the replacement annuity. It must be remembered, however, that such an arrangement bur- dens the future rate-paver to some extent for the benefit of the rate-payer in the early days of a plant’s life. Not more SO, however, than when, as is done by some appraisers, early losses are used as a measure of “going value.” It follows directly from the foregoing that even when earnings cover current average annual replacement requirements, the appraisal for rate-fixing purposes may still be the entire invest- ment without deduction for depreciation. This will be the case whenever it can be shown that past earnings were inade- quate to permit the accumulation of a fund, out of earnings in excess of reasonable interest on the investment, which, if it ex- isted, would offset in whole or in part the so-called accrued depreciation, 103% CHAPTER VI THE EFFECT OF NON-AGREEMENT OF ACTUAL WITH PROBABLE LIFE UPON THE DETERMINATION OF THE DEPRECIATION OR REPLACEMENT REQUIRE- MENT Depreciation Estimates are Approximations. — Consideration is now to be given to depreciation as a factor affecting the required earnings. It is not enough to know what the theo- retical depreciation will be if estimated from the probable life of any article. Any article in use may be considered as being gradually consumed in the service. When no longer useful, it must be replaced. The replacement requirement therefore must be estimated. To do this properly something more must be known besides the cost, probable life, and age. It will be nec- essary to take the condition of the article into account — to give consideration in other words to the question of whether it will outlast its probable term of usefulness or not. To dis- regard this fact results in crude approximation and loose meth- ods of accounting which are undesirable. Probable Life is Based on Experience. — The sum of all ex- perience, so far as the same has been made a matter of record, fixes the probable life of various classes of articles. Some arti- cles in every class will fail early, others will survive their prob- able life term. When any system of accounting is adopted under which the capital invested in individualized articles is to be retired during their probable life, some articles will fail before their cost is completely amortized and there will be others continuing to render efficient service after their cost has been completely amortized. The anomaly results of having to carry in the accounts a part of the cost of articles no longer in use but still in the process of amortization and also of having 104 ACTUAL AND PROBABLE LIFE ) wiped out the entire cost of others still in service, which judged by the accounts should have no value. Effect of Expectancy upon Present Value. — In order to weigh the advantages and disadvantages of these methods in their practical application some attention must now be given to the probable life and to the expectancy of the various ele- ments that go to make up a public service property. When it is desired to know the present value of any article, the question is not “ how old is it and what did it cost?” but “ how much longer will it serve and what will it cost to replace it”. The first question might be asked when the accrued amor- tization of capital is to be estimated. The second question is to be answered when the current depreciation or the current replacement requirement are to be estimated. How then shall the expectancy be determined? All estimates of annual depreciation and of accrued depreci- ation are based on premises which cannot be determined with accuracy. The probable life of any article when new and the life expectancy of any article which has been in use for some time cannot be determined with any great degree of precision. Conse- quently estimates of depreciation are only approximations. Academic Discussion Justified. — There is much uncertainty in such estimates under the ordinary conditions under which public utilities are operated. A wide range in the method of making the estimates has been the result. When, therefore, the correctness of methods is under discussion, this difficulty of making close estimates should not be lost sight of. Neverthe- less, the academic discussion which is being indulged in by the engineer and the economist relating to best and most convenient methods of procedure is justified, because the same will lead to an ultimate standardization of methods and finally to the gen- eral adoption of the most convenient and generally best method, fair to both the rate-payer and the owner. Although this limitation be recognized as well as the uncer- tainties that result from imperfect knowledge relating to the actual and to the probable life of the elements of any public 105 106 VALUATION, DEPRECIATION AND THE RATE-BASE service plant, and to the difficulty of determining the expect- ancy of those articles which have already been in use for some time, it is nevertheless important that the whole ques- tion be fully considered in order that a framework may be constructed into which the best data furnished by experience can be fitted. The non-agreement of actual life of individual items with their probable life and the extent to which this lack of agree- ment should be taken into account in estimating present worth and in estimating replacement requirements, in line with this thought, has been studied on various assumptions with inter- esting results. These will be briefly referred to, and the re- sulting tables are presented for use until, in the light of larger experience, they can be replaced with better ones. Assumptions Relating to Departure of Actual from Probable Life. — Unfortunately there are no records available from which absolutely dependable tables of expectancy could be prepared for each class of perishable articles in use in connection with public service properties, such as have been prepared by actu- aries for human beings. Any assumption in this regard is more or less conjecture. Nevertheless, it is interesting to note what the expectancy would be at various ages, if certain definite reasonable assumptions are made. When any large number of articles which have the same probable life, as, for example, ten years, is under consideration, there will be as many service years in the aggregate, represented by the failures to reach the probable life term of ten years, as there will be service years represented by those articles which outlast the ten-year term. It may also be accepted as a cer- tainty that there will be a greater number of articles per year to go out of use in the years just preceding and just following the term limit than at any other time. This suggests conform- ity with the law of probabilities. All articles in a group having a ten-year probable life might fail (a) exactly at the end of ten years, but this is highly improb- able. The individual articles might fail (0) at a uniform rate ACTUAL AND PROBABLE LIFE per year, one-twentieth each year, the last going out of service in the twentieth year. Or (c) there might be no failures at all for a number of years, as, for example, during the first half of the probable life term, and thereafter a uniform or an irregular rate of failures until some time after the end of the probable life term. Or (d) there might be a gradually increasing number of failures per year from the beginning to the end of the term of the probable life, and thereafter a gradually decreasing num- ber of failures. Of these various possible distributions of failures to a series of years the most probable one is unquestionably (d). For the sake of a definite basis for calculation it has been assumed that the increase in the number of annual failures up to the maxi- mum and thereafter the decrease in the number of annual failures is uniform; that annual increase before the maximum and annual decrease thereafter are the same and that the maxi- mum rate is one-tenth of the whole number and occurs in the tenth year. On these assumptions studies have been made to determine the expectancy of any article which has reached any age with rather interesting results. These are presented not only as an improvement in the method of estimating probable remaining life or expectancy of any article which is no longer new, though still in good condition, but also to encourage further study along these lines, in order that, where necessary, closer approximation of the actual accrued and annual depreciation can be made than has heretofore been attempted. It should be stated that other hypotheses in the matter of the rate of failures were tried, but that no other gave results that appeared as reasonable as those based on the hypothesis as just stated. Thus, for example, the assumption was tried that 3 per cent of all articles of ten-year life fail in the first year, 13 per cent in the second year, and so on, 93 per cent in the tenth, 97 per cent in the eleventh, 81 per cent in the twelfth, etc., and 3 per cent in the twentieth, but with less satisfactory results for application in estimating remaining value and re- placement requirements. 107 108 VALUATION, DEPRECIATION AND THE RATE-BASE And, again, the failures were estimated for each year on the assumption that they will occur according to the law of prob- abilities, coupled with the assumption that all failures will occur within a period twice as long as the probable life term. The results on this assumption will be again referred to. In so far as the results relating to replacement requirements obtained by the law of probabilities is concerned, it may be stated that these, while not at great variance with the adopted hypothesis, were yet too irregular in amount to warrant the use of the law of probabilities in place of the other more readily applied hy- pothesis. Either hypothesis of rates of failure may be used as a fair basis for approximation to actual conditions. There has appeared no good reason, therefore, for confining the study to the law of probabilities which after all would have to be applied with some such assumptions as made, of practically no survival beyond twice the probable life term and so per cent of all fail- ures within a period equal to four-tenths of the probable life term, or with other assumptions which would also be more or less of a conjectural nature. Tabular Illustration of Expectancy for 10,000 Articles. — In order to further consider the question of the expectancy of any article which is no longer new, let it be assumed that 10,000 articles are installed at the same time and that all of these have the same probable life. Let the probable life term be divided into ten periods. Then according to the hypothesis re- lating to the annual failures, as already stated, there will be 100 of these articles going out of use during the first period; 200 in the second period; and so on to rocco in the tenth period; thereafter goo in the eleventh period; 8oo in the twelfth period, etc., and too in the nineteenth period. On this hypothesis results are readily found as shown in Table 3, in which years may be regarded as representing periods. ACTUAL AND PROBABLE LIFE TABLE 3. EXPECTANCY The probable life of each article is 10 years or periods. For terms other than 10 years, each year in the table may be regarded as a period equal to one-tenth of the probable life term. (Based on the special hypothesis of failures as explained in the text) For 10,000 articles. Single article. Year or period, Remaining num- Remaining service Expectancy at Number of ber of articles at years at begin- beginning of year failures. beginning of year. ning of year. or period. 100 10,000 100,000 10.0 200 9,900 90,000 9.09 300 9,700 80,100 8.27 400 9,400 70,400 7-46 500 9,000 61,000 6.77 600 8,500 52,000 6.12 700 7,900 43,500 5.51 8oo 7,200 35,600 4.95 goo 6,400 28,400 4.44 . 1000 5,500 22,000 4.00 x 9oo 4,500 16,500 3.67 8oo 3,600 12,000 3433 . 700 2,800 8,400 2.00 i 600 2,100 5,600 2.67 500 1,500 3,500 2.33 1 400 1,000 2,000 2.00 fp 300 600 1,000 1.67 18 200 300 400 1.33 19 100 100 100 1.00 20 Oo o CG oO Merit of the Assumed Law of Failures. — Although, under the hypothesis of failures on which Table 3 is based, there may still be considerable departure from the actual number of fail- ures in any year, there can be no question that this hypothesis is, as already stated, a much nearer approach to the truth than the other hypothesis heretofore generally accepted as a basis for calculation, that each article will fail theoretically at ex- actly the end of its probable life term. The last column of Table 3 shows that on the hypothesis as explained, an article which has a probable life when new of ten years will, if it is still in service and in good condition at the beginning of the tenth year, have an expectancy of four years and at the beginning of the fifteenth year, its expectancy will still be 2.33 years. I0Q — Ty | ws . _ = EXPECTANCY IAGRAMS-TEN TS . ROBABE LIFE o 10,000 [unITS, < r —_— ———————— ——— —- Note:-These Curves are based on the Hypothesis that no unit will materially if at all survive twice ' its probable life, and that at the end of the prob- “ | able life term the rate of failures will be equal to > the original number of units divided by the prob- Te 9,007 able life Xe 8,000 lg LY 2 | 7,000 ? — [0 ' = 5 = 21 6,0008 mt Laas 5] <i : ¢ : = Fy re ad ph ro Ll + . » 1 2,600 5b - | = Cp i | wt 1,000 | <% 1 yo 4 BE mal 8 thet Fas CE TWEE TW 0 To = TW TT) Years Fis. I. ACTUAL AND PROBABLE LIFE 1 If the reasonableness of the assumption on which Table 3 Is based be admitted, or if it should be possible to prove by actual records of failures that these assumptions are near enough to the truth to be accepted as giving results substantially correct, then a further analysis will show that the actual replacement requirements under various conditions of investment will be as shown in Tables 4 to 6. In the preparation of these tables account has been taken of the failures that will occur among the replacements as well as among the units of the original installations. Diagrammatic Illustration of the Assumed Rate of Failures. — The basis for the results in Table 3 for articles with a probable life of ten years is shown diagrammatically in Fig. 1. The expectancy is found by dividing the remaining service years at any time by the corresponding number of surviving units. The reversed curve marked “Articles remaining in service ” clearly indicates the hypothesis of failures on which the table is based. It is to be noted that under this hypothesis there is no serious departure from the results that were obtained by assuming that the law of probabilities would apply. Tabular Presentation of Replacement Requirements for Groups of Articles. — The replacement requirements, as shown in Table 5, for numerous articles which when new have a probable life of ten years, if failures occur substantially as as- sumed, and if each failing article be at once replaced, would increase from $1 in the first year to about $10 in the ninth year for $100 of original investment, fluctuating thereafter be- tween $9 and nearly $12 per year and gradually settling down to $10 per year. For an annual investment of $100 per year (i.e., for a growing plant), the replacement requirements would gradually increase from $1 per year in the first year to $463 in the fiftieth year, or from $1 per $100 of investment in the first year to $6.01 in the tenth year to $8.16 in the twentieth and to $9.27 in the fiftieth year. In practical application, in other words, the annual replace- ment requirement in the case of a plant of full growth all parts XR II2 VALUATION, DEPRECIATION AND THE RATE-BASE of which have a probable life of # years, after the plant is » years older than any of these parts, will be about one nth of their replacement cost. In a plant which continues to grow, the theoretical annual replacement requirement will gradually approach but can never quite reach one nth of the total replacement cost. (See Tables 4 to 6.) TABLE 4. REPLACEMENT REQUIREMENTS NUMEROUS ARTICLES. PROBABLE LIFE 5 YEARS Each article is replaced as it goes out of use. For an original investment of $100 with no betterments or additions. Also for an investment growing at the uniform rate of $100 per year. (For the special hypothesis as stated in the text.) Plant of full growth, otigtanl Jioesiment Growing plant, annual investment $100. 100. Replacements per year. Replacements per year.| Rerlyenients Por $100 $ 4.00 $ 4.00 $ 4.00 8.16 12.16 6.08 12.65 24.81 8.27 17.64 42.45 10.61 23.34 65.78 13.16 21.07 87.75 14.62 21.16 108.91 15.56 20.54 129.45 16.18 19.73 149.18 16.58 Lo 18.31 167.49 16.75 II 19.73 187.22 17.02 12 20.37 207.60 17.30 1; 20.45 228.05 17.54 20.21 248.25 7-73 wr 19.90 268.16 17.88 16 19.87 288.03 18.00 2h 19.01 307.94 18.11 ¥3 20.03 327.92 33.22 ia 20.06 347.95 18.31 20 20.02 368.00 18.40 21 20.00 388.02 18.48 22 20.00 408.00 18.55 27 20.00 428.00 18.61 24 20.00 448.00 18.67 23 20.00 468 .00 18.472 Vear ACTUAL AND PROBABLE LIFE TABLE 5. REPLACEMENT REQUIREMENTS NUMEROUS ARTICLES. PROBABLE LIFE 10 YEARS Each article is replaced as it goes out of use. For an original investment of $100 with no betterments or additions. Also for an investment growing at the uniform rate of $100 per year. (For the special hypothesis as stated in the text.) Plant of full growth, original investment Growing plant, annual investment $100. Near. $100. Replacements per year. Replacements per year.’ Repiacsments per $10 $ 1.00 $ 1.00 $1.00 2.01 3.01 1.51 3.04 6.03 2.02 4.10 10.15 2.54 5.20 15.33 3.07 6.36 21.71 3.62 7.5% 29.28 4.18 8.87 38.13 4.77 10.25 48.39 5.38 1. 11.73 60.12 6.01 14 11.33 71.46 3.50 11.03 82.48 6.87 : 10.79 93.27 7.18 rT. 10.60 103.88 7.42 i 10.46 114.34 7.63 1 10.28 124.61 +.80 i 10.09 134.70 -.93 ! 9.85 144.55 1.08 1 9.53 154.08 5.12 Zo 9.10 163.18 4.16 21 9.53 172.72 +23 $ 9.84 182.56 .30 : 10.05 192.60 1.37 z 10.17 202.77 .45 i 10.22 212.99 32 2 10.22 223.21 “iy 7 10.17 233.38 .64 2. 10.11 243.49 «.69 2g 10.03 253.52 3.74 3u 9.97 263.49 8.78 or 9.99 313.31 8.95 40 10.01 363.40 9.09 4; 10.00 413.40 9.19 52 10.00 463.40 9.27 113 II4 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 6. REPLACEMENT REQUIREMENTS NUMEROUS ARTICLES. PROBABLE LIFE 20 YEARS Each article is replaced as it goes out of use. For an original investment of $100 with no betterments or additions. Also for an investment growing at the uniform rate of $100 per year. (For the special hypothesis as stated in the text.) Plant of full growth, . erigioal favesiment Growing plant, annual investment $100. Replacements per year. Replacements per year.| Begley $100 $o.25 $ o.25 $0.25 0.50 0.75 0.38 0.75 1.50 0.50 1.01 2.51 0.63 1.26 3-77 0.76 1.52 5.20 0.89 1.79 7.08 1.01 2.06 9.14 LS 2.33 11.47 1.28 10 2.61 14.08 1.41 IL 2.90 16.98 1.55 3 3.19 20.17 1.69 2 3.49 23.66 1.82 tL 3.80 27.46 1.07 4.12 31.58 2.17 TO 4.45 36.03 2.26 17 4.69 40.72 2.41 5 5.15 45.87 2.56 1Yy 5.51 51.38 2.79 20 5.89 57.27 2.86 21 5.74 63.01 3.00 22 5.67 68.68 3-12 Zi 5.60 74.28 3°23 : 5.53 79.81 3.33 3 5.46 85.27 3.41 2) 5.40 90.17 3.49 27 5.36 96.03 3.55 23 5-81 101.34 3.62 24 5.27 106.61 3.68 75 5.22 111.83 3-73 7 4.63 137.28 3-02 an 4.36 161.04 4.03 Ca 4.97 185.20 4.12 5> 5.10 210.54 4.21 £3 5.07 236.00 4.30 Go 4.99 261.20 4.36 65 4.98 286.09 4.40 70 5.00 311.04 4.45 Year. ACTUAL AND PROBABLE LIFE ; TABLE 7. THE REPLACEMENT REQUIREMENT IN THE CASE OF NUMEROUS ARTICLES AND A COMPARISON OF METHODS OF PROCEDURE PROBABLE LIFE 10 YEARS With due regard to expectancy at various ages. Numerous articles. All installed at same time. No additions to plant. Articles replaced as worn out. Original investment $100. Interest 6 per cent. Net earnings 6 per cent. ‘(Based on the hypothesis of failures as explained in the text.) pry, Straisht Line Method. + Equal Aunual Payment - ypmited Life Method. able ~~ ‘ - : = = “aT repl't 'Amorti-| peqrd Amorti-! Req'd Rem'g | Repl't | Requ'd + Rem'g zation q Rem’g zation a sem gr so equ requ't. - - t- , allow- - wale, allow | SR (value! allow! | fam ive. allow. Cearn $1.00/8100 $10 $16 .00/$100 87-59 [$13. 50! $100 $1.00] $7.00 2.01] Ox | 10 15.46] 093 8.0or 13.59 100 2.01] 8.o1 3.04] 83 10 14.98 87 18.37 13.59 100 3.04 9.04 4.10, 76 10 14.56] 81 18.73 13.59 100 4.10] 10.10 5.200 "70 Io 14.20 76 19.03 13.59] 100 5.20 11.20 ' 6.36] 65 Io 13.90 7I 19.33 13.59 I0O A 12.36 . y 1.57] 62 10 13.72) 68 | 9.51 13.59, 100 ¢ 7.57] 13.57 8.87] 39 10 13.54| 66 19.63 13.59 100 8.87: 14.87 10.25] 58 10 13.48) 64 9.75 13.590 100 10.25 16.25 12 11.73] 58 10 13.48| 64 9.75 13.59 1I00 II.73} 17.73 ll 11.331 6o 10 13.60 65 9.69 13.59 100 11.33] 17.33 2 11.03 61 15 - 13.66) 66 | 9.63 13.59 100 11.03 17.03 10.79] 62 10> 13.721 67 9.57 13.59) 100 10.79 16.79 10.60, ¢ is 13.78) 68 |, 9.51 13.59 100 10.60 16.60 - 10.46, 6: 1 13.84) 69 | 9.45 13.59 100 ' 10.46 16.46 ty 10.28] 6 > 13.84) .... | .... 13.59 100 10.28 16.28 1’ 10.091 10 3.0 c+eo | +... 13.59] I00 10.09 16.09 , 9.85 10 13.90] .... | .... 13.59 100 9.85 15.83 1) 9.53] 3 13.90] .... 4 «a 13.59 TOO 9.53 15.53 «> 9.10 22 13.84 69 | 9.45 13.59 100 9.10 I5.IO ‘I 9.53 ie 13.78] Lo bu. 13.59 100 9.53 15.53 or 9.84 3 13.78 .... | .... 13.59 100 9.84 15.84 : 10.05] b- 13.78" .... | .... 13.59 100 10.05 16.05 2. 10.17 br 13.78 .... | .... 13.59] 100 710.17] 16.17 % 10.22 1 13.78 68 | 9.51 13.59 100 10.22] 16.22 2 10.22! | 15 13.78] .... | .... 13.59] 100 | 10.22] 16.22 Zz: I0.17/ 000% fod 13 cove | +... 13.59 100 | 10.17 16.17 2 10.11 €; 8) 13.781 .... ; ...." 13.50] 700 }'10.11 16 XX 29 10.03 64 Io 13.84 ...., JS. 13.50, 100 10.03 16.03 30, 9.97 64 TORE IS. B41 +» al vee 13.50] 100 | 9.97] 15.97 Departure of Actual Failures from Assumed Laws. — While it may be granted that in the long run the failures of individual articles in any class will follow some definite law (perhaps a law IIc v. 116 VALUATION, DEPRECIATION AND THE RATE-BASE similar to that which has above been cited as more probable than failure always at the end of the probable life term), the fact remains that in no particular case, no matter how large a plant may be, will there be absolute conformity with any as- sumed law. Consequently figures determined on the basis of any reasonable hypothesis of failures can be used to prepare smoothed-out curves and from such curves, tables for general use can be prepared. It is enough to know for the present that ordinarily it may be assumed that the replacement require- ment of a large number of articles with a probable life of » years should increase progressively year by year to about one ath of the cost of effecting complete replacement of all articles and that this rate of one nth would be reached at about the nth year. Table 7 has been prepared to show for numerous articles, all of which when new have a probable life of ro years, the re- placement requirements on the assumption that failures actu- ally occur according to the hypothesis already explained, and to show their relation to the remaining value, the current amor- tization, and the required annual earnings estimated by the Straight Line and by the Equal Annual Payment methods of procedure, also the remaining investment, the replacement allow- ance, and the required earnings if estimated by the Unlimited Life Method. These methods of procedure, when rates for public utilities are to be fixed, are explained in Chapter IX. Expectancy of an Equivalent Single Article.— When numerous articles are under consideration, it may be desirable to know the expectancy of an equivalent single article, representing the aggregate of all the separate articles, which may be used to simplify the estimates of accrued and current depreciation. If the Straight Line Method of procedure is adopted and if nu- merous articles of the same kind and same individual cost are involved, and if it be assumed that actual life in each case will agree with the estimated probable life, then the expectancy of the equivalent single article will be the average of the remaining ages of the individual articles. But under all other methods of ACTUAL AND PROBABLE LIFE 17 procedure, even with the assumption of agreement between actual and probable life, this will not be the case. A full dis- cussion of this fact would be superfluous, but it is here stated as a caution against a possible erroneous assumption. * However, in view of the fact that the termination of service or failure of any article does not occur at the exact end of its probable life term, there would be no sense in attempting to establish the remaining probable life for group values unless hard and fast appraisal rules are laid down by those charged with the regulation of public utility rates coupled with adequate assurance that such rules will be adhered to. The Assumed Hypothesis of Failures. — It may be repeated that the foregoing Tables 4 to 7 are based on the hypothesis that failures of any group of articles of the same probable life will be most numerous near the end of the probable life term; that there will be a gradual uniform increase in the number of annual failures from the beginning to the end of this term; and that but few, if any, of the articles will have a life in excess of double that of the probable life of the article new. It may be repeated, too, that this hypothesis is not based on adequate experience, that it probably departs further from aver- age results than would be found under strict adherence to the law of probabilities, which is the basis of Table 1 3, and that it remains subject to modification as experience may determine. Until suitably modified, it offers, however, a better means of approximating remaining value of any article than is afforded when calculations are made from probable life tables without regard to the condition of the article at the time of the valuation. Failures and Expectancy according to the Law of Probability. — A study has been made, as already stated, to see where the law of probability would lead, and the result of the comparison will be of interest. * The remaining life of an equivalent single article, when computations are made by the Sinking Fund Compound Interest Methods, is noted in a paper in Transactions American Society of Civil Engineers, Vol. XXV, p. 836, with ex- amples on a 4 per cent interest basis. int 118 VALUATION, DEPRECIATION AND THE RATE-BASE Let it again be assumed that practically no article of a large group, all of which have a ro-year probable life, will survive 20 years or twice the probable life term, and that one-half or very nearly one-half of the failures occur within the two years just preceding and the two years just following the end of the prob- able life term. Then, according to the law of probability, and on the assumption that the failures may be bunched at the end of the successive years, there will be failures in each successive year as shown in Table 8. These are noted only to the nearest 5 in 10,000, and in other respects are offered only as approxima- tions to demonstrate a law rather than the result of accurate computation. TABLE 8. FAILURES AND EXPECTANCY ACCORDING TO THE LAW OF PROBABILITY ON THE ASSUMPTION THAT NO ARTICLE SURVIVES TWICE THE PROBABLE Lire TERM. 10,000 ARTICLES. PROBABLE LIFE = 10 YEARS For 10,000 articles. Single article. Remaining num- Remaining service Number of . Eo Expect ib = EE SR 15 10,000 100,000 10.00 35 9,985 00,000 9.00 | 8s 9,950 80,015 8.05 | 180 9,865 70,065 7.11 330 9,685 60,200 6.22 550 9,355 50,515 5-40 80s 8,805 41,160 4.78 | 1065 8,000 32,355 4.04 {£203 6,935 24,355 3.52 1 1340 5,670 17,420 3.08 0 1265 4,330 11,750 2:7% i 1065 3,065 7,420 2.42 8os 2,000 4,355 2.18 550 1,195 2,355 1.97 ; 330 645 1,160 1.80 Ib 180 315 515 1.64 ml 8x 135 | 200 I.50 18 3s 50 65 I.25 19 135 3 15 1.00 20 [a o 0 2 iy 1 Yer ACTUAL AND PROBABLE LIFE ; In addition to the probable failures from year to year, Table 8 also shows the number of original articles in a group of 10,000 that will be still in service in any year; the probable remaining service years in the surviving articles of the original group; and the expectancy of any single article at any age. TABLE 9. REMAINING VALUE AND REPLACEMENT REQUIREMENT REMAINING VALUE oF Numerous ARTICLES WHICH HAVE ALL COME INTO USE AT THE SAME TIME AND ALSO THE REPLACEMENT REQUIREMENT. RE- MAINING VALUE OF A SINGLE ARTICLE. ORIGINAL INVESTMENT $100. PROBABLE LIFE 10 YEARS Failures assumed to occur according to the law of probability. 6 per cent interest. Single article. Numerous articles. Remaining value. CL Vear. Expectancy ~ Ryman R placemany Begin. : :~ ' Equal Annual ua requirement gore Sone ne Same! Ail Gini. ginning of year, ginning of year 10.00 $100.00 $100.00 $100.00 $ o.15 9.00 90.00 92.41 92.55 ©.35 8.05 | 80.50 84.57 84.94 0.85 7.IY 71.10 76.79 78 .00 | 1.80 6.22 62.20 68.80 69.61 3.31 5.40 54.00 61.06 63.34 5.53 4.78 47.80 55.00 59.63 8.12 4.04 40.40 47.49 56.23 10.80 3.52 35.20 41.92 56.56 12.95 3.08 30.80 37.18 58.99 13.96 2.71 27.10 33.01 tie nn 13.62 2.42 24.20 29.70 teens 12.23 2.18 21.80 26.96 FEN 10.47 : 1.97 19.70 24.53 en, 9.01 . 1.80 18.00 22.50 81.67 8.11 I 1.64 16.40 20.55 ein sine 8.04 i 1.50 15.00 18.87 sein ke 8.53 I> 1.25 12.50 15.84 ok Salty 9.33 I) 1.00 10.00 12.82 EE 10.16 20 Src nvre see Viele Jute 62.86 10.67 21 of sts 6 aioe io 0 ox . anwin’s 10.93 22 Ses nd . viniaole oat wa ceemi ly 10.87 : Morte, IPRA as + sibel 10.56 7 was vin <aiviesle Yen'aaie Tr Tires 10.18 a Se a aha wets sat 65.85 9.82 26 | aie Te wine od eran s $e ons 9.58 27 a *loveinlote vv itinie a Suits ain 9.56 28 dvds Salen roe wis Wwe 9.64 29 teleais ie aiaiele TA fuels 9.82 3 Per ay el st 64.47 9.92 110 120 VALUATION, DEPRECIATION AND THE RATE-BASE Remaining Value and the Replacement Requirement according to the Law of Probability. — Table ¢ has been prepared to show for numerous articles, all of which have a probable life term of 10 years, the probable annual replacement requirement on the assumption that failures occur according to the law of probabili- ties, all articles going out of use within 20 years. There is also shown in the table the remaining value of these articles if esti- mated by the Equal Annual Payment Method, and also the expectancy of a single article with a ro-year probable life and its remaining value if computed by the Straight Line Method and by the Equal Annual Payment Method. Computation of Annuities to Meet Actual Replacement Re- quirement. — The computation of the annuities which would re- place each lot of annually failing articles, if the same be assumed to fail on any hypothesis similar to those already suggested, can readily be made and will prove instructive. It will be found that in every case the sum of all such annuities will exceed the annuity computed in the ordinary way from the average or prob- able life. If the computation be then extended to cover all articles remaining in service from year to year and to include also the new articles which have been added to replace the fail- ures, it will be found that in the early years the sum of the annuities is larger than the annuity computed by the use of probable life, in the ordinary way, that after a period in excess of the probable life term, the sum of the annuities will be a minimum and somewhat less than that computed in the ordi- nary way, and that thereafter it will increase again to about the amount computed by the Straight Line Method. It will be unnecessary to introduce a complete calculation to illustrate this point and only the results for articles with a prob- able life of To years will be briefly referred to. Let it be supposed that of 10,000 articles, which all have a probable life of 10 years, 100 fail at the end of the first year; 200 at the end of the second, 300 at the end of the third and so on to Toco at the end of the tenth, goo at the end of the elev- ACTUAL AND PROBABLE LIFE : enth, 8oo at the end of the twelfth, and so on to the last 100 at the end of the nineteenth. By substituting dollars for articles and computing the annuity at 6 per cent interest required for the replacements of each year it will be found that an annuity of $94 will be required to replace the failures of the first year, an annuity of $97 to re- place those of the second year, an annuity of $94 to replace those of the third year, an annuity of $91 to replace those of the fourth year, and so on to the nineteenth year. The sum of these annuities is $1101 or 11.01 per cent. If the articles which fail each year are replaced and the re- quired annuities for these replacements are also taken into account then the sum of the annuities at 6 per cent interest will be: 11.01 per cent the first year, 10.17 per cent the second, 9.41 per cent the third, 8.78 per cent the fourth, 8.26 per cent the fifth, 7-86 per cent the sixth and so on to a minimum in about the fourteenth year of a little over 7 per cent, and thereafter grad- ually increasing to about 11 per cent in the thirtieth year. Had the determination been made in the usual way, based on the assumption that no distinction need be made between the actual and the probable life, the allowance for replacements would have been 7.59 per year, continuously from the beginning. Conceding a moderate or even a wide range of error due to an almost arbitrary though reasonable assumption of the probable annual failures when average life is known, the result of the computation of what should be set aside annually on the annuity basis, to meet the replacements, when compared with the an- nuity determined from probable life new, shows that the latter is insufficient. The computation also shows that the required earnings based on this determination would be undesirably high at the begin- ning, in the early years, when they should be low. No further demonstration than the above will be needed to show the futility of depending on the Sinking Fund Method and the Equal Annual Payment Method as usually applied, when estimating the replacement requirements. I271 122 VALUATION, DEPRECIATION AND THE RATE-BASE The legitimate and always applicable method of procedure when public utility rates are to be fixed, is that which the author calls the Unlimited Life Method. This does not involve any estimate of accrued depreciation, and only reasonable care in determining the annual replacement requirement. The replace- ment fund is kept apart and if error has been made in the as- sumption of the life of the items and the fund becomes either too large, or inadequate, the necessary correction can be applied in subsequent years. CHAPTER VII THE PURPOSE OF THE APPRAISAL General Statement Various Purposes of Appraisal. — The owner of an operating property is interested more in knowing what it has cost him than he is in the value of the property, until the time comes when a transfer of ownership is to be made or the business is to be capitalized. Generally, however, when any enterprise of considerable magnitude is involved the owner should, at all times, have a clear conception of its value. This can only be obtained by making the analysis of the investment and of oper- ating expenses in relation to revenue, and involves much more than a study of financial records. The condition and adapta- bility of a plant to the uses to which it is being put are involved and must be considered by the appraiser. Valuation, therefore, may be required: a. As a basis for a purchase and sale transaction. b. When the property is to be pledged as a security for a loan or as the basis for a bond issue. ¢. When the rates of a public utility are to be fixed or regu- lated, because the earnings resulting from the rates should be adequate to bring a suitable return on the investment and be- cause the charge for the service should be reasonable. d. As a basis for taxation. The taxation value bears or is intended to bear some definite relation to market value. This is not only true in the case of ordinary taxation, for the purpose of carrying on government, but also in the innumerable cases in which it becomes neces- sary to apportion to the property which is benefitted, the cost of some improvement in proportion to the benefits which it confers. 123 124 VALUATION, DEPRECIATION AND THE RATE-BASE Elements of Value. — No definite and final rules can be laid down as a guide for the appraiser in reaching his conclusions relating to value. He is directly concerned with the ascertain- ment, as definitely as circumstances will warrant, of the net revenue both present and prospective. He must give considera- tion to: The cost of construction. The cost to reproduce the property new. The relation of the property to actual or possible competing properties. The condition of the property, including its adaptability to the intended purpose. The weight to be given to these items and the method of applying them in making valuations will be discussed in the proper chapters of this publication. When property with a salable output is valued for purchase or sale, or for capitalization, or bonding, the investigation must be extended to cost of operation and the market value, present and prospective of the service rendered or of the commodity furnished. In the regulation of rates, also, consideration should be given to the value that will result from the earnings and this likewise involves a comparison of operating costs with earnings, present and prospective, from whatever source. Valuation for Purchase or Sale When property is to be valued for purchase or sale, both the seller and the purchaser desire to know the value as determined from the excess of the earnings over the cost of operation. First Step — Determination of the Cost. — The first question to be answered in determining the amount that may reasonably be assumed to be invested in the property will be what has the property cost or what may it reasonably be assumed to have cost. Perhaps this can be ascertained from the cost records with due consideration of losses from unprofitable operation and with proper allowance for excessive promotion costs, for exces- THE PURPOSE OF THE APPRAISAL 125 sive salary payments, for unprofitable or useless expenditures and losses by accident. When cost cannot be thus ascertained or whenever there is a doubt and the importance of a close ap- proximation warrants such procedure, the cost of reproducing the property is to be estimated. Proper allowance must be made, too, for all expenses of whatever nature connected with construction and with the establishment of the business. Second Step — Deferred Maintenance and Depreciation. — The second step will be to ascertain the deferred maintenance, if any, and the accrued depreciation. The accrued depreciation will be the difference between the cost of reproduction new and the present or remaining value of the items which make up the property and which are subject to depreciation. Third Step — Cost of Operation. — The third step will be the determination of the cost of operation. According to the na- ture of the business this may be directed to the aggregate out- put of commodities or service, or it may cover a segregated analysis of cost of operation for a variety of services or commod- ities. But the essential fact to be ascertained is the total out- lay including interest on the investment, salaries and wages, supplies, maintenance and repairs, current depreciation or re- placement requirements, and in the case of a franchise, or patent right with a limited life term, or in the case of an oil well or a mine with a limited oil or ore body, including also an amortization increment. Fourth Step — Earnings, Present and Prospective. — The fourth step will be the determination of the earnings, current and prospective, that will result from such charges for service or for the commodity as may reasonably be assumed to be proper and dependable. It is here, in the case of the public utility, that there may be much uncertainty due to the difficulty of fore- casting the attitude of the rate-regulating authorities toward the public service corporation. For while it is true that private property may not be taken for public use without due process of law and that there must be no confiscation through inade- quate earnings, there is yet some uncertainty relating to the 126 VALUATION, DEPRECIATION AND THE RATE-BASE compensation which the owner may expect for establishing and managing the utility and also as to whether, in every case, the value of the service rendered has really justified the enterprise. There is much uncertainty, in other words, in relation to the earnings in excess of interest on the investment that will be permitted by the public service commissions, and, when value depends largely upon prospective business, there may be uncer- tainty, too, relating to the forecast of earnings on which the estimates of profits are based. Fifth Step — Determination of Profits. — The fifth step in- volves a comparison of the cost of operation with the antici- pated gross income. The excess of the income over cost of operation represents the profits of the business. The profits may be actual or they may be prospective. The profits both current and prospective in excess of interest on the investment, when capitalized, create an increment of value in excess of the investment. This increment of value may, according to circumstances, be apportioned to “franchise,” ‘going value,” ““ good-will,” “ patent right,” or any other classification of value that may seem appropriate. Real Estate Value. — The valuation of real estate may acquire special consideration. But here, as in the case of other revenue- producing property, the real test of value is the amount of the revenue which the property will produce. What is the rental value of the property? This is the question to be answered. The appraiser will direct his inquiry to the gross income, imme- diate or prospective, which is dependable. He will ascertain the taxes and probable assessments for improvements to which the property is liable, and he will determine from these various items the net revenue which the property will produce. This net revenue, immediate and prospective including appreciation, will then determine the value. When the right of eminent domain is exercised to acquire real estate for some special purpose due consideration must be given to its serviceability for the intended use. This subject is further considered in Chapter X. THE PURPOSE OF THE APPRAISAL Appraisals as a Basis for Fixing Rates Protection of the Investment. — In determining the invest- ment on which the investor in public service properties should be allowed a reasonable return, all attendant circumstances must be duly considered. It may be stated, however, that, apart from the determination of the rate of interest which should result from the investment, it will be equitable and fair to con- sider the public service corporation as the agent of the State or municipality, as the case may be, and to determine in what situation the State or municipality would have found itself had there been no intermediate owner or public service corporation. Let it be assumed that the owner of a public service plant has made his investment under good expert advice, and that the plant is in every respect the same as, or equal to, what the people would have constructed for themselves. Let it be fur- ther assumed that the plant is free from debt, that it will have no residual value, and that it and all its parts will have an actual useful life of # years. The owner will then be entitled: First. — To a reasonable interest on his investment; Second. — To operating expenses; including maintenance, re- pair and replacement expenditures; Third. — To an annuity which, in » years, at compound in- terest, will amount to his investment; Fourth. — To reasonable compensation for managing the busi- ness which may be based on the volume of business transacted, and on the general prosperity of the community. Purpose of the Accumulating Replacement Fund. — If it be now supposed that the owner actually received these amounts, estimated on a proper basis, and that he allows the annuity at compound interest to accumulate so that amortization will be an accomplished fact at the end of # years, then, as he has command of the amortization fund, he will have a decreasing amount of capital actually tied up in the plant. This decreas- ing capital or remaining value of the plant is the complement of the growing amortization fund. This fund, in the case of a 127 128 VALUATION, DEPRECIATION AND THE RATE-BASE plant which is to continue in service beyond the term of # years, is supposed to be held inviolable for the replacement of the plant at the end of its life. The owner reaps no benefit from it what- ever, beyond holding it as the means for replacing a worn-out plant. The value of the plant in its varied stages of depreciation, plus such amortization fund, should at all times be at least equal to the original investment. The owner, even if he gets an an- nuity, as here assumed, is entitled at all times to the interest, not on a plant valued at first cost or investment less deprecia- tion, but on the entire first cost. Had he determined, instead of building the plant, to keep his funds invested in safe securities at ordinary interest rates, he would, at the end of # years, have been in possession of his entire capital plus interest on the full amount thereof for the entire time. If, under the assumed facts, he were not allowed interest on the full amount invested in the public service plant, an injustice would be done. This is true even when replacement takes the place of amorti- zation. The owner in this case is entitled to interest on the entire capital invested in the plant, and, at the end of the plant’s usefulness, he is also entitled to a return of the capital itself. Suppose that a city constructs a plant, paying cash for it, and collects rates which will just yield a fair rate of interest on the investment. At the end of # years the plant is replaced with a new one of the same capacity. As the city has not included in its rates, theretofore charged, an increment for amortization, it now finds itself in possession of a new plant and a total investment twice as great as the cost of the first plant. Applying the same principles to the second plant, as to the first, rates should be doubled. This, of course, would be an absurdity. A charge by a city for service rendered which is less than sufficient to amortize the cost of the plant within its life may yet be equitable and proper, when the cost of the plant is inten- tionally put upon the whole community and not upon the rate- payer. THE PURPOSE OF THE APPRAISAL : Rate-Base with and without Deduction of Depreciation. — The application of the fundamental principles, elsewhere noted, to any public utility plant will show that the determination of a rate-base without deduction from the capital actually but rea- sonably invested is a proper proceeding, provided, of course, that the replacement requirements are not overlooked and are computed by some proper method. It may be repeated that, when depreciated value or invest- ment less accrued depreciation is taken into account as a basis for computing necessary earnings, the current depreciation or amortization must be computed on the basis of depreciated value or investment and the remaining life of the plant or of its parts. This can best be made clear by an illustration: Let it be supposed that the passenger rates and the freight tariff on a steamboat line are subject to regulation, and that some one going into the steamboat business builds a steamer for the ser- vice. Let it be assumed, too, that in connection with this busi- ness he requires no capital investment other than the cost of the steamer; that terminal facilities, office space, and whatever else he needs, are obtainable by rental. For the purpose of this illustration, let it be further assumed that the volume of busi- ness is such that there is no doubt about the income, so that the element of hazard is eliminated. If the steamboat has a life of 20 years, it will gradually depreciate in value and will go out of service at the end of a 20-year period. Ignoring its possible scrap value, which is immaterial for the purpose of this illustration, the following questions are to be considered. At the end of 10 years, with interest at 6 per cent per annum, and earnings just sufficient to yield interest plus an amortiza- tion, figured for a 20-year life at $0.027185 on each dollar of the investment: 1. What will be the value of the steamboat to the owner at the end of ro years? 2. What will be the amount that a purchaser can afford to pay for the steamboat at the end of 10 years? 120 130 VALUATION, DEPRECIATION AND THE RATE-BASE 3. What should be the earnings during the time the steam- boat is in possession of the original owner? 4. What should be the earnings during the time the steam- boat is in the possession of a purchaser after 10 years of service? The first and second questions are answered elsewhere. The owner, by one line of reasoning, finds the remaining value in the steamboat to be 64.17 per cent; the purchaser, by a different line of reasoning, finds the same value. The third question, too, is answered elsewhere. The original owner is entitled to a net return during the entire period of his ownership of 6 per cent on his investment, which is at all times 100 per cent. No deduction is to be made for depreciation because the fund which results from the accumulation of the amortization annuity, together with its interest, is available for no other purpose than the replacement of the steamboat at the end of its period of usefulness. It is dead capital, and remains dead until the property is disposed of or until required to replace the worn-out steamboat. The original owner, therefore, is en- titled to a return of 6 + 2.72 = 8.72 per cent per annum on his investment. In considering the fourth question, it may at first appear as though the purchaser, having invested only $64.17 on each $100 of original cost, could claim a return on this investment alone — that he should be allowed, in addition to the amortiza- tion as above determined, net earnings of $3.85 (6 per cent on $64.17) per annum on what he paid for each $100 of the original cost of the steamboat; that the valuation for rate-fixing purposes, in other words, should be the original investment less depreciation. Under the adoption of this view, it will be seen that, if the steamboat were sold repeatedly, there would be a constantly decreasing appraisal for rate-fixing purposes. In the last year of its service the valuation entitled to con- sideration in fixing earnings would be only 8.23 per cent. This view is unfair to the owner of the property, who should be assumed to be planning a continuation of the steamboat busi- ness. When he takes possession of the steamer, its value to THE PURPOSE OF THE APPRAISAL LI him, as already set forth, is $64.17 on each $100 of original cost, but, as owner, he at once finds that, of his capital ordi- narily available for other purposes, an amount equal to 35.83 per cent of the cost of a new steamboat is, to all intents and purposes, tied up in his steamboat business. It has become dead capital, for all purposes except replacement, so long as he remains in the steamboat business. This 35-83 per cent at interest at 6 per cent is necessary to supplement the annuity regularly going into the amortization fund, together with which at the end of the 20-year period it will just replace the steamer. Whether or not the 35.83 per cent is actually set apart is immaterial; the fact remains that ownership of the depreciating steamer renders this amount of capital as already stated unavailable or dead for any purpose other than replacement, and the new owner is entitled to interest on this 35.83 per cent just as well as on the 64.17 per cent which he paid for the steamer. The demonstration of this fact may be made as follows: The purchaser of the steamboat, who buys the boat when it has a remaining period of usefulness of ro years, invests, as has been explained, $64.17 for each $100.00 of the original cost of the steamboat. He is unquestionably entitled to interest on this sum, together with amortization, which at the assumed interest rate of 6 per cent will be: Interest at 6 per cent on $64.17 perannum................... 8s Amortization annuity for the remaining ro years, during which the investment of $64.17 is paid back to the purchaser (87-59 on each $100)............. et ’ This is exactly the same as though, instead of the value of the steamboat, the capital originally invested had been taken into account, in which case the original owner or purchaser would be allowed: Interest at 6 per cent on the investment of $100 per annum...... $6.00 Amortization annuity to retire $100 of the investment within the life of the steamboat, that is, within 20 years................ + 72 Total. os crs eeveaviirasens 23070 I2 132 VALUATION, DEPRECIATION AND THE RATE-BASE Although it may be superfluous, one more illustration of this principle will be given: Let it be supposed that the owner borrows money from a bank at 6 per cent per annum to build a steamboat, and that he earns 6 per cent plus the amortization increment of 2.72 per cent. Of the $8.72 to his credit at the end of each year’s business for every $100 of capital invested, he pays the bank $2.72 on account of principal and so much of the remaining $6 as may be necessary to meet the interest then due. This will be all of the $6 the first year, and a decreasing amount thereafter until the end of the 20-year period, when his steamboat is re- tired. He then finds that he has paid back to the bank on account of the borrowed capital twenty annuity increments of $2.72, amounting to $54.40, and that there is still due to the bank $45.50. He also finds that the various amounts remaining in his hands from year to year, $0.16 at the end of the second year, $0.34 at the end of the third year, $o.52 at the end of the fourth year, and so on, together with interest thereon at 6 per cent, when computed for the 20-year period, will amount to the $45.50, the balance due at the bank. The owner finds he has earned nothing. He has invested no money of his own and has received no return, which is as it should be in this hypothetical case. The rates, however, throughout the entire 20 years were fixed on the principle that 6 per cent per annum should always be allowed on 100 per cent of the capital invested, together with the amortization annuity, but without any deduction for depre- ciation. They could not have been fixed lower without entailing loss to the owner. Unlimited Life. — The value of a revenue-producing property when the earnings thereof include an amortization annuity has already been discussed. It remains to consider the case of a property which, in addition to the accepted reasonable rate of interest (net), is without limit as to its time of serviceability, earning the estimated annual replacement requirement deter- mined by some formula, as above explained, instead of the annuity computed from amortization tables. THE PURPOSE OF THE APPRAISAL -.3 In this event the plant may be regarded as having unlimited life. Each part thereof as it wears out is replaced out of cur- rent earnings. The owner does not maintain an amortization fund, neither is any of his capital rendered dead or unavailable. To him the value of the property is at all times 100 per cent, so, too, in the case of a purchaser. Knowing that all replacement requirements are fully covered by the earnings, the purchaser is willing to pay roo per cent for the plant, regardless of the amount of accrued depreciation. The case may be considered of a public service property whose earnings have been inadequate to supply any amortiza- tion increment, but which will in the future be able to earn the actual annual replacement requirement. The original invest- ment in this case having been 100 per cent and there having been no amortization annuity in the past, there can be no trans- fer of the property at less than roo per cent without loss; but if, by reason of inadequate returns, the market value could not be maintained at roo per cent, and a sale has been made at less than this sum, the new owner will be compensated and pro- tected if, on his investment which is not original cost, he earns reasonable interest and an adequate amount for replacements. This must be so, because, in the future, actual replacement re- quirements being covered by the earnings, the worn-out parts will be replaced without cost to the owner. This replacement neither increases nor decreases his investment; but, if the property is extended and new parts are added, such additions represent newly invested capital to the full amount of their cost, and in such a case his investment, expressed as a percentage of the total cost, will gradually increase. At all times, however, without causing loss to the new owner, that part of the plant which he bought at a depreciated value could be valued at his purchase price, while all extensions sub- sequent to the purchase, on the assumption that replacements are met out of earnings and that there is no amortization of capital, should, for rate-fixing purposes, be appraised at roo per cent. Such a course, however, would deprive the new owner of 3: 134 VALUATION, DEPRECIATION AND THE RATE-BASE the opportunity for profit, of which he probably thought to avail himself when he bought a plant of depreciated value, and would place the rate-payer in the position of having made a profit at the expense of the original owner. This fact explains why the market value of stocks and bonds is cited so frequently as an indication of value. Improper Use of the Term * Value.” — It may be held that a determination of value for rate-fixing purposes, on the princi- ples herein set forth, is not a determination of value at all. This may be true, but it then becomes a matter of defining “ value,” as used by the courts in order that a distinction may be made between value and the appraisal of the investment on which rates may be properly based. The term ¢ value ” has been very generally used in matters involving the fixing of rates in the past. When fundamental principles are better understood, more attention will be paid to the capital reasonably and properly invested. Under a system of permitting the owner of public service properties to earn from year to year the actual average replace- ment requirements, the necessity for a close distinction between repair and replacement disappears. This is of some advantage, as it is at best difficult to discriminate between small items of replacement and large repair items. Basis of Rates in the Knoxville Case. — The United States Supreme Court in the Knoxville case Knoxville vs. Knoxville Water Co. (212 U. S. 1; 29 Sup. Ct. Rep. 148) says: “ A water plant, with all its additions, begins to depreciate in value from the moment of its use. Before coming to the ques- tion of profit at all the company is entitled to earn a sufficient sum annually to provide not only for current repairs, but for making good the depreciation and replacing the parts of the property when they come to the end of their life. The company is not bound to see its property gradually waste, without mak- ing provision out of earnings for its replacement. It is entitled to see that from earnings the value of the property invested is kept unimpaired, so that, at the end of any given term of years the original investment remains as it was at the beginning. It THE PURPOSE OF THE APPRAISAL 135 is not only the right of the company to make such a provision, but it is its duty to its bond and stock holders, and, in the case of a public service corporation, at least, its plain duty to the public. If a different course were pursued, the only method of providing for replacement of property which has ceased to be useful would be the investment of new capital and the issue of new bonds or stocks. This course would lead to a constantly increasing variance between present value and bond and stock capitalization — a tendency which would inevitably lead to dis- aster either to the stock-holders or to the public, or both. If, however, a company fails to perform this plain duty and to exact sufficient returns to keep the investment unimpaired, whether this is the result of unwarranted dividends upon over issues of securities, or of omission to exact proper prices for the output, the fault is its own. When, therefore, a public regula- tion of its prices comes under question, the true value of the property then employed for the purpose of earning a return cannot be enhanced by a consideration of the errors of manage- ment which have been committed in the past.” According to this statement by the Court, the owner of a public utility should be required to exact prices for his output, which, at the beginning of operation and at all times thereafter, will cover the current depreciation of the physical elements of his plant. Yet, as elsewhere explained, in the early years, this is frequently impossible, and in nearly every case is inadvisable and would work unnecessary hardship upon the consumer. Losses in the early years when rate-payers are few are often- times unavoidable and these losses deserve consideration. Past history cannot be ignored if rates are to be so fixed as to be fair alike to the owner and to the rate-payer. In other words, not all shortage of earnings in the past is to be ascribed to errors of management. It is difficult to reconcile the language of the Court with this principle even as it is difficult to under- stand why so many of the Courts have held that value which results from earnings must be made the starting point when rates are to be fixed. “ Value ” Defined in the Minnesota Rate Cases. — Justice Hughes in delivering the opinion of the U. S. Supreme Court in the Minnesota Rate Cases (June 9, 1913) (230 U. S. 352) said: I 36 VALUATION, DEPRECIATION AND THE RATE-BASE “ The depreciation in question is not that which has been over- come by repairs and replacements, but is the actual existing depreciation in the plant as compared with a new one. It would seem to be inevitable that in many parts of the plant there should be such depreciation, as, for example, in old struc- tures and equivalent remaining on hand, and when an estimate of value is made on the basis of reproduction new the extent of existing depreciation should be shown and deducted. . . . And when particular physical items are estimated as worth so much new, if in fact they be depreciated, this amount should be found and allowed for. If this is not done, the physical valuation is manifestly incomplete. And it must be regarded incomplete in this case.” In the Minnesota Rate Cases the Master, in ascertaining a basis for rate fixing, had allowed the cost of reproduction new without making any deduction for accrued depreciation. The Master did not deny that there was depreciation but found that the same was more than offset by the appreciation in value of certain items. It was this finding which the Supreme Court refused to approve. The Supreme Court in its decision as usual makes value the starting point. Consequently the court says that depreciation must be deducted from the cost of reproduction new. But cost of reproduction is not “value.” Not even the value of the property new is exactly determined by its original cost. The opinion of the court becomes illogical if it be conceded to be unnecessary to make value the starting point when rates are to be fixed. But the Master, too, seems to have overlooked this point and sought to find something, appreciation in this case, to offset depreciation. He was quite as much at fault as the Supreme Court. And yet the allowance of appreciation in de- termining present value as a basis for fixing rates or for the issue of bonds is not uncommon. Railroads claim appreciation of their road-beds. Though it may be granted that the com- pacted road-bed, long in service, is worth more than a recently constructed bed, this should have nothing to do with the fixing of rates, no more than accrued depreciation should have. The THE PURPOSE OF THE APPRAISAL J new road-bed requires more careful watching and greater ex- pense for upkeep. Consequently the net earnings are lower than they would be with the same volume of business, the same rates and a well-compacted old road-bed. If the resulting earnings are inadequate in the early years of business, the defi- ciency may be treated as a temporary investment to be amor- tized out of the larger net earnings of later years. Depreciation in the Pocatello Water Company Case. — The Supreme Court of Idaho in a recent decision (1915) in the Pocatello Water Company case, Murray vs. Public Utilities Commission (150 Poc. Rep. 47, p. 50), reversing the Public Service Commission of that State says in reference to deprecia- tion: “So far as the question of depreciation is concerned, we think deduction should be made only for actual tangible depreciation and not for theoretical depreciation, sometimes called ° accrued depreciation.” In other words, if it be demonstrated that the plant is in good operating condition and giving as good service as a new plant, then the question of depreciation may be entirely disregarded.” This decision is in substantial accord with the minority report of the Commission which had been made by A. P. Ramstedt and in which he said: “ A person having invested his money in a continuous busi- ness enterprise for the benefit of others must always be ready to replace the constructive portions of his plant as they wear out. A person having embarked on such an enterprise is justly entitled to compensation to cover this depreciation in addition to a fair return, over and above expenses, upon the reasonable value of the property. Allowance for depreciation cannot, in my judgment, be considered as profit or an earning factor in the business. ... The fact that in an investigation of the petitioner’s property . . . it is found that the market value of his physical property employed for public use has depreciated $77,188.39 does not, in my judgment, justify the commission, in its determination of a fajr value for rate purposes, to deduct the amount of depreciation from the present estimated cost of reproducing the property new, and thereby reduce the earning power of his property.” 13” 138 VALUATION, DEPRECIATION AND THE RATE-BASE The fact is evidently being recognized in Idaho as elsewhere, that the service rendered should always be zoo per cent good even though rendered by a plant whose physical parts are per- ishable and that if a roo per cent valuation for rate purposes is fair when the plant is new it is equally fair when the plant is old. Wisconsin Railroad Commission on Investment as the Rate- base. — The view which the author takes relating to making the necessary original cost and not “value »” the starting point when rates are to be fixed finds some support in the following statement by the Wisconsin R. R. Commission in the City of Appleton Case (Wis. R. C. R,, Vol. 5, p. 220). « For rate-making purposes the actual total investment, sub- ject to certain qualifications, seems to be the basis for deter- mining the reasonableness of the charges that may be exacted of the public for the services rendered or product furnished in certain jurisdictions. Of course where such information is not available, the reasonable value of the investment would have to be ascertained by some method of appraisement, and in such event the ¢ actual total investment’ doctrine would be inappli- cable.” Appraisals for Taxation Purposes The Taxation Value. — The tax value is usually intended to bear some definite relation to the market value. In some of the older Eastern cities of this country the tax value is intended to represent the full market value. Generally, however, this is not the case. Real estate will usually be found to be valued for taxation purposes at from so to 75 per cent of its market value and personal property sometimes still lower. The appraiser of tax values is therefore interested in market value and must give consideration to all the elements that go to establish market value, such as supply and demand, earning capacity present and prospective, rate of appreciation and the like. But this is a subject which is foreign to the purposes of this volume and may be dismissed with the above broad state- ment. THE PURPOSE OF THE APPRAISAL Appraisals for the Purpose of Capitalization Capitalization. — The primary matter to receive consideration when a property is to be valued for the purpose of capitaliza- tion is its earning capacity. What are the net earnings, pres- ent and prospective? When this question can be satisfactorily answered the problem has been solved. Inquiry must therefore be made relating to the total annual outlay involved in con- ducting the business enterprise. Operating expense of every kind including an adequate annual replacement requirement and an amortization increment if the life of the enterprise is limited, must be weighed against the assured present and prospective income. The resulting net earnings capitalized at the interest rate, which an enterprise of the nature under consideration should yield, will indicate the upper limit of value for capitali- zation. When a public utility is under consideration the problem may be complicated by the fact that rates and therefore the earnings are subject to regulation and in consequence of the control and regulation exercised by the public through its public service commissions, any great precision in estimating the gross present and prospective earnings may be out of the question. This may prove embarrassing particularly in those cases where the actual investment of capital is small but the volume of current business is large. In all cases the actual properly in- vested capital will be a first approximation of value for capital- ization purposes and usually the lower limit of such value if the property is one in successful operation. 130 CHAPTER VII1 THE FIXING OF RATES Public Utilities and the Regulation of Public Service Ownership of Public Utilities. — In the older countries the public utilities are generally owned and managed by the State or municipality. In the countries, on the other hand, which are but sparsely populated and in which the potentiality of natural resources is large, private enterprise is usually depended upon to make the development. Certain utilities are almost universally publicly owned. This is true of city streets, very largely of country roads and bridges and, in most countries, of the sewers. There is probably not a city in the United States in which a charge is made for the service rendered by the sewer system. The benefit, in this case, to the community as a whole, of properly disposing of human excrement and such domestic waste as can be floated away with water, is generally recognized. There is no apportionment of cost to individuals, in other words, according to the value of the service. The cost of establishing and maintaining the sys- tem is raised by taxation. The streets and public roads, too, are generally built at public expense. But there are other utilities such as water-works, electric light and power works, gas-works, telephone systems, railroads and other transportation systems which may be either publicly or privately owned. The private ownership is usually exercised through a corporation. That this should be so is natural for the reason that stability of management is thereby secured, the element of uncertainty in the matter of the life of the owner being eliminated. Quasi-public Character of Public Utilities. — While the public service corporation is subject to the same general laws which TAC THE FIXING OF RATES IAT control other corporations operating for profit, they are accorded certain rights and privileges which give them a quasi-public character. They have the right of eminent domain, i.e., the privilege of taking, under due process of law, private property for their uses (subject, of course, to the making of adequate compensation therefor) and they may be accorded the privilege of occupying streets, roads and public places subject to reason- able regulations. The tendency of the day is to give the public service corpora- tions more and more monopolistic character and to trust to regulation and control for the protection of the public interest. This seems wise and should make for good service at reasonable rates, always provided that regulation be not too stringent and onerous and that the public service corporation be allowed to make a fair profit. The Disadvantage of Frequent Modification of Rates. — In some of the States, as until within recent years in California, the right to regulate has found its main expression in laws re- quiring the rates of certain utilities to be fixed annually. The water and gas rates have thus been under annual investigation in San Francisco, and the occasional establishment of rates which were thought inadequate has led to much long drawn- out litigation which has rarely resulted satisfactorily to either of the litigants. As the result of such litigation relating to water rates estab- lished by San Francisco for 1902-03 and for the years subsequent thereto, the court has allowed, temporarily, the collection of rates by the Spring Valley Water Company in excess of the limit fixed by the city authorities and the excess collected has been impounded and now (1915) amounts to over $1,500,000. It is only fair to say, however, that by recent amendment of the charter of the city, the rates will hereafter be subject to regu- lation by the California State Railroad Commission (Public Service Commission). When the established rate is made subject to frequent change and the owner of the utility is not allowed to earn more than 142 VALUATION, DEPRECIATION AND THE RATE-BASE some predetermined interest return on his investment, the in- centive to improve the service falls away, because, if the owner succeeds in economizing, in producing his output at a lower cost, the immediate result will be lower rates and less earnings. The gross income may be reduced though, perhaps, the value of the service to the rate-payer may remain unaffected or may even be increased. Rates should not therefore be subject to change too frequently. If there must be a term during which the established rates will apply, let it be at least 5 years. Control and Regulation. — The acceptance of the privilege to operate a public utility carries with it a submission to such regulation as may be demanded by the public which grants the privilege. This regulation must be reasonable. The public utility owner is in business for profit. He invests his capital and applies his ability and experience to the development of enterprises that would otherwise remain dormant for a longer or shorter period. He brings within reach of the community, means of transportation, an adequate water supply, light, power and heat, telegraph and telephone facilities which all contribute to the growth and prosperity of the community. He does this because he considers his enterprise a good business venture. In the case of the commercial and industrial enterprise, too, a tendency may be noted toward monopoly which is likely to lead in time to regulation and control similar to that of the public utility. Whenever the operation of any concern acquires such magnitude that it can and does destroy the business of its com- petitors, it becomes monopolistic in character and the state is bound, sooner or later, to exercise its right to regulate and con- trol not only the method of conducting business, but in the end, perhaps, the prices to be charged for its output. Excessive and Fictitious Profits. — Where, in the rapid tran- sition from a frontier region to a state with stable industrial and commercial conditions, the advance in the value of real estate has been rapid and the opportunity for profit in many lines of business has been large, the owner of the public utility has fre- quently taken advantage of the opportunity and has capitalized THE FIXING OF RATES i43 inordinate profits, sometimes real and sometimes fictitious. Where there were no public service commissions — and these are a relatively new institution, — the accounts were kept in a fashion to suit the manipulator. Apparent profits were used as the basis for a distribution of dividends and for the issuance of stocks and bonds, and the rate-payer was charged to the limit. The Right to Regulate Rates. — The right to regulate rates is now quite generally recognized. Without such right every cor- poration which has a monopoly would have the public at its mercy and could charge for its service all that the traffic will bear. The right to regulate, if properly exercised, should in the long run prove of advantage to the owner of the utility. Fair regu- lation will insure to the owner what he is entitled to and will protect him against unfair competition such as has frequently been the result of opportunity to capture with a relatively small outlay the cream of the business. Under proper regulation the owner of every public utility whose existence is justified by all attendant circumstances, should get the protection of his legitimate reasonable investment, also a fair interest return on this investment and should recover all the necessary operating expenses including replacement requirements. He should receive such treatment that at some time, by amor- tization of the capital which he has invested, or by a sale to some purchaser, he can withdraw from the business without loss, provided of course, that he has exercised due foresight and has not met with unavoidable losses such as may be caused by floods or earthquakes. Regulation Essential. — The necessity for regulation has now become apparent. The practice of granting perpetual franchises with unwise privileges has fallen into disfavor. This first be- came manifest in laws permitting the periodical regulation of public service rates by local, municipal and county authorities. Thus, for example, in California the Constitution of the State (in effect Jan. 1, 1880 but now modified) provided: ~— an 144 VALUATION, DEPRECIATION AND THE RATE-BASE ‘““ The use of all water now appropriated, or that may here- after be appropriated, for sale, rental, or distribution, is hereby declared to be a public use and subject to the regulation and control of the State, in the manner to be prescribed by law; provided, that the rates or compensation to be collected by any person, company or corporation in this State for the use of water supplied to any city and county, or city or town, or the inhabi- tants thereof, shall be fixed annually by the Board of Super- visors, or City and County, or City or Town Council, or other governing body of such city and county, or city or town, by ordinance or otherwise, in the manner that other ordinances or legislative acts or resolutions are passed by such body, and shall continue in force for one year and no longer. Such ordinances or resolutions shall be passed in the month of February of each year, and take effect on the first day of July thereafter. (Art. XIV, Sec. 1) (1880) “The right to collect rates or compensation for the use of water supplied to any county, city and county, or town, or the inhabitants thereof, is a franchise, and cannot be exercised ex- cept by authority of and in the manner prescribed by law.” (Art. XIV, Sec. 2) (1880) “In any city where there are no public works owned and controlled by the municipality, for supplying the same with water or artificial light, any individual, or any company duly incorporated for such purpose, under and by authority of the laws of this State, shall under the direction of the Superinten- dent of Streets, or other officer in control thereof, and under such general regulations as the municipality may prescribe for damages and indemnity for damages, have the privilege of using the public streets and thoroughfares thereof, and of laying down pipes and conduits therein, and connection therewith as far as may be necessary for introducing into and supplying such city and its inhabitants either with gas light or other illuminating light, or with fresh water for domestic and all other purposes, upon the condition that the municipal government shall have the right to regulate the charge thereof.” (Art. XI, Sec. 19) (1884) San Francisco Charter Provisions relating to Rates. — The Charter of the City and County of San Francisco (in effect January 8, 19oo) mentions, among the powers of the Supervi- SOIS: THE FIXING OF RATES ‘5 “To fix and determine by ordinance in the month of F ebruary of each year, to take effect on the first day of July thereafter, the rates of compensation to be collected by any persons, com- pany or corporation in the City and County, for the use of water, heat, light or power, supplied to the City and County or to the inhabitants thereof, and to prescribe the quality of the service.” The enforcement of such laws as these has, at times, proven embarrassing to the public service corporations, and has given rise to charges of corruption, to wrangling and to litigation, unfortunate alike for the corporations and for the public. The remedy has been sought in national and state control, this con- trol being exercised through National and State Commissions. The Interstate Commerce Act. — The Interstate Commerce Act in line with this idea was approved on F ebruary 4, 1887. The purpose of this Act may be stated as follows: “ The principal objects of the Interstate Commerce Act were to secure just and reasonable charges for transportation, to pro- hibit unjust discrimination in the rendition of like services under similar circumstances and conditions ; to prevent undue or un- reasonable preferences to persons, corporations or localities; to inhibit greater compensation for a shorter than for a longer distance over the same line; and to abolish combinations for the pooling of freight.” (Interstate Commerce Commission vs. Baltimore & Ohio Railroad Co., etc., 145 U. S. 263.) Public Service Control in Massachusetts. — The creation of a Board of Railway Commissioners in Massachusetts in the early sixties may be noted. A Gas and Electric Light Commission followed in 1885. The Board of Highway Commissioners in that State controls the Telegraph and Telephone Companies. Public Service Control in California. — The Constitution of California, which went into effect on Jan. 1, 1880, contained a provision for a Railroad Commission. But its powers were lim- ited and its work was not effective. By an amendment to the Constitution in 1911 the powers of the Commission were more clearly defined and its work speedily met with deserved approval. By further amendment the powers of the Railroad Commission were extended (Mar. 28, 1911) to all other public utilities so Is: 146 VALUATION, DEPRECIATION AND THE RATE-BASE that the Railroad Commission of California is now in effect a public service commission. Sec. 23 of Art XII of the California Constitution now pro- vides: “ Every private corporation, and every individual or associa- tion of individuals, owning, operating, managing or controlling any commercial railroad, inter-urban railroad, street railroad, canal, pipe line, plant or equipment, or any part of such railroad, canal, pipe line, plant or equipment, within this State, for the transportation or conveyance of passengers or express matter, or freight of any kind, including crude oil, or for the transmission of telephone or telegraph messages, or for the production, gen- eration, transmission, delivery or furnishing of heat, light, water or power or for the furnishing of storage or wharfage facilities, either directly or indirectly, to or for the public, and every common carrier is hereby declared to be a public utility subject to such control and regulation by the Railroad Commission as may be provided by the Legislature, and every class of private corporations, individuals or association of individuals hereafter declared by the Legislature to be public utilities shall likewise be subject to such control and regulation. The Railroad Com- mission shall have and exercise such power and jurisdiction to supervise and regulate public utilities, in the State of Califor- nia, and to fix the rates to be charged for commodities furnished, or services rendered by public utilities as shall be conferred upon it by the Legislature, and the right of the Legislature to confer powers upon the Railroad Commission respecting public utilities is hereby declared to be plenary and to be unlimited by any provision of this Constitution.” The California Public Utilities Act by an amendment in effect August 10, 1913, provides: “ The Term ‘ public utility,” when used in this act, includes every common carrier, pipe line corporation, gas corporation, electrical corporation, telephone corporation, telegraph corpora- tion, water corporation, wharfinger and warehouseman, where the service is performed for, or the commodity delivered to, the public or any portion thereof. The term ‘ public or any portion thereof,’ as herein used, means the public generally, or any lim- ited portion of the public including a person, private corpora- tion, municipality or other political subdivision of the state, for THE FIXING OF RATES 147% which the service is performed or to which the commodity is delivered, and whenever any common carrier, pipe line corpora- tion, gas corporation, electrical corporation, telephone corpora- tion, telegraph corporation, water corporation, wharfinger or warehouseman performs a service or delivers a commodity to the public or any portion thereof for which any compensation or payment whatsoever is received, such common carrier, pipe-line corporation, gas corporation, electrical corporation, telephone corporation, telegraph corporation, water corporation, wharfinger or warehouseman is hereby declared to be a public utility subject to the jurisdiction, control and regulation of the commission and the provisions of this act. F urthermore, when any person or cor- poration performs any service or delivers any commodity to any person or persons, private corporation or corporations, munici- pality or other political subdivision of the state, which in turn either directly or indirectly, mediately or immediately, perform such service or deliver such commodity to or for the public or some portion thereof, such person or persons, private corpora- tion or corporations and each thereof is hereby declared to be a public utility and to be subject to the jurisdiction, control and regulation of the commission and to the provisions of this act.” Public Service Control in New York. — In New York there has been for many years a Railroad Commission. In r1go3 a Commission was established for the contro] of gas and electric corporations. In 1907 these commissions were superseded by two public service commissions, which were not however given control over water companies. Public Service Control in Wisconsin. — In Wisconsin, too, the need for regulation of transportation rates first found expression in the creation of a railroad commission and, as in the case of California, the powers of this Commission were subsequently extended so that it is now a public service commission. This Commission exercises the same control over municipally owned utilities as over those which are privately owned. It has accom- plished much of the pioneer work in standardizing methods of procedure and its work is of great value in establishing the fun- damental principles of valuation as a basis for the fixing of rates. Public Service Control in Other States, — Many other states have public service commissions or railroad commissions with 148 VALUATION, DEPRECIATION AND THE RATE-BASE duties and powers of a public service commission. Georgia, Ore- gon, Nebraska, Oklahoma, Maryland, Colorado, Florida, Illinois, Indiana, Iowa, Maine, Missouri, Pennsylvania, Rhode Island, South Carolina, Vermont and other states started off with a railroad commission. Arizona, Kansas, Nevada, New Jersey, New Hampshire and Oklahoma have their public service com- missions more or less liberally endowed with powers of regula- tion and control. Supreme Court of Wisconsin on the Powers of the Railroad Commission. — All the powers which a public service commis- sion has are conferred upon it directly by the people or by legislative enactment. Its function is to make administrative regulations. Its powers are not legislative. On this point the Supreme Court of Wisconsin says (Minn. St. Paul and Sault Ste Marie Ry. Co. vs. Railroad Com. of Wis., 136 Wis. 146): “ The division of the governmental powers into executive, legislative and judicial, while of great importance in the creation or organization of a State, and form the viewpoint of institu- tional law and otherwise, is not an exact classification. No such exact delimitation of governmental powers is possible. In the process of enacting a law there is frequently necessary the pre- liminary determination of a fact or a group of facts by the Legislature, and it is well settled that the Legislature may de- clare the general rule of law to be in force and take effect upon the subsequent establishment of the facts necessary to make it operative or to call for its application. . . . The Legislature may delegate any power, not legislative, which it may itself rightfully exercise. This power to ascertain facts is such a power as may be delegated. . . . This law established, and thenceforth assumes the existence of rates, charges, classifica- tions and services, discoverable by investigation but undisclosed, which are exactly reasonable and just. It commits to the Rail- road Commission the duty to ascertain and disclose that par- ticular rate, charge, classification or service. The law intends that there is only one rate charge or service that is reasonable and just. When the order of the Commission is set aside by the Court, it is because this reasonable and just rate, charge, classifi- cation or service has not yet been correctly ascertained. When the order of the Commission has been rescinded or changed by THE FIXING OF RATES 29) the Commission because of the changed conditions it is because there is a new reasonable rate to be ascertained and disclosed, applicable to such new conditions and fixed by force of law immediately when the new conditions came into existence. But the theory and the mandate of the law is that this point is always discoverable although not always discovered. Until it is discovered and made known the former rates and service pre- vail. The order of the Commission is prima facie evidence that the rate, charge or service found and fixed by it is the particular rate, charge or service declared by the Legislature in general terms to be lawful and to be in force. If jt were conceded that the Commission had power or discretion to fix one of several rates, either of which would be just and reasonable, it would be hard to say that this was not a delegation of pure legislative power to the Commission. But the theory of this law is to dele- gate to the Commission the power to ascertain facts and to make mere administrative regulations. “ The notion that commissions of this kind should be closely restricted by the courts, and that justice in our day can be had only in courts, is not conducive to the best results. Justice dwells with us as with the fathers; it is not exclusively the attribute of any office or class, it responds more rapidly to confidence than to criticism, and there is no reason why the members of the great Railroad Commission of this State should not develop and es- tablish a system of rules and precedents as wise and beneficent within their sphere of action as those established by the early common-law judges. We find the statute well framed to bring this about.” Competition in the Public Service. — Before the advantage of cooperation and combination leading to monopolistic control was fully realized by the owners of business ventures, it was common belief that free and unrestricted competition should be encouraged and would result in permanent advantage to the public. The fallacy of this view when large public service con- cerns are involved is now generally recognized. The competi- tion in the case of such concerns may result in a momentary lessening of rates but in the long run the rate-payer or the security holder will be the sufferer. The temporary advantages may be- come a permanent burden. TAC 150 VALUATION, DEPRECIATION AND THE RATE-BASE Cotperation Between the Public and the Owner. — The treat- ment of the public service corporation should be such as to en- courage the undertaking of other public service enterprises. It should not be a hard and fast rule that a fixed rate of return will be allowed in all cases. The owner should feel that good man- agement will be rewarded. There is perhaps no better way of securing the desired hearty and cordial cooperation between the owner of the utility and the public than by the introduction of a system of profit sharing. This has been done with apparently great success in Chicago and other cities where revenue in excess of an agreed interest return on an appraisal of street car lines is divided on a reasonable basis between the city and the owner. So, too, in Boston, for every decrease of 5 cents per 1ooo cubic feet in the charge for gas the Gas Company is permitted to increase its dividend rate one per cent. The consumer benefits by the lower rate, the Gas Company by the larger dividend. Attitude of the Public Service Commissions. — Public ser- vice commissions were not created to assume an attitude hostile to the public service corporations. While they must protect the public against excessive charges for the service rendered and must see to it that there will be no discrimination against in- dividuals, they are likewise charged with the duty of allowing the corporations to do business on a fair basis. It must not be expected, however, that mistakes will not be made. As the records to date are read, such mistakes will be found in both directions. On the whole the attempt to be fair is generally recognized and the confidence of the people in their public ser- vice commissions is growing from day to day. The Rate-Base Net Earnings as a Basis of Value. — When there is no com- petition and no restriction by law or otherwise upon the charges which may be made by public utilities for commodities furnished or for service rendered, it is safe to assume that these charges will be fixed on the broad principle of “ all the traffic will bear.” This does not mean all that the rate-payer would be willing to THE FIXING OF RATES C1 pay rather than to be deprived of the commodity or of the ser- vice, but that amount which the owner finds to be best adapted to maintain and increase his aggregate profits. He will in deter- mining this amount give consideration to all elements of cost, to his investment, to the hazards of the business, to the possible profitable extension of his business, to the value of the service and to profit. When rates are thus established by an owner, the net earnings bear no definite or fixed relation to the invest- ment and the value of the business is to be determined from a consideration of the present and prospective net earnings and of those elements which determine the permanency of the business. In such a case, in other words, it is proper to capi- talize assured net earnings to determine value. When value thus ascertained is in excess of cost, the excess represents profit and such excess has been all too frequently used as a basis for “ watering” stock and for over-bonding. Not only has this been the case, but, by ignoring depreciation, or by making inadequate provision for the replacement of worn-out parts, it has sometimes been possible to make the net earnings appear greater than they actually were, and thus to further swell the apparent though, in part, fictitious value. It is fundamentally sound policy to encourage the develop- ment of the natural resources of any country, state or region by permitting those who establish public utilities to earn a rea- sonable profit on the investment made for the benefit of the public, and to earn a fair interest rate, provided that the invest- ment has been wisely made. The Public Utility Affects the Value of Other Property. — No necessary public utility can be established without at once adding to the value of all real property in the district which it serves. The profit resulting from the establishment of the utility is general. No water-supply system can be put in to serve a municipality, no work for the improvement of a water-supply, such as high pressure fire protection can be added to the system without adding value to vacant lots as well as to those already built upon. Value is added when gas and electricity are brought ig: 152 VALUATION, DEPRECIATION AND THE RATE-BASE within reach, when streets are improved, when sewers are built, when tunnels or bridges for better intercommunication are con- structed. The addition of this value cannot always be imme- diately capitalized but it is nevertheless an asset and should not be entirely lost sight of when rates are to be fixed. This point is here brought out in order that the reasonable- ness of allowing the owner of the public utility a fair profit in addition to ordinary interest on his investment may be realized. Public Contribution to the Revenue of Public Utilities. — The owner of real estate or other property even when not served by the utility, may reasonably be required to make a direct contri- bution toward its earnings. Not all of the revenue should, in other words, come from the rate-payers. It is frequently prac- ticable to secure a contribution from the property owner who is not a rate-payer by establishing a high rate for the service rendered to the public and thereby reducing the rate for the service to the rate-payer, or by a remission of local taxes in whole or in part, or by granting a bonus when a new installa- tion is involved. When an effort was made some years ago by a rival telephone company to secure permission to operate in San Francisco, the inducement of free service for all city departments was held out. The advisability of accepting the offer of the outside com- pany was passed upon by the author, who was at that time City Engineer of San Francisco, and the disadvantage of com- petition in the telephone service was pointed out. The new company did not acquire the requested privilege at that time, though it did so under a later administration. The acceptance of the offer to render service free to the City, while attractive, was unfair to the rate-payer who is thereby made to carry, not only the full burden entailed by the telephone service of which a part should be carried by the vacant lot, but also the additional amount which is saved to the City by free service. While it would be correct in principle and economically sound to let a suitable part of the revenue of every public utility be provided by a general tax, the application of this principle is THE FIXING OF RATES og not as simple nor as easy as appears at first view. The main difficulty lies in the fact that tax rates are already high and that the layman sees the force of the argument that the payment for the individual service rendered should be measured by the cost of the service. It is convenient to ignore the unearned increment that goes to the parties who are not served by the utility and it has become Customary to ignore the same, conse- quently, the practice of letting the rate-payer carry the full burden may be expected to continue with only rare exceptions. Cost of Rendering the Service as a Modifier of Rates. — In the case of the service rendered by certain utilities special effort is made to determine the cost of serving various classes of cus- tomers in order that the charge for the service may bear some direct relation to the cost of rendering the service in each class. This may be unwise. The prime consideration is what should the rate-payer in each class be asked to pay when his ability to pay is weighed against that of the rate-payers in other classes. Perhaps the establishment of class service is not always the best procedure, but it is legitimate and at present apparently the only practicable way of conducting certain business enterprises. There is no intent to find fault with the system except only to say that, if cost to serve the individual rate-payer were made the criterion of the charge for the service, there would be practi- cally as many rates as there are rate-payers. In the application of the principle, therefore, whether always sound or not, it has become customary to classify the service and within the estab- lished classes to make the charge uniform. Consideration is to be given, then, when rates are to be fixed, not alone to the total amount of the earnings, but also to their distribution to various classes of consumers. This is a subject which will not be taken up in this volume, in which the problem under discussion is concerned with aggregate earnings and not with the distribution thereof to the individual rate-payer. Deficient Earnings in Early Years. — N early every public utility begins operating at a loss. There may be a number of years during which the earnings will not be sufficient to cover IQ” 154 VALUATION, DEPRECIATION AND THE RATE-BASE ordinary operating expenses (including depreciation) and these years are generally followed by others in which the return is not commensurate with what the investment should earn. The deficiency in the earnings of the early years in the case of any legitimate public utility should be made good to its owner in some way at some time. This may be done by treating any ascertainable deficiency in the earnings as a permanent invest- ment representing cost of establishing the business or by mak- ing suitable provision to amortize it in a reasonable time. When, therefore, the appraisal of a rate-base or the fixing of rates for a long-established public utility is in question, it should be as- sumed to be quite as likely that past history will show a defi- ciency as that it will show an excess of earnings over what should be considered a reasonable return. It follows that past history relating to insufficient earnings should be brought under review and that there may be cases in which the contrary opinion of the U. S. Supreme Court, as expressed in the case of Knoxville vs. Knoxville Water Company (212 U. S., p. 14) (29 Sup. Ct. Rep., p. 148), does not strictly apply. In this case, quoted at greater length on p. 134, the Court says: “ Tf, however, a company fails to perform this plain duty and to exact sufficient returns to keep the investment unimpaired, whether this is the result of unwarranted dividends upon over- issues of securities, or of omission to exact proper prices for the output, the fault is its own.” The omission to exact prices for the output that would keep the investment unimpaired may be due to the fact that the service rates necessary to accomplish this would have been greater than the service would bear. The failure to secure ade- quate earnings is not always the fault of the owner of the prop- erty. It may even be the deliberate program to let the ample returns of future years make good the early deficiency as, for ex- ample, when the Unlimited Life Method of procedure is adopted. In the Kennebec Water District Case (97 Maine 185; 54 Atlantic 6) the Court in its instructions to the appraisers of the properties of the Maine Water Co. said: THE FIXING OF RATES 3 “ The actual rates which may have been charged heretofore, and the actual earnings, are both admissible and material in determining the value of the plant. The value of the evidence, however, will depend upon whether the appraisers shall find that the rates charged have been reasonable.” The Basis of the Calculation when Rates are to be Fixed. — Enough has been said to show that, when an appraisal is to be made as a basis for establishing the rates to be charged for the commodity or the service output of a public utility, something else is needed besides value. The starting point in the last analysis is not the value of the property, but the amount of the legitimate investment necessary to establish the business sup- plemented by the volume of the business transacted. The legitimate investment is not necessarily the actual cost of con- structing and developing the property and bringing it to a paying basis, but it is the amount which may reasonably be assumed to have been properly and legitimately invested in the public ser- vice. This amount may for convenience be called the * rate- base,” and as here defined is to be distinguished from “ value.” It is to be understood that this definition of the rate-base is more or less academic and has not yet obtained general recog- nition. The ordinary practice has been to attempt to make “ present value ” the basis of the calculation when fixing rates. The endeavor to do this, with inclusion in the amount on which an interest return is to be computed, of certain elements of value which can have no existence unless created by adequate earnings, has met with only indifferent success and has led the rate-fixing bodies into much confusion from which there now appears to be a strong desire to escape. The “ rate-base,” as thus defined, may include some or all of the cost of establishing and developing the business. It would be unwise to lay down an inflexible rule that the entire cost of establishing and developing the business should be included in the rate-base because any such rule would result in placing a premium upon inefficient management. The aim should be to include a reasonable allowance for this item which in one case I5¢C 156 VALUATION, DEPRECIATION AND THE RATE-BASE may be determined from cost records while in other cases it may have to be estimated from less dependable data and as- sumptions. The rate-base should be made the basis of the calculation. The earnings present and prospective should be adequate to yield a proper return on the rate-base and they should more- over also be adequate to create some value in addition thereto which will be compensation to the owner for having established and for managing the utility and may be in lieu of appreciation which under this method of procedure would not always appear in the rate-base. The Effect of a Bonus upon the Rate-base. — Attention has already been called to the fact that when the owner has received a bonus, in order to encourage construction, the original cost to him is reduced by the amount of the bonus. This circum- stance should not be overlooked in determining the rate-base. How the bonus paid to the owner may affect the rate-base can be made clear by an illustration. The case can readily be conceived of an irrigation system constructed at an average cost of $30 per acre. The right to take water from this canal system is made the matter of contract, each land owner who takes water for a given tract paying to the canal owner a bonus of $20 per acre. When all the land within the area to be served by the canal has acquired the right to take water from the canal, the owner will be out of pocket only $10 per acre and not $30. Full justice will be done to both the owner and to the irrigator if the rate-base in this case be estimated at $10 and not at $30 per acre, due consideration being given to all other elements that should be included in the rate-base. Two Procedures may be Followed in Determining a Rate- base. — There arc two standpoints from which the matter of determining the rate-base may be approached and the proce- dure in the matter of making an appraisal which is to serve as a basis for fixing rates will vary according to the standpoint taken. In the one case, the investment is regarded as unimpaired, and no deduction is made for amortization or depreciation, and THE FIXING OF RATES iy the amount of the investment properly determined is made the rate-base. In the other case the amounts earned as depreciation and re- maining unexpended are considered as being applied to the re- tirement of capital, in which event the rate-base is the properly invested capital less the accrued depreciation (it being assumed that current depreciation has actually at all times been earned and collected). These two views have led to various procedures when the fair earnings of a public utility are to be determined — these will be given further attention in following pages. The late Commissioner J. W. Eshleman, in writing the deci- sion of the Railroad Commission of California in the matter of the application of James A. Murray and Edward Fletcher for an increase of water rates in the county of San Diego, Cal., says: “My own view is that the nearest and fairest approximation which may be made to a correct © value ’ upon which a public utility shall be allowed to earn is the amount of the investment wisely made, and this view is not at all in conflict with the position of the courts in this regard.” The Commissioner as appears from this statement recognizes the desirability of mak- ing ““ investment ” and not “ value ” the basis of the calculation but apparently feels the necessity of reconciling the use of the amount invested with the decisions of the courts, which, for the most part, still hold “ value ” to be the starting point. Factors to be Considered in Establishing the Rate-base. — In determining what should be regarded as the legitimate rea- sonable investment in any public utility to serve as a basis for computing rates, some consideration may be given to certain factors which aid in determining what the value of the property resulting from net earnings should be. Such factors are the capitalization of the business enterprise, the original cost, the cost of reproduction new, the depreciated or present value, the taxation value and the reasonable charge for the service rendered. There should be taken into account, too, in the broad problem of determining net earnings, the past history, id I 58 VALUATION, DEPRECIATION AND THE RATE-BASE sacrifices made by the owners to establish the business, finan- cial aid by the public, the quality of the service, the cost of like service rendered elsewhere and other similar matters. The aim will be to establish, first, a rate-base on which the owner is to get a fair interest return and, second, to ascertain what the net earnings should be in addition to this return to create such a value as will be fair to both the owner and to the public. Comments on Base Physical Cost by the Wisconsin Railroad Commission. — Referring to the use of the original cost of the properties of the LaCrosse Gas and Electric Co. as the basis of the calculation the Wisconsin Railroad Commission states (Wis. R. C. R., Vol. 2, p. 16) in substance that it is quite likely that, because of local conditions or the manner in which the plants have been acquired, the cost of these plants to the present owner is considerably higher than the figures given (cost of reproduction). Owing to progress in the electrical field most plants have had to be rebuilt or re-equipped. The cost to pres- ent owners of such plants is likely therefore to be much greater than either the cost of the original plant or the cost of repro- duction new. The Commission in the Antigo Water Case (Wis. B.C. R., Vol. 3, p. 631) says: “ The original cost, the cost of reproduction new and the present value bear a very close relation to the physical prop- erty of the plants and are therefore of the greatest importance in determining the value of the same. As to which one of these three elements is of the greatest importance in fixing this value, is a matter that largely depends upon the circum- stances in each case and may also be more or less affected by the purposes for which the valuation is intended. . . . No matter what the differences between these three cost values may amount to, each one of these items constitutes evidence of the true value and should therefore be carefully considered.” The Commission also says that the burden of unreasonably high construction cost should not be charged to the rate- payers. THE FIXING OF RATES , Comments on Value and Depreciation by the Wisconsin Railroad Commission. — Substantial recognition of the principle that present value is not a proper rate-base is found in the findings of the Wisconsin Railroad Commission in the case of the Superior Commercial Club vs. Duluth Street Railway Co. (Wis. R. C. R,, 1912, Vol. 11, p. 1 to 21). The Commission makes the following statement: “ A valuation of the physical property of the Superior division of the company as of June 30, 1911, showed a cost new of $717,538 and a present value of $487,236. When the present value of the physical property of 1911 is increased by the pres- ent value of that part of the property located in Duluth, but chargeable to Superior and which cannot greatly exceed $70,000, when additions of about $10,000 are made for working capital and when proper allowances for depreciation and going value are added, it will be found that the total amount does not quite reach the cost value new. In fact, it does not greatly exceed $700,000. This sum finds support in the cost of reproduction of the plant and the business as well as in their original cost. . . . As under normal conditions investors are entitled to have their property or investment kept intact, it follows that the amounts, which have been properly set aside for such pur- poses or for depreciation, in accordance with the provisions of the law and the rules of the Commission, should in the instant case be included in the amount on which returns are allowed. On the other hand amounts earned for depreciation but with- drawn or used for other purposes than provided by law should not be so included.” Again in the case of the Stevens Point Lighting Co. relating to service and rates the Commission says (Wis. R. C. R., Vol. 14, p- 364): ““ The failure of a utility to make allowance for depreciation if the earnings have been sufficient is tantamount to a with- drawal of capital from the business and the cost of reproduction new must be diminished in determining the fair value upon which the reasonable return allowed is to be based when an adequate reserve for depreciation has not been provided. The utility is, however, entitled to earn an amount sufficient to off- set future depreciation.” 150 160 VALUATION, DEPRECIATION AND THE RATE-BASE Other Factors Affecting Rates. — While it is important to establish a rate-base whenever rates are to be fixed, there may be cases in which other circumstances are of equal moment with the rate-base as a guide to the allowable earnings. It may happen that the public service requires only a small invest- ment of capital compared with the volume of the business that is transacted, and it may then be more desirable and equitable to bring the compensation of the owner into some relation to the volume of business transacted rather than to the capital which is invested in the business. The case may readily be conceived of a concern such as an express company which rents its office facilities and operates under contract with railroad and steamship companies and which, outside of its trucks and other vehicles for the local distribution of the parcels entrusted to its care, has made no investment of any moment. It would be vain in such a case to attempt a regulation of rates based solely upon a fair return upon the invested capital. The whole field must be brought into view. The volume of business transacted, and the value that would be created if earnings are allowed which exceed, in some definite fashion, the cost of conducting the business, should receive due consideration. If earnings are thus allowed which exceed the cost of operation by 10 to 15 per cent, this would not seem un- reasonable unless the resulting rates are, in fact, more than the traffic can or should bear. Compensation for Hazard. — The risk of loss assumed by the owner when he undertakes the development of a public service enterprise is an element for consideration when a limit is to be set upon the allowable earnings. This fact is generally recog- nized. The compensation for this risk should be determined on the basis of the risk that may be justly contemplated by those who enter upon similar ventures under like conditions. This principle is clearly set forth by the Supreme Judicial Court of Maine in its instructions to the appraisers of the Maine Water Company’s properties in the Kennebec Water District Case (97 Maine 185; 54 Atlantic 6): THE FIXING OF RATES 2 “ The reasonableness of the rate may also be affected, for a time, by the degree of hazard to which the original enterprise was naturally subjected; that is, such hazard only as may have been justly contemplated by those who made the original in- vestment, but not unforeseen or emergent risks. And such allowance may be made as is demanded by an ample and fair public policy. If allowance be sought on account of this ele- ment, it would be permissible at the same time to inquire to what extent the company has already received income at rates in excess of what would otherwise be reasonable, and thus has already received compensation for this hazard.” Earnings in Relation to the Rate-base and to the Volume of Business. — If it can be accomplished without making rates un- reasonable, there should be not only an interest allowance upon the rate-base equal to the current rate on money invested in industrial and related enterprises, preferably about 6 per cent per annum, but also some additional allowance, perhaps gener- ally less than 5 per cent, unless conditions are unusual, as a reasonable participation in the general prosperity of the com- munity (this in lieu of appreciation), plus some percentage al- lowance on the reasonable cost of operation (not including in this cost the interest on the invested capital). This latter allowance should, perhaps, be so graded that it will be small when the investment is large in relation to cost of operation and that it will approach 10 per cent or, in some cases, be even more, if the investment in relation to the cost of operation is small. The objection which may be urged to such an arrange- ment, that it will make it to the interest of the owner to inflate the cost of operation, is to be weighed against the danger of discouraging investment in public utilities if any less liberal policy is pursued. Moreover, under the control which is now exercised over the public utility by the public service commis- sions, this objection will lose much of the force which it might otherwise have. The capitalization of the percentage allowance on the cost of operation, plus any other allowance (except amortization) in excess of a fair interest on the investment, will represent the 163 162 VALUATION, DEPRECIATION AND THE RATE-BASE sum of intangible values, in excess, of course, of such portions thereof as have found a place in the rate-base. The Franchise Value and the Rate-base. — While recognizing that earnings may be so high that a franchise has value the Wisconsin Railroad Commission places itself squarely on record against the inclusion of such value in the value which is made the basis for fixing rates. The Commission in the Antigo Water Co. case (Wis. R. C. R., Vol. 3, p. 727) says in substance that though earnings may be high enough to yield a surplus that may be made the basis for determining a franchise value, properly sub- ject to taxation, this fact by no means implies that these earn- ings or any value based thereon should also be the basis for rate-fixing. Taxation, according to the Commission, is based on the ability to pay. Rates should be based on the cost of service (measured by expenses) including a fair return on the investment. The Commission apparently recognizes, what the author endeavors to make clear, that taxation value” and therefore “ market value ” really depends on the earnings and therefore, too, upon the rates. In the case of the City of Appleton vs. Appleton Waterworks Co. the Commission again says (Wis. R. C. R., Vol. 5, p. 282) that in estimating capital upon which return is to be made the franchise has no value, because franchise value is produced by the rates charged. It is proper, however, to tax the company on its franchise value which would be paid for if the business were sold. The Commission in the case of the State Journal Printing Co. os. Madison Gas and Eleciric Co. (Wis. R. C. R., Vol. 4, p. 586) declares franchises to be monopolistic in their nature. They belong to the community. Their value has been created by the growth of population and by economic and social devel- opments rather than by individual effort. Belonging to the public, the right of control and of the disposal thereof also rests in the community. Under these conditions according to the Commission, there appear to be no good grounds upon which the value of exclusive privileges of this kind should become private property. CHAPTER IX POSSIBLE PROCEDURES WHEN THE RATES FOR A PUBLIC SERVICE ARE TO BE FIXED The Prime Consideration. — When a method of procedure is to be selected under which the necessary earnings of a public utility are to be determined, the first consideration will be the fairness of this procedure both to the rate-payer and to the owner of the utility. Although there are various methods of procedure which have been adopted throughout the country, and which may be shown to be correct under various restric- tions as to application and under the assumption that their application is continuous from the beginning, it will not do to accept any particular one as equitable or advisable in every case. It is elsewhere shown that when capital is assumed to be retired at a rate which keeps pace with theoretical depreciation, serious consideration must be given to the departure of actual life from the probable life of the various parts of the utility which have a limited period of serviceability. It is made clear that a proper accounting system must be adhered to and that a change of procedure may result to the disadvantage either of the owner or of the rate-payer. The Preferable Method of Procedure. — Apart from the fair- ness which is essential, the adopted method of procedure should not impose unnecessary burdens upon either party. That method which requires the least earnings in the early years of their life will be preferable in the case of newly established enterprises. In the case of properties that have been long in use, past history must be taken into account, as it will not do to arbitrarily assume that the business has been a profitable one from the beginning. The presumption should rather be the 1F- “V3 1604 VALUATION, DEPRECIATION AND THE RATE-BASE other way; the probability that there were losses in the early years should not be overlooked. The various methods of procedure have had their origin in the various plans that have been adopted for making provision for amortization of capital and the replacement or renewal of discarded articles. When the distinction between amortization and the replacement requirements is disregarded, such methods of procedure as the Straight Line Method and Equal Annual Payment Method are the result. When amortization is treated as a matter apart, such methods as the Sinking Fund Method and the Unlimited Life Method are the natural outcome. The Sinking Fund Method. — The ¢ Sinking Fund Method ” of making appraisals and of determining necessary earnings is a method under which the annual allowance for replacements is uniform in amount. This replacement allowance (frequently referred to as depreciation) is the annuity which, together with compound interest at the rate of the net earnings of the prop- erty, will during the probable life of an article amount to its replacement cost. The replacement, it is assumed, is to be accomplished at the end of the probable life of that article. There is no repayment of capital. The investment remains undimin- ished. This is, therefore, a 100 per cent valuation method.* The amount which goes into the replacement fund does not retire capital. It generally remains in the business and may be assumed to earn the same amount as any other capital used in the business. Nevertheless, it is held by some authorities that this fund should be treated as though invested in absolutely safe securities and that, therefore, the interest rate introduced into the calculation should be about 4 per cent. But whether the fund be invested in outside securities or in the business, it is a fund which should be separately accounted for. Its earnings are earnings of the business and make the amount which must be collected from the rate-payer correspondingly less. When the fund remains in the business, it should be charged with the regular interest rate of return and this amount of the earnings * Trans. Am. Soc. C. E., Vol. LXXV, p. 828. POSSIBLE PROCEDURES IN FIXING RATES 325 should be added to the fund and will not be available for dis- tribution as profit. To illustrate — if the investment is $1,000,000 and out of surplus earnings $100,000 are invested in betterments, the total investment becomes $1,100,000 of which $100,000 is due to the replacement fund. If the net earnings are 6 per cent or in the aggregate $66,000 per annum, only $60,000 of this will be avail- able for distribution to the owners and the other $6000 must be added to the replacement fund. Equal Annual Payment Method. — The “ Equal Annual Pay- ment Method,” as described in the report of the American Society of Civil Engineers’ Special Committee on Valuation, presented to the Annual Meeting of January 21, 1914, refers to a method which makes the annual depreciation, or amortization increment an amount increasing, from year to year according to a definite law. The annual depreciation is estimated by sinking fund methods. It is equal to the annuity which will retire the remaining value in the remnant of the original prob- able life term and, when added to the interest on the remaining value (uniformity of interest rates being assumed), the sum will be uniform from year to year throughout the probable life term. When depreciation allowances computed by this method are actually earned, they are considered as refunds of invested capi- tal. The remaining investment in that case decreases as the earned depreciation decreased by expenditures for replacements accrues. Depreciation earnings may be regarded as being thus applied to retire capital, but this method of estimating what should be earned from year to year is undesirable, because it involves frequent, elaborate and cumbersome re-estimates of remaining value, requiring the service of experts, while as usually applied, it is identical in results with the Sinking Fund Method, which has the advantage of simplicity. The Straight Line Method. — The Straight Line Method ” of estimating the annual depreciation or the annual amortiza- tion installment is that method which makes the annual amorti- zation of capital uniform throughout the probable life of an is “ayn 166 VALUATION, DEPRECIATION AND THE RATE-BASE article. The annual amortization installment is estimated from the original cost of an article less residual value and its probable life, by dividing the cost less residual value by the number of years of probable life. This method, like any other amortiza- tion method, is justified on the theory of the immediate applica- tion of the annual depreciation installment to the retirement of capital. In this respect both this method and the Equal Annual Payment Method differ essentially from the Sinking Fund Method and from the Unlimited Life Method, under neither of which any retirement of invested capital is taken into consideration. Unlimited Life Method. — The “ Unlimited Life Method ” of procedure, when rates are to be fixed, is justified by the fact that public utilities may generally be regarded as having per- petual life and that, ordinarily, capital need not be retired un- less the property is to be purchased. A public service property taken in its entirety may be treated, therefore, as though it had unlimited life. The property is kept in good condition by the repair of its parts and by replacements, as these parts become useless and have to be discarded. No part of the investment, if there be unlimited life, need be returned to the owner, but as the plant grows old and one part after another has to be replaced, he must be allowed to recover in the earnings the cost of each article as replaced. It is on this principle that many complex and, particularly, publicly owned properties are operated. In the early years of the life of a property made up of many parts, such as rails and ties, the replacement requirements will be small. As the property acquires age, the replacements — pro- vided that extensions are relatively unimportant and negligible in comparison with the extent of the property under considera- tion — will gradually increase to nearly the amount indicated by the Straight Line Method. The departure from this amount will be dependent upon the annual extensions of the system in relation to the entire investment. There will be ultimate agree- ment between the replacement requirement and the amount estimated by the Straight Line Method if the plant is one that has ceased to grow. The valuation for rate-fixing purposes POSSIBLE PROCEDURES IN FIXING RATES z under the Unlimited Life Method of procedure will be the amount of the investment without deduction of depreciation, and the replacement requirements, until definitely ascertained by experience, will be approximated from the estimated cost of effecting the replacements, with due consideration of the age and expectancy and the probable life new of the individual parts of which the property is made up. Sinking Fund Method Illustrated. — Some of the principles that govern the establishment of rates may be made clear by the use of an illustration. An electric generator with a 20-year life will serve the purpose. Assume, in the absence of any accepted method of procedure, that remaining value is deter- mined by deducting from cost the accrued depreciation esti- mated by compound interest sinking fund methods. Suppose the generator to be a part of a light and power system and suppose, further, that it has reached the last year of its useful life and will have no scrap value. A purchaser will value the generator, if he estimates interest on a 6 per cent per annum basis, at about 8.23 per cent of its original value and this js all that he will pay for the same. He takes upon himself, when he buys the light and power plant, an obligation to replace the generator with a new one at the end of another year. He must then renew the investment represented by this article. The obligation which he voluntarily takes upon himself at the time of his purchase to replace the generator in a year is 91.77 per cent of the cost of a new generator. At the end of the life of the generator, he will have received in his earnings the last increment of the original investment in the generator, or 8.23 per cent of its cost, and he will meet his obligation to continue in business by acquiring a new generator and thereby renewing the full original investment in this particular appliance. It makes no difference whether there is only one generator, or whether there are 20 in use. The principle is always the same. Moreover in such a simple case as that of 20 generators of all possible ages, each with a useful life of exactly 20 years, the accrued obligation to replace these generators when worn 16% 168 VALUATION, DEPRECIATION AND THE RATE-BASE out (6 per cent per annum interest being again used for purposes of illustration) will be 38 per cent as shown by the formula on page 93. In other words, the remaining value of the 20 generators (cost less depreciation, as ordinarily noted) will be about 62 per cent. No purchaser would include the 20 generators in his valuation of the property at more than 62 per cent of their aggregate cost; but he would, nevertheless, and with reason, expect to be allowed to earn interest on 100 per cent of their cost new, claiming rightfully that he is entitled to the same rate of income return on unexpended annual replacement incre- ments as he is entitled to earn on the rest of his invested capital. He will justify this claim by pointing out that the earnings on any accumulated replacement fund are not available for any other use than the replacement of worn-out property; that such earnings do not, therefore, represent income; and that it is for this reason he is entitled to have the aggregate annual replace- ment allowance, together with accumulated interest, treated as interest-bearing capital. California Law Restrictions upon the Depreciation Fund. — In this connection attention may be called to the laws of Cali- fornia (Statutes of 1grz, First Extra Session, Ch. 14, Sec. 49), which prescribes that the Railroad Commission (having the duties of a public service commission): “ may from time to time ascertain and determine and by order fix the proper and adequate rates of depreciation of the several classes of property of each public service utility. Each public service utility shall conform its depreciation accounts to the rates, so ascertained, determined and fixed, and shall set aside the moneys so provided for out of earnings, and carry the same in a depreciation fund, and expend such fund only for such purposes and under such rules and regulations, both as to the original expenditures and subsequent replacement as the Commission may prescribe. The income upon investments of moneys in such fund shall likewise be carried in such fund.” It is here apparently recognized that the depreciation fund should be used for the sole purpose of replacing worn-out parts POSSIBLE PROCEDURES IN FIXING RATES =] and that in regulating rates, consideration need be given only to the amount of capital reasonably and properly invested without any deduction for depreciation. The earnings, in other words, to be adequate, must include at least operating expenses of every character, a proper allow- ance for present and prospective replacements (so-called current depreciation) and a reasonable income computed at the proper interest rate on the invested capital. Comparison of Sinking Fund and Equal Annual Payment Methods. — Enough has already been said to show that the so-called Sinking Fund Method of procedure, when no distinc- tion is made between actual and probable life, is exactly equiv- alent in its results to the Equal Annual Payment Method. The former, in which the rate-base is roo per cent of the invest- ment, involves a single computation of the annuity which at compound interest will amount in the probable life term to the capital invested in any article. The latter, under which accrued depreciation is deducted from the investment, requires a re-estimate of the current amortization (depreciation) incre- ment from year to year and a new annual estimate of accrued depreciation. Amount of Amortization or Amount in the Replacement Fund. — If under any method of procedure the owner of a plant of numerous parts and all possible ages is required to place all sums earned as “ depreciation ” or earned to meet “replacement requirements ” into a special fund, and the depreciation or re- placement requirement has been actually earned from the begin- ning, the amount of amortization accomplished out of such a fund or the theoretical balance on hand, after meeting all current replacement requirements, will be as follows: Under the Straight Line Method of estimating amortization for old plants of full growth, the theoretical accumulation should be 50 per cent of the investment in perishable property — this accumulation is independent of the interest rate and this fund’s earnings are of no concern to the rate-payer. Under the method of estimating the “accrued obligation to 167 170 VALUATION, DEPRECIATION AND THE RATE-BASE replace ” by the Sinking Fund Method, for old plants, with interest at 6 per cent and the hypothesis that actual life will conform to probable life, the theoretical accrued obligation to replace or what is equivalent, the theoretical accumulation in the fund as shown in Table 2, page 94, will be: Per cent For articles having 5 year life, about 38 6¢ [44 10 [44 4 40 fC ¢ 20 < ¢¢ 38 [14 6 30 (44 £¢ 34 14 (4 40 ¢ i’ fx cc SL ED {¢ € . 3 [49 ¢ 60 né © 5 These percentages apply strictly, of course, only to cases in which the age of the plant is greater than the life of its parts. They indicate the extent, however, to which an accumulating replacement or depreciation fund may exceed the demands upon it. In some measure, approximating this unexpended surplus, such a fund is available for outside investments. Interest on the same, when it represents the obligation to replace, must be earned by the owner for the benefit of the plant, consequently, it makes no difference to what purpose he applies this surplus, provided only that ample assurance remains that replacements will actually be made when necessary. Interest is to be added to this fund even when the same is invested in the plant and by the amount of such interest, the earnings will not be available for distribution as profit. When the capital is being amortized, the accumulations in the amortization fund are the absolute property of the owner. They are not subject to control by the rate-payer, yet, here, too, proper assurance may be expected that replacements will be duly made and it would not be unreasonable to expect an adequate special fund to be maintained to meet emergencies. Soundness of 100 Per Cent Appraisal as Rate-base. — In order to show beyond all question that the method of valuing at the investment without deduction of the depreciation in fix- POSSIBLE PROCEDURES IN FIXING RATES 11 ing rates, under continuous application from the beginning, is correct and proper, an electric generator with a life of 20 years, which has served 15 years, may again be taken as a basis for an illustration. The usual assumption is made, for the purpose of this illus- tration, that there is no change in the cost of this article during its life, that it has no scrap value and that it will go out of service when exactly 20 years old. Interest in this illustration is taken at 6 per cent per annum. By the “ Equal Annual Payment Method ” (correct if applied from the day the article went into use and if there were, in fact, agreement between actual and probable life): Original IVESUMENT. . [..\.\ us «oer $100.00 Lie (nem hr rr 20 years Time in service... uh alas alle 15 years Remaining life...) ooo vinoa ls 5 years Accrued depreciation (amortization to date)............... 963.27 Remaining value.................... .. Bese. ua. Be3iize Interest on remaining value. . ....... a $2.20 Annual depreciation or annual amortization increment for sixteer FOAL . vir vas eS 6.52 Required net earnings. .......... es +. 2 5.72 In this case the depreciation in the 16th year is that amount which, invested annually at 6 per cent, will retire the remaining value $36.73 in the remaining 5 years of life. By the “Sinking Fund Method ” (correct under continuous application from the beginning and agreement between actual and probable life) the computation is as follows: Permanent investment. ......................... $100 Life (ew). i a - 20 years Time fn service... ... i. vd. 2ars Remaining life....... ........ 0.8 ars Interest on the investment............. Ee al 36. OO Annual depreciation or annual replacement increment for any Required net earnings. ....... 2 cess srs a sa $8.72 While it can be shown that for each year the earnings should be $8.72 on $100 of original capital investment, a new cal- ey 172 VALUATION, DEPRECIATION AND THE RATE-BASE culation is necessary, as already stated, for each perishable article and for each year under the Equal Annual Payment Method, while for the more rational Sinking Fund Method, a single simple calculation suffices for each group of articles of the same probable life term. For comparison the application of the other methods of pro- cedure to the same generator may be of interest. By the “ Straight Line Method ” (correct under continuous application from the beginning and agreement between actual and probable life) there will be: Original investment. ........vovusvareseecernaeasese + °D Life (new)... ik ial aah ol te aloe eels |] 20 YEATES IIE IT) SCTVACE le is - «in ula elalrela ia i 5 ale ule losis BESES VERTS Remaining dife...h L000 LG LAL LL CLR IEEDS Years Accrued depreciation (amortization to dafe).ln hl 4g Remaining value... chin Ue LL iio 25 Interest on remaining value. ................ cee ov. $1.50 Annual depreciation or amortization increment for sixteenth Year. LiL ni as ce vv v.04 io MS5. OO Required net earnings. ......-- -. Ls eixla ia i waa ts MIR GO. SO By the “ Unlimited Life Method ”’ on the assumption that there is only a single generator and that the annual replacement increment is estimated by the compound interest annuity method: Original investment .........coeverenenrneeceeeenenn. wi Lie (NeW) dual aie cles sins oaisiainis sols laiel, LJE20 YEOTS TIME A SCEVICE. Jina v4 =n lee asl alates a years Remaining life... ...coeeun.enatn ; years Interest on the investment. .............. « ceeieeaeeie cnn $6.00 Annual replacement increment. .............ceeeeee 2.72 Required net earnings. .. oo. vxvocesvesncnsrasesencnananee $8.72 The foregoing comparisons, as above stated, are based on the assumption, which can never be fully realized, that there is ab- solute agreement between the actual and the probable life of each article. Effect of Departure of Actual Life from Probable Life. — To illustrate the application of the various methods of procedure with some regard to the fact that of many articles having the BIO Rr POSSIBLE PROCEDURES IN FIXING RATES 173 same probable life when new, some will actually serve a shorter and others a longer time, let it be assumed that a group of articles is under consideration whose average life, and therefore whose probable life, is 5 years. Let it be further assumed in order to give definiteness to the problem that there will go out of use and be replaced 4 per cent of these articles at the end of the first year; 8 per cent at the end of the second year; 12 per cent at the end of the third year; 16 per cent at the end of the fourth year; 20 per cent at the end of the fifth year; 16 per cent at the end of the sixth year; 12 per cent at the end of the seventh year; 8 per cent at the end of the eighth year; and 4 per cent at the end of the ninth year. This hypothesis of failures has already been referred to and its basis explained in Chapter VI. Two courses are open. Either the allowance for amortization or so-called depreciation is extended for each article throughout the period of its probable life, regardless of whether the article fails early or survives, or, as an alternative, the annual allowance of amortization or depre- ciation is continued throughout actual life and stops with the failure of each article. Each article which takes the place of another which is discarded is supposed to receive the same consideration and the same treatment in the accounts as an original article. The result is shown in Table 10. Explanation of Table 10. — In Table 10 there is noted for the Equal Annual Payment Method in column A the amortization requirement computed from amortization tables, entering the tables not with age, but with probable life new less the expect- ancy; and in column B, the amortization requirement as deter- mined from Table 20 by taking the difference between the re- maining value at the beginning of successive years, giving, as explained, consideration to the new articles introduced each year to replace discarded articles. When amortization of capital con- tinues during the actual life of each article, terminating when the article goes out of use, the Equal Annual Payment Method is no longer, strictly speaking, an equal annual payment method 174 VALUATION, DEPRECIATION AND THE RATE-BASE because the interest on the remaining value plus the annual de- preciation is no longer constant in amount. TABLE 10. COMPARISON OF RESULTS TaE SINKING FUND, EQUAL ANNUAL PAYMENT AND UNLIMITED LIFE METHODS When consideration is given to the requirements for periods determined either by probable life or by the actual life of articles. FivE-YEAR PROBABLE LIFE. NUMEROUS ARTICLES Failures as noted in the text — 6 per cent interest . Unlimited em driest Sinking Fund Method. Equal Annual Payment Method. | On Eh d ii iti : 2 = 100 of orig. Tonti ; pe invest. = Wh Amort. fr Replace- beginning 2 Lin Si during __ mentre of year prob, lic Mhactal Sie prob. life. A | Z quirement $100.00 $17.74 $17.74 $17.74 $17.74 $15.10 $ 4.00 2 4.00 18.45 T7.74 19.51 18.66 17.46 8.16 HER 19.89 17.7400 022.13 19.3% 19.63 | 12.65 1 12.65 22.13 17.74 25.72 20.09 17.30 17.64 . 17.64 25.26 17.94 30.40 19.89 10.40 ' 23.34 ) 23.34 11.66 17.74 12.63 19.64 20.30 21.97 ‘ 21.97 0 14.85 17.74 16.32 19.69 20.60 21.16 : 21.16 17.37 17.74 10.11 19.34 2I.IO 20.54 2) 20.54 18.58 17-74 20.98 | 20.41 19.70 19.73 10 19.73 19.95 17:94 21.46 20.44 18.30 18.31 For comparison with the Sinking Fund Method and the Equal Annual Payment Method, there are noted in the last column of Table 10 the annual replacement requirements, which are the amounts to be provided if the Unlimited Life Method of pro- cedure is adopted. By the plan of amortizing the cost of each article or for providing a fund for its replacement in the exact term of its probable life, there will be a rapid accumulation in the replacement or depreciation fund, or a rapid amortization of capital in the early years, which is an undesirable feature of operation. To find the necessary earnings by each of the several methods, interest on the capital remaining as an investment is to be added to the amounts noted in the table. POSSIBLE PROCEDURES IN FIXING RATES «3 Amortization During the Probable Life Term. — When only a single article is involved, as in the case of a steamboat, the disadvantage of adopting the plan of amortizing its cost or of providing a replacement fund in the exact term of its probable life is apparent. The steamboat may meet with an accident in the early years of its life. If it does and is replaced with a new one, amortization of the remaining value of the first steam- boat plus the amortization of the cost of the new steamboat will be necessary. The burden will fall upon the rate-payer. Under the alternative plan of continuing a uniform annual amortization allowance during the actual term of the steamboat’s service there will be no effect apparent upon the required earnings by an early failure of the steamboat. The loss of the first steam- boat will fall upon the owner, but, if rates are equitably estab- lished, the loss will be made good to him in the course of time by reason of the survival of other steamboats and the continu- ance of the depreciation or amortization allowance after original cost has been amortized. The wise plan is the one in which there is the least disturb- ance of the rates and in which, so far as may be, the required earnings will be least in the early years. The Book Accounts Under Various Methods of Procedure. — The book accounts relating to the foregoing tabular illustration when numerous articles all with a probable life new of 5 years are involved would show the following for each $100 of original investment: a. Sinking Fund Method with a replacement allowance for the term of the probable life of each article, regardless of the time of its actual failure. (Each article which replaces a fail- ing article is here treated as a new article.) Dr. side of Ledger Cr. side of Ledger 1st yr. To depr. or amort. allowance $17.74 By renewals $4.00 2nd yr. To int. on balance $13.74 0.82 To depr. or amort. allowance 18.45 By renewals 8.16 3rd =. To int. on balance 24.85 1.49 To depr. or amort. allowance 19.89 By renewals 12.65 4th yr. To int. on balance 33.58 2.01 To depr. or amort. allowance 22.13 By renewals 17.64 IJK 176 VALUATION, DEPRECIATION AND THE RATE-BASE sth yr. To int. on balance 40.08 2.40 To depr. or amort. allowance 25.26 By renewals 23-34 6th To int. on balance 44.40 2.67 To depr. or amort. allowance 11.66 By renewals 21.97 7 To int. on balance 36.76 2.21 To depr. or amort. allowance 14.85 By renewals 21.16 8t:- To int. on balance 32.66 1.96 To depr. or amort. allowance 17.07 By renewals 20. 54 oth yr. To int. on balance 3I.25 1.88 To depr. or amort. allowance 18.58 By renewals 19.73 1oth yr. To int. on balance 31.08 1.92 To depr. or amort. allowance 19.95 By renewals 18.31 Totals $203.04 $167.50 Balance _ 35.54 At the end of the tenth year the amount in the depreciation fund would be $35.54 for each $100 of original investment. b. The Sinking Fund Method accounts, if the replacement re- quirement or depreciation were estimated during the actual life of each article, would be charged, at the end of each year with $17.74 and interest on the annual balance. It would be given credit for $4.00 renewals the first year, $8.16 the second year; $12.65 the third year and so on. Dr. side of Ledger Cr. side of Ledger 1st yr. To repl. allowance $17.74 By renewals $4.00 2nd yr. To int. on $13.74 0.82 To repl. allowance 17.74 By renewals 8.16 ard =. Toimt.on $24.14 1.45 To repl. allowance 17.74 By renewals 12.65 4th =. To int. on $30.68 1.84 To repl. allowance 17.74 By renewals 17.64 sth -—= Toint.on $32.62 1.96 To repl. allowance 17.74 By renewals 23.34 6th vr. To int. on $28.98 1.74 To repl. allowance 17-74 By renewals 21.07 7th v=. Toint. on $26.49 1.50 To repl. allowance 17.74 By renewals 21.16 8th v= Toint.on $24.66 1.48 To repl. allowance 17.74 By renewals 20. 54 oth yr. To int. on $23.34 1.40 To repl. allowance 17-74 By renewals 19.73 1oth yr. To int.on $22.75 1.37 To repl. allowance 17.74 By renewals 18.31 Totals $191.05 $167. 50 Balance 23.55 POSSIBLE PROCEDURES IN FIXING RATES 177 At the end of the tenth year there would be in the replacement fund $23.55 for each $100 of original investment. ¢. The amortization and replacement account in the case of the Equal Annual Payment Method, if amortization be allowed during the probable life term of each article, regardless of whether the article fails early or survives, would be about as follows: (Every article which replaces another is here treated as a new article.) Dr. side of Ledger Cr. side of Ledger 1st yr. To allowance for amort. and repl. $17.74 By renewals $4.00 2nd yr. To allowance for amort. and repl. 19.5I By renewals 8.16 3rd yr. To allowance for amort. and repl. 22.1 3 By renewals 12.63 4th yr. To allowance for amort. and repl. 25.72 By renewals 17.64 sth yr. To allowance for amort. and repl. LY ) By renewals 23.34 Totals $115.50 $55.79 Balance NO $59.71 Balance $50.71 6th yr. To allowance for amort. and rep. 12.63 By renewals $21.97 7th yr. To allowance for amort. and repl. 16.32 By renewals 21.16 8th yr. To allowance for amort. and repl. 19.11 By renewals 20.54 oth yr. To allowance for amort. and repl. 20.98 By renewals 19.73 roth yr. To allowance for amort. and repl. 21.46 By renewals 18.31 Totals $150. 21 $101.71 Balance _ 48.50 The amount available for amortization at the end of the fifth year should be according to this account about $50.71 for each $100 of original investment and $48. 50 at the end of the tenth year. In actual bookkeeping the account would have been balanced at the end of each year. The remaining investment, or the present value, is shown by this account to have been $40.29 on each $100 at the end of the fifth year and $51.60 at the end of the tenth year. The large reduction of capital which results from this method of applying the Equal Annual Pay- ment Method shows its undesirability. d. The amortization and replacement account in the case of the Equal Annual Payment Method, if amortization be esti- mated during the actual life of each article (plan A, Table 10) and the balance is applied at the end of each year to retire capital, would show: 178 VALUATION, DEPRECIATION AND THE RATE-BASE Dr. side of Ledger Cr. side of Ledger ist yr. To allowance for amort. and repl. $17.74 By renewals $4.00 2nd yr. To allowance for amort. and repl. 18.66 By renewals 8.16 3rd yr. To allowance for amort. and repl. 19.31 By renewals 12.65 4th yr. To allowance for amort. and repl. 20.09 By renewals 17.64 sth yr. To allowance for amort. and repl. 19.89 By renewals ~~ 23.34 Totals $95. 69 $65.79 Balance 19.90 Balance $19.00 6th yr. To allowance for amort. and repl. 19.64 By renewals $21.97 7th yr. To allowance for amort. and repl. 19.69 By renewals 21.16 8th yr. To allowance for amort. and repl. 19.34 By renewals 20. 54 oth yr. To allowance for amort. and repl. 20.41 By renewals 10.73 roth yr. To allowance for amort. and repl. 20.44 By renewals 18.31 Totals $110.42 $101.71 Balance 17.7% In actual bookkeeping the account would have been balanced every year. The amount available for amortization at the end of the fifth year should be about $19.90 and at the end of the tenth year about $17.71. e. The amortization and replacement account, in the case of the Equal Annual Payment Method, if amortization be esti- mated during the actual life of each article (plan B, Table 10) and the balance is applied at the end of each year to retire capital, would show: Dr. side of Ledger Cr. side of Ledger 1st yr. To allowance for amort. and repl. $15.10 By renewals $4.00 2nd yr. To allowance for amort. and repl. 17.46 By renewals 8.16 3rd yr. To allowance for amort. and repl. 19.65 By renewals 12.05 4th yr. To allowance for amort. and repl. 17.30 By renewals 17.64 sth yr. To allowance for amort. and repl. 0.40 By renewals 23.34 Totals $88.91 $65. 70 Balance o 23.12 By Balance $23.12 6th yr. To allowance for amort. and repl. $20.30 By renewals = $21.97 7th yr. To allowance for amort. and repl. 20.60 By renewals 21.16 8th yr. To allowance for amort. and repl. 21.10 By renewals 20. 54 oth yr. To allowance for amort. and repl. 19.70 By renewals 19.73 roth yr. To allowance for amort. and repl. 18.30 By renewals 18.31 Totals $122.82 $101.71 Balance 21.11 POSSIBLE PROCEDURES IN FIXING RATES 1 3 The amount available for amortization at the end of the fifth year is shown by this account to be $23.12 for each $100 of original investment and $21.11 at the end of the tenth year. J. The amortization and replacement account in the case of the Straight Line Method (5-year probable life) would show the following: Dr. side of Ledger Cr. side of Ledger 1st yr. To allowance for amort. and repl. $20.00 By renewals $4.00 2nd yr. To allowance for amort. and repl. 20.00 By renewals 8.16 ard yr. To allowance for amort. and repl. 20.00 By renewals 12.635 4th yr. To allowance for amort. and repl. 20.00 By renewals 17.64 sth yr. To allowance for amort. and repl 20.00 By renewals 23.34 Sub-Totals $100.00 $05. 79 Balance 34.21 By Balance $34.21 6th yr. To allowance for amort. and repl. 20.00 By renewals $21.97 7th yr. To allowance for amort. and repl. 20.00 By renewals 21.16 8th yr. To allowance for amort. and repl. 20.00 By renewals 20.54 oth yr. To allowance for amort. and repl. 20.00 By renewals 19.73 1oth yr. To allowance for amort. and repl. 20.00 By renewals _ 18.31 Totals $134.21 $101. 71 Balance __ 32.50 These figures show that at the end of the fifth year about 34 per cent of the total cost of the depreciating articles would have been returned to the owner and at the end of the tenth year about 32.5 per cent. The remaining investment at 3 years would have been about 66 per cent and at the end of the tenth year about 67.5 per cent. g. The replacement account in the case of the Unlimited Life Method would show the following: Dr. side of Ledger Cr. side of Ledger 1st yr. To allowance for repl. $4.00 By renewals $4.00 2nd yr. To allowance for repl. 8.16 By renewals 8.16 3rd yr. To allowance for repl. 12.65 By renewals 12.65 4th yr. To allowance for repl. 17.64 By renewals 17.64 sth yr. To allowance for repl. 23.34 By renewals 23.34 6th yr. To allowance for repl. 21.97 By renewals 21.97 7th yr. To allowance for repl. 21.16 By renewals 21.16 8th yr. To allowance for repl. 20.54 By renewals 20.54 oth yr. To allowance for repl. 19.73 By renewals 19.73 roth yr. To allowance for repl. 18.31 By renewals 18.31 HC 180 VALUATION, DEPRECIATION AND THE RATE-BASE Theoretically there would be no accumulation in the replace- ment fund because in the case of numerous articles the annual demand on the fund would be offset by the replacement allowance. The simplicity of the Unlimited Life Method, as well as its advantage in requiring least earnings in the early years, appears from a comparison of such accounts as above presented. Before leaving this subject attention may be called to the fact that the balance which these figures show to be probable in a replacement fund under the Sinking Fund Method of pro- cedure and the amount of the amortization under the Equal Annual Payment Method do not agree with what would be found on the impossible hypothesis that all articles serve through- out their probable terms of usefulness and no longer. On this purely hypothetical assumption (see page 94) the fund should contain about 38 per cent of the cost of the depreciating articles after five years of operation (5 years probable life being here under consideration). If the various methods of procedure and fixed rules of account- ing are closely adhered to and a comparison of results be made at the end of the tenth year, numerous articles all having a probable life of 5 years being under consideration, the results in so far as the amount of amortization or the amount in the re- placement funds are concerned should be about as follows: On the hypothetical assumption of agreement between actual and probable life, and an amortization allowance estimated by com- pound interest methods, the original invest- ment should have been reduced by about. . 38 per cent By the Sinking Fund Method, if the replace- ment allowance continues during probable life, the amount in the replacement fund should be about........ . RT. ss per cent By the Sinking Fund Method, if the replace- ment allowance continues during the actual life, the amount in the replacement fund should be about... -.. hl leblesitt LL. 24 per cent POSSIBLE PROCEDURES IN FIXING RATES By the Equal Annual Payment Method, if the amortization allowance be continued during probable life, the original investment should have been reduced (so-called accrued de- preciation) by about......... _....... 48 per cent By the Equal Annual Payment Method, if the amortization allowance be continued during the actual useful life, the original invest- ment should have been reduced (so-called depreciation) as follows: a. According to the plan 4 of estimating the annual allowance by about. .... 18 per cent b. According to the plan B of estimating the annual allowance by about. .... 21 per cent By the Straight Line Method, the original in- vestment should have been reduced by ghoul..." rN - -B 33 per cent By the Unlimited Life Method there would be no reduction of the invested capital and there would theoretically be no accumula- tion in the replacement fund. Rental Value as an Aid in Determining Present Value. — Rental value is a convenient aid in forming a clear conception of present or remaining value of any item of property. Take, for example, a high-duty pump and assume that the same be rented by Smith, the owner of a water-works property, from Jones on such terms that Jones will recover the cost of the pump during its life and interest on his investment. The care and the maintenance of the pump falls upon Smith. The rental value may be so determined that as the business grows the return to Jones of capital will be increased, but ordinarily, the pump being assumed to be in full service all the time, the rental value remains uniform throughout the period that the pump renders efficient service. If the interest rate agreed upon is 6 per cent and if it be further agreed that the probable life of the pump is 25 years, Jones will expect $7.82 per annum 181 182 VALUATION, DEPRECIATION AND THE RATE-BASE throughout the probable life term of the pump for each $100 of its cost. The agreement will provide that he gets this sum annually so long as the pump remains an efficient appliance and that the payment shall cease as soon as the pump becomes use- less. The present value of this pump to Jones for each $100 of its cost, at any time of its life, will be the present value of an annuity of $7.82 for the expectancy or remaining life of the pump. This will be true if he is under no obligation to replace it and if scrap value be disregarded. When the pump is new, the probable life or expectancy is 25 years and the present value will be roo per cent. When the pump is 10 years old, its expectancy may be about 17 years and the remaining value at that time $82 for each $100 of first cost or 82 per cent. When the pump is 25 years old and still in good condition, its expectancy may be about g years and the remaining value of each $100 of original cost at that time would be the present value of an annuity of $7.82 for g years or $53 or when compared with the total original cost, 53 per cent thereof. If the pump is defective or is put out of service by some accident before it has served 25 years, Jones will be a loser. If it serves beyond the term assumed as the limit of its usefulness or beyond 25 years, Jones will be the gainer. If Jones is in the business of supplying pumps in large numbers on these terms he will find, if probable life has been correctly determined, that his capital is yielding 6 per cent per annum. Further Comparison of Methods with Tables and Diagrams. — A further comparison of the various methods of procedure which have found favor when rates for the output of public service properties are to be fixed, is given in the following pages with tables and diagrams where practicable. These comparisons are strictly theoretical and are based in each case as noted on the impossible assumption that the actual life of every item which goes to make up the property will coincide with the prob- able life of that item. The comparison nevertheless shows where these methods, if consistently applied from the beginning, would POSSIBLE PROCEDURES IN FIXING RATES 183 lead and are therefore of value to the appraiser and to the prop- erty owner, as well as to the rate-regulating authority. Tables 11 and 12 illustrate forcefully the fact that under the Equal Annual Payment Method the amount to be earned annu- ally from the beginning of operations is uniform and that under the Straight Line Method the amount of earnings should be greatest at the beginning. TABLE 11. STRAIGHT LINE METHOD (Hypothetical) Cost of plant $100. Probable life ro years. Interest 6 per cent. No distinction is made between probable and actual life. The annual amor- tization or depreciation increment is $10. Accrued depre- Present value, re- Year. ot andor dining investment Interest on rate- Ss ine zation - . . year. ginning of year. $10 $100 $6.00 $16.00 20 go 5.40 15.40 30 8o 4.80 14.80 | 40 ”"y 4.20 14.20 Cv | to 3.60 13.60 60 i 1.00 13.00 on . 2.40 12.40 so : : 1.80 11.80 : 90 24 I.20 11.20 13 100 Iv 0.60 10.60 TABLE 12. EQUAL ANNUAL PAYMENT METHOD (Hypothetical) Cost of plant $100. Probable life 10 years. Interest 6 per cent. No distinction is made between probable and actual life. Present value Annual depre- Accrued depre- ininc ip A 1 J Yer amortiation amoripaton ‘Stmentorrate. Intereston Ame amor increment. at end of year. bate &2 begins Interest. $7.59 $7.59 $100.00 $6.00 $13.59 8.04 15.63 92.41 5.55 13.59 8.53 24.15 84.37 5.06 13.59 9.04 33.19 75.85 4.55 13.59 9.58 32.77 66.81 4.01 13.59 10.15 52.92 57.24 3.43 13.59 10.76 63.68 47.08 2.83 13.59 1I.41 75.09 36.32 2.18 13.59 12.09 87.18 24.91 1.50 13.59 12.82 . 100.00 12.82 0.77 13.59 184 VALUATION, DEPRECIATION AND THE RATE-BASE The Sinking Fund Method, if correctly applied, involves, as already stated, only a one time calculation of the annual depre- ciation or replacement increment and its result agrees with that of the Equal Annual Payment Method. The Unlimited Life Method is the most flexible. It may be so applied as to give identical results with the Equal Annual Payment and the Sinking Fund Method, or it may be applied to vary somewhat therefrom so as to make the earnings require- ments least in the early years. Under the Sinking Fund Method, on the above assumption with reference to absolute agreement of actual with probable life, the annual requirement for $1oo of cost would be interest of $6 and the amortization or depreciation increment of $7.59 for each of the to years of life making a total of $13.59 for each year. Under the Unlimited Life Method, the replacement incre- ment may be estimated as in the case of the Sinking Fund Method, in which event the required annual earnings would be $13.59 or they may be graded from a smaller amount in the earlier years to a larger amount in the later years, in which event the required annual earnings would appear on an increas- ing scale. The extreme case has been assumed for the illustration of the Unlimited Life Method in Table 13, that no provision whatever is made for replacement until the article to be replaced fails. This will account for the sudden increase noted for the eleventh and twenty-first years, in each of which the replacement require- ment is increased by $100. The first of the original articles fails in the tenth year (actual life being assumed the same as the probable life), and thereafter $100 of the original investment goes out of use and has to be replaced annually until and after the twenty-first year when the annual replacement requirement is $200. POSSIBLE PROCEDURES IN FIXING RATES 183 TABLE 13. COMPARISON OF METHODS OF PROCEDURE (Hypothetical) Annual investment $100. Probable life of all parts of the property 10 years. Interest 6 per cent. No distinction is made between probable and actual life. i i - qs Unlimited Lif; “fidthod 0 Pee ELEY" Sinking Fund Method, Unlimited Lit Year. PE . Rate- Rat base be-| Required ones Required Relates Required base bel Required nk earnings. of year. earnings. of year. earnings. Sonne earnings. $100 $16.00 $100.00 $13.59 $100.00 $13.59 $100 $6.00 I90 31.40 192.41 27.17 200.00 27.17 200 12.00 270 46.20 276.78 40.76 300.00 40.76 300 18.00 | 340 60.40 352.63 54.35 400.00 54.35 400 24.00 400 74.00 419.44 67.94 500.00 67.94 3500 30.00 450 87.00 476.68 81.53 600.00 81.53 600 36.00 490 99.40 523.76 95.12 700 .00 95.12 700 42.00 520 111.20 560.08 108.69 800.00 108.69 | 800 48.00 540 122.40 584.99 122.28 900.00 122.28 goo 54.00 95 550 133.00 597.81 135.87 1000.00 135.87 1000 60.00 rT 650 149.00 697.81 149.46 1100.00 149.46 1100 166.00 : 740 164.40 790.22 163.05 1200.00 163.05 1200 172.00 Lj 820 179.20 874.59 176.63 1300.00 176.63 1300 178.00 t 8go 193.40 950.44 190.22 I400.00 190.22 1400 184.00 | 950 207.00 1017.25 203.81 1500.00 203.81 13500 190.00 Pa I000 220.00 1074.49 217.40 1600.00 217.40 1600 196.00 1040 232.40 IIII.57 230.99 1700.00 230.99 1700 202.00 : 1070 244.20 1147.89 244.56 1800.00 244.56 1800 208.00 19 1090 255.40 1172.80 258.15 1900.00 258.15 1900 214.00 20 I100 266.00 1185.62 271.74 2000.00 271.74 2000 220.00 21 | 1190 282.00 1278.03 285.33 2100.00 285.33 » 2100 ' 326.00 One more comparison may be of interest as shown in Table 14. TABLE 14. COMPARISON OF METHODS OF PROCEDURE (Hypothetical) The property is made up of numerous items of all possible ages, the combined cost of which is $100. The probable life of each item is ro years. All considerations are theoretical and no distinction is made between actual and probable life. Interest 6 per cent. The property is supposed to have reached its full growth and to be more than 10 vears old. Raledese Annual de- Le-De Interest preciation R : etka of pradize vars mtebue orreplace Cid ment. Straight line amortization method $55.00 $3.30 $10.00 $13.30 Equal annual payment amortiza- tionmethod.. ..... .. =ss" 59.78 3.59 10.00 13.59 Sinking fund replacement method 100.00 6.00 7.59 13.59 Unlimited life replacement method 100.00 | 6.00 | 10.00 : 16.00 186 VALUATION, DEPRECIATION AND THE RATE-BASE The total required earnings appear largest for the Unlimited Life Method for the reason that the required earnings in the early years of the plant’s life are supposed to have been low. When rates are to be fixed for a public service property which is long established, concerning which past records are unrelia- ble, but which is legitimate, rendering a necessary service and entitled to fair income, the question as to which method of procedure should be adopted presents itself. Let it be supposed that the records indicate a fairly normal development and growth with some years of inadequate earnings and no conclusive evidence that any part of the invested capital has been repaid, but that worn-out parts have been renewed as necessary and that the service rendered has been satisfactory. In this assumed case the application of the various methods of procedure will theoretically produce results as shown in Table 14. If any of the methods except the Unlimited Life Method be adopted, recourse will probably be had to an addition of large values for intangible elements in order that no injustice may be done to the owner of the property. In most cases the Unlimited Life Method will be indicated as most nearly equi- table. This will be yet more apparent when the effect of the non-agreement of actual with probable life upon the application of the various methods of procedure is taken into account. The comparison of results by the methods of procedure which have been under discussion has been visualized, for the special case of a single item which cost $100, in a diagram, Fig. 2. It has been assumed in the preparation of this diagram that in the application of the Unlimited Life Method to a single article the replacement requirement will be anticipated and will be estimated by the compound interest Sinking Fund Method. In the practical application of this method a close approximation of the replacement requirements is not essential because no part of the replacement increment goes to the repayment of capital. This entire increment remains in the replacement account and will be subject to being decreased or increased from time to time as this account shows to be necessary. COMPARISON OF METHODS OF PROCEEDURE Investment $100, Probable Life 10 Years Intaraat; #74 gl REIT TE wide with Probable Lis. SC. Actual Life assumed to colncide with Probable Life, aS — - —————— to 20.00 Annual Ts Debreciation 19.00 or ope Roquir 18.00 Interest shown thns, 17.00 Rauive Hoarnin F ry 16.00 - FF ="5 Bye 1 15.00 I 14.00 ne : Ee TN— Er ET. ge ¢ 120 Ge | + 1L00 Annual Amortization- Depreciation- or Replacement. . 5 1000 . ory ? = wh in 8 1 9.00 rei hed. - — i . re £4 E00 “ing-Fund-an imited-Tife-Meth~*- 7.00 LE —— _— 6.00 limited Life and Sinking Fund * 5:00 mf a—— ) 5.00 ra G A.00 | nnpat oo x Ya | : lt A n_ 3 20 7 | 100 Mawr —_—— p—— — a — Years ; Fs... g - i BT 2, Q0 “YY 188 VALUATION, DEPRECIATION AND THE RATE-BASE The Obligation to Replace. — In further substantiation of the advantage which results from use of a rate-base computed from the investment without any deduction of depreciation, attention may be called to the obligation to replace worn-out or discarded essential parts of every public utility plant which goes with the ownership thereof. It does not matter, in the case of any in- dividualized article, such as a steamboat, whether a replacement fund is being set apart to be kept inviolate and is accumu- lating interest at a rate which will bring it to the value of the steamboat in its life or whether there is no such fund. The owner of the steamboat is burdened with the obligation to re- place and this obligation is as real and as binding as though it were represented by an accumulated fund. It is optional with him whether to set apart a fund if none exists and let its earn- ings go toward a new steamboat or to simply let the obligation stand and to provide funds for the new steamboat when the old one goes out of use. To the extent of this obligation, that is, to the amount which should be in a replacement fund, any cap- ital which he commands is available for no other use than the replacement when the time comes. The interest on this fund, real or imaginary, is available for this use only and as the fund, together with the remaining physical value of the steamboat, is equal to the amount originally invested in the steamboat, it is plain that there is no need of annually drawing the dividing line between the remaining physical value and the amount which should be in the replacement fund (the so-called accrued depreciation). The remaining physical value plus the obliga- tion to replace is the invested capital on which the interest is to be computed whenever earned depreciation or replacement allowances are not regarded as amortizing capital. Period and Rate of Amortization. — When a municipality con- structs improvements under a bond issue or otherwise, suitable provision is made for the replacement of any of the worn-out parts of these improvements at the time that these parts go out of use. This is in strict conformity with the procedure under the Unlimited Life Method. But in the case of the municipal- POSSIBLE PROCEDURES IN FIXING RATES I%) ity the bond issue, if any, is also to be taken care of. The cost of the improvement is, in other words, to be distributed fairly to those that will benefit thereby. This is usually done by so fixing the term of the bonds that the cost will be distrib- uted over a sufficiently long period. of time. The determina- tion of this time period need not be in any definite relation to the life of the parts of the improvement. The improvement itself will usually be one that may be regarded as having un- limited life, such as parks, playgrounds, streets, and the like. When the term of the bonds of longest life has been fixed on the basis of the probable life of the main elements of the improve- ment, or in some other way, then a determination must be reached as to the best and most equitable rate of amortization. This amortization may take place at a uniform rate per year, bearing heavily on present day property owners — Straight Line Method. It may take place at an increasing rate per year: (a) According to the scheme outlined under the Equal Annual Payment Method. (6) According to any arbitrary scheme that will approximate the compound interest Sinking Fund Method of estimating the annual amortization increment. Or, it may be deferred for a time and then take place accord- ing to either of these methods. In the case of a public service property constructed by a municipality the amortization of capital usually begins at or soon after the acquisition of the property and in the case of a utility constructed by a private owner, the amortization of capital should begin under the Straight Line Method and the Equal Annual Payment Method at the beginning of operation, and, theoretically under the Sinking Fund Method or the Un- limited Life Method as herein fully explained, not at all in so far as rate-base determination is concerned, during the continu- ance of full private ownership. In Fig. 3 a comparison is made between the annual amortiza- tion allowance computed by the Straight Line Method and the De $ AMORTIZATION ALLOWANCE AND REPLACEMENT REQUIREMENTS. NUMEROUS ARTICLES. PROBABLE LIFE 10 YEARS. INTEREST 6 PER CENT. = , - TF - ——— TT = a be | + S814— : 3 = g 13 . 5 2 5 12} — A 1} a) | 10 : § | oF i 8k a —— oie ae 1 ‘ No. L.—Replacement requirements. +i.uy . 1+ __owth. Hailures as shown in Fig. « No. 2~Replacement requirements, Plant made up ot uniform annual additions. } Failures as shown in Fig. 1 t= No. 3~Replacement requirements. Plant of full growth, Failures estimated by the - law of probabilities. = No. 4 =Replacement requirements. Plant made up of uniform annual additions. CL m Failures estimated by the law of probabilities. fa No. 5~Amortization allowance. By the Straight-Line Method. T— No. 6—Amortization allowance. By the Equal-Annual-Payment Method. All articles of ) the same age and renewals assumed to be made at the end of the probable life term. : %, 'No. T—=Amortization allowance. By the Equal-Annual-Payment Method. Plant made ° : up of uniform annual additions. 1 ES SS = =r = ; , Jv. Cr de— eh : So u; ve . 5 + 5 6 7.8 007 B13 14 151617 18 19 20 21 22 2 2 2 2% 5 8 HD = Years FIG. 2. POSSIBLE PROCEDURES IN FIXING RATES z Equal Annual Payment Method and the probable annual re- placement requirements as these would be estimated by the hypotheses of failures which are referred to in Chapter VI. These curves show the wide departure of the results by the Straight Line Method and by the Equal Annual Payment Method from the actual maintenance requirement and demon- strate the desirability of proceeding under the Unlimited Life Method. The replacement requirements line represents ap- proximately the expenditures which are necessary from time to time for renewals to keep the plant in an efficient condition. The wide departure of these from the amortization lines deter- mined by the common methods of estimating depreciation are made apparent by the diagram. Further comment is hardly necessary, except to say that under the Unlimited Life Method the actual replacement requirements may be assumed to ap- proximate lines 1 and 3 for a number of articles of the same probable life in a plant of full growth and to approximate lines 2 and 4 for articles distributed in equal amounts to all possible ages (plant made up of uniform annual additions). Advantage of the Unlimited Life Method. — The comparison of methods of procedure when valuations are to be used as the basis of fixing rates may be summed up in the broad statement that a close approximation of the rate-base and of the necessary annual earnings is not possible by any method of appraisal which makes the ascertainment of accrued depreciation neces- sary; that the use of any such method requires trained experts and involves cumbersome calculations and that the uncertajn- ties of the determination of depreciation affect not alone the valuation but also the required annual earnings, while, on the other hand, the methods which make use of the amount of capital reasonably and properly invested as a rate-base are simpler and free from uncertainties except in the matter of the provision which should be made either for current depreciation under the Sinking Fund Method or for replacements under the Unlimited Life Method. The last-named method has the unique advantage of easy adaptation to any situation that may develop, IO: 192 VALUATION, DEPRECIATION AND THE RATE-BASE particularly in the matter of adjusting the amount which annu- ally goes into the replacement fund to the amount found, by actual experience, to be necessary for any special plant. This method, when selected for a new plant, also has the advantage over other methods that the required earnings in the early years are less than those estimated by any of the others. It will therefore show for the same amount of earnings a smaller annual loss or a larger annual profit in the early years than the other methods. Careful investigation might show that the Unlimited Life Method is but an old method under a new name. Industrial establishments and public utilities could without doubt be found which had been operating in substantial conformity with this procedure before they came under control of public service commissions. As the method is theoretically sound and has weighty advantages in its favor both from the standpoint of the rate-payer who wants the burden light in the early years of the utility’s life and of the owner who wants his invest- ment protected without the uncertainty and confusion of present value considerations, it seems probable that it may come into general favor despite the present-day leaning of the public service commissions and the courts in another direction. A good illustration of the difficulty of dealing with depreciat- ing property and of the undesirability of using-depreciated or remaining value of physical property in the rate-base will be found in the general principles enunciated by the Engineering Board, Division of Valuation, Interstate Commerce Commission, as submitted to the Commission in November, 1915. The Board lays down the following general rules: ‘“ When depreciating property under the several accounts, the following general rules shall apply: “1. Ordinarily, service condition per cent shall be the ratio between the remaining service life and the total service life. When the depreciation of an item of property is based upon the weighted average of the parts, the service condition of each part shall be determined by this ratio. POSSIBLE PROCEDURES IN FIXING RATES 103 “2. When a normal life for a particular item of property has been prescribed for use in determining depreciation, that life must not be departed from unless an investigation of the records of the carrier or actual inspection in the field, or the two com- bined, warrant such departure. In no case shall a remaining service life of an item of property be taken at more than the prescribed normal life. “3. When no normal life is prescribed, the total service life and remaining service life shall be determined from observation of actual conditions and the examination of records and data from reliable sources. “4. Salvage and scrap will be allowed in cases where such values actually exist. Whether allowance shall be made in a given case for salvage or scrap shall be left to the discretion of the member of the Engineering Board. If an allowance is made this fact shall in all cases be stated upon the pricing sheet even though at the time the amount of the allowance cannot be given.” The complex operations involved in applying these rules when rates are to be fixed, is in strong contrast with the simple opera- tions involved in proceeding under the Unlimited Life Method which requires no estimate of accrued depreciation. The Use of Cost Records and Cost of Reproduction New. — The purpose of the valuation of the public utility may be as already stated: a. To fix a sélling price. b. To establish a basis for an issue of securities. ¢. To establish a rate-base. d. To serve as a basis for taxation. The ascertainment of the rate-base is important. By adding to or subtracting from the same, various facts relating to values can be ascertained. It may be possible to determine cost of construction from the cost records. When this can be done, there should be a check by means of estimates of the cost of reconstruction to make certain that the actual reported cost is legitimate and that it does not include too much overhead expense nor too large expenditures for abandoned or discarded items, i.e., for items that were intended for temporary use 194 VALUATION, DEPRECIATION AND THE RATE-BASE only or that failed for any reason to fulfill their intended purpose. The cost records are not always dependable and they may have to be either entirely disregarded or largely supplemented by cost estimates. Recourse may be had in such cases to the cost of reproduction as a means of approximating the amount that may reasonably be assumed to be properly invested in the property. In making the estimate of the cost of reproduction it is not advisable to use the prices of materials and labor momentarily prevailing but rather the average for a consider- able time period, preferably about 5 years. Tabulation of Field Results. — The results of the field exami- nation, including a classified enumeration of the physical items that go to make up the property, should be tabulated in con- venient form on sheets which will show in appropriate columns information about as follows: 1. The year of installation. 2. The age. >», The probable life new. +» The expectancy or estimated remaining years of service. The cost to reconstruct, itemized. . The sub-totals of (3). 7. The contractor’s profit. 8. The totals of (6) and (7). 9. The allowance for overhead expenses. 10. The total investment, estimated as the sum of (8) and (9). 11. The residual or scrap value. 12. The present value, in per cent, computed from (3) and (4) (sometimes called condition per cent). 13. The remaining or present value in dollars (computed from (10), (11), and (12)). 14. The accrued depreciation (10) — (13). 15. The current rate of depreciation (computed from (3), (4), (10) and (11). It will be noted that according to this tabulation the cost to reconstruct and the residual or scrap value are considered when POSSIBLE PROCEDURES IN FIXING RATES 105 estimating the remaining value from the remaining years of service. Theoretically this cost of effecting the replacement should be taken into account, but it is sometimes convenient to let the original cost less residual value take its place. According to the selected method of procedure, the rate-base is computed from the tabulated information by adding the cost of establishing the business and of any other definitely ascer- tainable items of intangible character, such as the cost of the franchise, or the cost of the water-right, to the sum of items in column (10) for the Sinking Fund Method or for the Unlimi- ted Life Method of procedure; or by adding these items of intangible character to the sum of the items in column (13) when the Equal Annual Payment Method or the Straight Line Method of procedure is to be adopted. The Effect of Method of Procedure on Market Value. — When a market value of a successfully operating plant is to be fixed on the assumption that there is accrued depreciation but that there is no deferred maintenance, special consideration must be given to the method of procedure followed by the rate- fixing authority: If the Unlimited Life Method has been the procedure, the owner may not have recovered any part of the accrued depreciation in the earnings but only enough to meet replacement requirements. The market value in that event should not be less than the rate-base in column (10) determined from the investment without deduction of depreciation, plus some addition for value due to net earnings in excess of interest on the rate-base. But if, under the Unlimited Life Method or under the Sinking Fund Method of procedure, the owner has received some annual amount to forestall the replacement requirement and retains possession of whatever amount there may be in the replacement fund, the market value will be less than the amount determined on the other assumption by the amount which should theoretically be in the re- placement fund. 196 VALUATION, DEPRECIATION AND THE RATE-BASE If the Equal Annual Payment or the Straight Line Method of procedure has prevailed from the beginning and a continuance thereof is a certainty, the market value will be ascertained from the rate-base, column (13), determined from the investment less depreciation to which may be added something for value due to net earnings in excess of interest on the rate-base. Rate-base Determination. — When a rate-base is to be estab- lished, the totals of columns (ro) or (r3) will be used in com- bination with all or a part of any allowance for establishing the business and the cost of the ascertainable items of intangible character such as franchises and water-rights. The sum of these items with the total of column (10) will be the rate-base for the Unlimited Life Method and the Sinking Fund Method of procedure, and the sum of these items with the total of column (13) will be the rate-base for the Equal Annual Payment Method and the Straight Line Method of procedure. This is subject to the proviso that past history will show that accruing depre- ciation has actually been offset by earnings. Unless there has been a surplus in the earnings over a fair net return which is to be allowed on the investment, there will have been no amorti- zation, despite the fact that depreciation is obvious. The ac- crued depreciation as ascertained for any particular time does not always measure the amount of accomplished amortization. This is only the case when the allowance for depreciation, under these two methods of procedure, has actually been earned and has been collected. CHAPTER X NOTES ON THE DETERMINATION OF THE VALUE OF REAL ESTATE IN EMINENT DOMAIN PROCEED- INGS AND FOR RATE-FIXING PURPOSES Market Value of Real Estate and the Rate-base. — The market value of real estate is not to be confounded with the amount at which it is carried in the rate-base. While consider- ation must sometimes be given to market value in fixing the rate-base this is not always necessary. In fact the determina- tion of the rate-base should ordinarily be independent of market value because it is not “value” but “investment” which should be made the guide and control when rates are to be fixed. When there is uncertainty about the reasonable cost or when the first dependable valuation for rate-fixing purposes is made long after the acquisition of the property, circumstances may, however, point to market value at some agreed time as the best starting point. Market Value Defined in Court Decisions. — The U.S. Supreme Court in Boom Co. vs. Patterson (08 U.S. 403, 408; 25 L. Ed., 206) says in discussing market value: “ The inquiry in such cases must be what is the property worth in the market, viewed not merely with reference to the uses to which it is at the time applied but with reference to the uses to which it is plainly adapted; that is to say, what is it worth from its availability for valuable uses. . . . Its capa- bility of being made thus available gives it a market value which can be readily estimated.” In this case the Boom Company had brought suit in Minne- sota against Patterson, a citizen of Illinois, to condemn three islands which were desired for use in connection with a series of log booms. A verdict was returned by the jury for $9358.33, 107 198 VALUATION, DEPRECIATION AND THE RATE-BASE the value of the islands having been found to be $300 aside from any consideration of their value for boom purposes and $9058.33 due to their adaptability for this special use. The Court granted a motion for a new trial, unless the owner would consent to accept $5500. This amount was acceptable to the owner and judgment for this amount was entered in his favor. The Boom Company then appealed. The Court is perhaps a little over-confident in saying that the market value can be readily estimated. In all other respects the statement is clear and logical. The proposition is being generally recognized by the courts that, when the right of eminent domain is exercised, the ques- tion to be considered is What is the value of the property for the most advantageous uses to which it may be applied ?” See Goodin 7s. Cincinnati and Whitewater Canal Co. (18 Ohio St. 169). Young vs. Harrison (17 Ga. 30). U.S. vs. Chandler-Dunbar Water Power Co. (229 U.S. 53, 76). In this last-named case referring to the award of special value for canal and lock purposes it was said: “ The exception taken to the inclusion as an element of value of the availability of these parcels of land for lock and canal purposes must be overruled. That this land had a prospective value for the purpose of constructing a canal and lock parallel with those in use had passed beyond the region of the purely conjectural or speculative. That one or more additional parallel canals and locks would be needed to meet the increasing demands of lake traffic was an immediate probability. This land was the only land available for the purpose.” See also Shoemaker vs. U.S. (147 U.S. 282). In the case of “San Diego Land and Town Co. vs. George Neale ef al” (78 Cal. 63, 68; 30 Pac. Rep. 372; 3 L. R. A. 372) the majority of the Court says: “ The consensus of the best-considered cases is that for the purposes in hand the value to be taken is the market value, by DETERMINATION OF THE VALUE OF REAL ESTATE 100 which is undoubtedly meant, not what the owner would realize at a forced sale, but the price that he could obtain after rea- sonable and ample time, such as would ordinarily be taken by an owner to make sale of like property.’ . .. But in many instances, as in the case before us, there is no actual demand or current rate of price, either because there have been no sales of similar property, or because the particular piece is the only thing of its kind in the neighborhood, and no one has been able to use it for the purpose for which it is suitable and for which it may be highly profitable to use it. . . . From the neces- sity of the case the value must be arrived at from the opinions of well-informed persons, based upon the purposes for which the property is suitable. . . . What is done is merely to take into consideration the purposes for which the property is suit- able, as a means of ascertaining what reasonable purchasers would in all probability be willing to give for it, which, in a general sense, may be said to be the market value. And in such an inquiry it is manifest that the fact that the property has not previously been used for the purposes in question is irrelevant. The current of authority sustains these views.” What a Purchaser can Afford to Pay is not Market Value. — The value to the person who desires to acquire the property, the amount, in other words, which such person can afford to pay for it, is not its market value. In the Chandler-Dunbar Water Power Co. case above referred to the U.S. Supreme Court says (229 U.S. 80): “In a condemnation proceeding the value of the property to the Government for its particular use is not a criterion. The owner must be compensated for what is taken from him, but that is done when he is paid its fair market value for all avail able uses and purposes.” Reference may also be had to the “ Minnesota Rate Cases ” (230 U.S. 352, 451). And also to “ Five Tracts of Land in Cumberland Tp., Adams Co. Pa. v5. U.S.” (101 Fed. 661, 664). U.S. 5s. Honolulu Plantation Co. (122 Fed. 581, 584; 58 Circuit Ct. Appeals 279). The proposition that the necessity of the party desiring to 200 VALUATION, DEPRECIATION AND THE RATE-BASE acquire property by eminent domain cannot be made the measure or market value is further made clear in: Tidewater Canal Co. vs. Archer (9 Gill and J. Md. 431; 22 Md. 307). Gardner vs. Inhabitants of Brookline (127 Mass. 358). Burt vs. Wigglesworth (117 Mass. 302). Reading and Pottsville R. R. Co. vs. Balthasser (126 Pa. St. 1). Dorlan vs. East Brandywine and W.R. 46 Pa. 520. The Stockton and Copperopolis Railroad Co. vs. Vincent Galgiani (49 Cal. 130). Admissibility of Evidence Relating to Value for a Special Purpose. — The question relating to the admissibility of evi- dence bearing directly upon the value of a tract of land for reservoir purposes is quite fully discussed in Spring Valley Water Works vs. Drinkhouse (92 Cal. 528, 532; 28 Pac. Rep. 681). The view expressed in that case that value of the land for reservoir purposes might be shown appears however to be controverted in the more recent case of ‘ Sacramento Southern Railroad Co. vs. Heilbron” (156 Cal. 408) which involves the condemnation of a strip of land for railroad purposes. It was contended in this case that the rule as laid down in California permits evidence of value for the use of the land for a particular purpose in terms of money. In reference to this contention the Court says: “Tt is seen, therefore, that this Court by its latest utterances has definitely aligned itself with the great majority of the courts in holding that damages must be measured by the market value of the land at the time it is taken, that the test is not the value for a special purpose, but the fair market value of the land in view of all the purposes to which it is naturally adapted; that therefore while evidence that it is valuable’ for this or that or another purpose may always be given and should be freely received, the value in terms of money, the price, which one or another witness may think the land would bring for this or that or the other specific purpose is not admissible as an element in determining that market value.” Apparently, if this rule is strictly adhered to, it will debar DETERMINATION OF THE VALUE OF REAL ESTATE 201 from consideration the economic features which determine whether and to what extent the enterprise which involves the acquisition of the land can be made profitable. It may make it impracticable to get before the court that information which a prudent purchaser would seek when making up his mind relating to the price which he would be justified in paying. The presentation, then, in court of the evidence on which the valuation of real estate is to be based is not always a simple matter. The information wanted is the market value. The expert who testifies to value must inform himself what the value is, all purposes for which the property is suitable being taken into account. Recent court rulings appear, as above shown, to be against allowing evidence which will show the value in money for any special purpose. The local dealer in real estate who knows what sales have been made in recent years and who knows or is supposed to know the effect that the adaptability of any particular tract of land to a particular purpose has upon the market value of that land is, according to such rules of procedure, the proper value expert. His opinion relating to the money value of an island for boom purposes, or of a tract suitable for a dam site or for a reservoir site or for some other public use, is allowed to go before the judge or jury that fixes the value while the trained engineer- ing expert who may have made a careful analysis of all eco- nomic features involved but who may have no knowledge of the land value for other than one special purpose, is not allowed to testify to the value which the same property would have for the special use to which it is about to be put for the benefit of the public. He is restricted to a statement of the nature of such use and may present facts relating thereto but he must not express an opinion relating to value in terms of money unless he is in a position to say that he has given consideration to all possible uses. This rule of the courts is intended to stop the introduction of evidence too speculative and remote in character. The possi- bility of growing a special crop at an estimated annual profit 202 VALUATION, DEPRECIATION AND THE RATE-BASE per acre and a determination of the land value from the net return resulting from growing such a crop is held to be too speculative and no doubt with reason. But the court should not be denied such information as would be collected by a pru- dent purchaser who neglects no source of information when he makes up his mind what would be a reasonable price to pay for the property sought to be acquired, and there should be no testimony excluded which will throw light on the circumstances which affect or fix the market value. The favorably disposed purchaser will not restrict himself to the questioning of those only who are supposed to have general knowledge of the market value resulting from every possible use. He will rather make inquiry along every possible line and will not neglect special adaptability to a particular purpose. He will want to know the strategic value of the property when made use of for the special purpose to which it is supposed to be best adapted. If the value for such a special purpose can be ascertained with due consideration of all elements involved — adaptability to special uses with due allowance for risk, the cost of development, the cost of operation, the immediate or deferred market for the output or service and the prospective net return that will result from the use of the property, — the knowledge so obtained will aid the purchaser in reaching his conclusion concerning what a well-informed public would consider such a property worth. The amount which a particular municipality or a person who is seeking to condemn a property can afford to pay cannot, how- ever, be made the measure of the market value. This may define an upper limit. More cannot be paid by that munici- pality or person. The purchase at the full amount determined by such necessity would deprive the person, who wishes to utilize the property for the special purpose to which it is adapted, of a margin of profit to which such person is entitled. In the light of the foregoing it would seem reasonable to exclude from the consideration of the courts in condemnation proceedings evidence relating to the value expressed in money for such special uses as can be exercised only by the person who DETERMINATION OF THE VALUE OF REAL ESTATE 203 seeks to condemn the property, as in the case of land required by the Government for fortification purposes, or for a light house, but in all cases where the adaptability to the special use is recognized and the property can be applied to that use by any one suitably circumstanced, the evidence relating to the effect of such adaptability upon market value should be admissi- ble. It should be admitted even though somewhat speculative. The court must determine what weight to give to evidence of value for special uses which only remotely affect the market value. In the case of a mine on land whose surface has value for no other purpose than grazing, it will, unquestionably, be proper to ascertain the value of the land for the special purpose of min- ing. If the land has value for mining and at the same time for reservoir purposes or as a dam site, there should be no objection to a consideration of these values separately for each specific purpose, just as the same would be considered by the prudent purchaser when he makes a study of market value. The con- sideration of the effect of availability for these purposes upon market value is not to be classed as too speculative. If use for any such purpose lies in the future, due allowance must be made for the lapse of time before the ultimate value resulting from that use can be realized. If the time is uncertain and remote, the effect of the special adaptability upon market value will be small when compared with what this effect might be if immediate use were a certainty. The Value Multiple. — Other considerations, too, may limit this market value. It has, for example, become a practice, almost standard, to value rights of way for railroads and high- ways at from 1.5 to 3.0 times the market value of adjacent lands of similar character. Custom has given land required for such uses such values. There are no frequent transfers of such property as in the case of town lots or farms. Consequently the determination of the value multiple which may be regarded as generally customary in the region where a right of way is to be valued may be the best guide in fixing this value. 204 VALUATION, DEPRECIATION AND THE RATE-BASE In the case of a storage reservoir from which water may be required for an immediate high use, such as a municipal supply, and where the most profitable other use to which the reservoir land can be put is grazing, there may be a wide difference be- tween values if determined for these two purposes. And yet in such a case the fact that this particular property will sooner or later be used for water development purposes may have given it a market value that cannot be ignored when the right of eminent domain is exercised. If the public has correctly deter- mined this market value, it will lie somewhere between the value of the land for grazing and the amount which a person can afford to pay who wishes to use it for the storage of water. This does not mean that the original owner is to share the increment of special value equally with the party who is going to put the land to a special use but merely that he should share, to some extent, in the same. When the value of land for a special purpose is but little in excess of the value of the land for ordinary uses, the division of the excess might, perhaps, equitably be on the basis of an equal division between the original owner and the person who desires to acquire the land. When, however, this excess is relatively large, then it may be proper and fair to assume that the larger portion of the excess value created by the enterprise should go to the person who is ready to take the risk of a successful carry- ing out of the enterprise and this fact should not be lost sight of in estimating market value. When lands are to be taken for fortification and other similar purposes where consideration of the value expressed in money for the special purpose is not admissible, consideration should be given to the fact that the owner is forced to part with property for the good of the public and is entitled to receive for it some- what more than the price which would obtain between a willing seller and a buyer, and also to the fact that whenever the adaptability of a piece of property for a special use is gen- erally recognized, such property must have acquired greater value than other similar property not available for such use. DETERMINATION OF THE VALUE OF REAL ESTATE 205 The owner who is forced to part with his property in such cases should obtain a reasonable reward for his foresight in acquiring property of special adaptability to some important use. This reward should, whenever practicable, bear some reasonable rela- tion to the value for other uses to which the property can be put. There may be cases in which a 2 5 or 50 per cent allowance will be adequate, and there may be others in which this allowance may exceed the value for other uses two-, five- or even ten-fold, and there may also be occasional cases where a reasonable allow- ance not capable of demonstration, but yet fair when all cir- cumstances are considered may be out of all relation to value for other uses. The value multiple, as applied in any locality to railroad rights of way, and the unit price per pole of a power line are the outcome of numerous adjustments resulting from a regard to considerations as above set forth, and where such multiples are recognized, they, in turn, as already stated, have an effect upon market value of other similar easements. The Value Multiple in the Minnesota Rate-Cases. — In con- nection with the valuation of rights of way and other lands as a part of the appraisal to be taken into account when the rates of public utilities are to be fixed, the decision of the United States Supreme Court in the Minnesota Rate-Cases is of interest (230 U. S. 352; 33 Sup. Ct. 729, June 9, 1913). Justice Hughes, in writing the decision of the court, says: “ The increase sought for ° railway value’ in these cases is an increment over all outlays of the carrier and over the values of similar land in the vicinity. It is an increment which can not be referred to any known criterion, but must rest on a mere expression of judgment which finds no proper test or standard in the transactions of the business world. It is an increment which in the last analysis must rest on an estimate of the value of the railroad use as compared with other business uses, it involves an appreciation of the return from rates (when rates themselves are in dispute) and a sweeping generalization em- bracing substantially all the activities of the community. For an allowance of this character there is no warrant. 2006 VALUATION, DEPRECIATION AND THE RATE-BASE ~ “Assuming that the company is entitled to a reasonable share in the general prosperity of the communities which it serves, and thus to attribute to its property an increase in value, still the increase so allowed, apart from any improvements it may make, cannot properly extend beyond the fair average of the normal market value of land in the vicinity having a similar character. Otherwise we enter into the realm of mere conjec- ture. We, therefore, hold that it was error to base the estimates of the value of the right-of-way, yards and terminals upon the so-called ‘railway value’ of the property. The company would certainly have no ground of complaint if it were allowed a value for these lands equal to the fair average market value of similar land in the vicinity, without additions by the use of multipliers, or otherwise, to cover hypothetical outlays.” The Court in this decision may be correct in stating that market value should be determined without the use of multi- pliers. Nevertheless the fact that rights of way are actually costing from 25 to 200 per cent more than lands of similar char- acter in the same vicinity will have an unquestioned effect upon the market value of lands required for other rights of way and this effect cannot well be ignored when such lands are to be valued. Right-of-Way Value in the Georgia Railway Case. — Special Master Thorington, in the Georgia Railway Case (Central of Georgia Railway Company vs. Railroad Commission of Alabama, U.S. Dist. Court, Middle Dist. of Ala., Northern Division, Report of Wm. S. Thorington, Special Master, Jan. 8, 1912), after stating that the fact that the railroad company is com- pelled to pay in addition to its market value a further sum due to damages or because it is a railroad company making the purchase adds nothing whatever to the actual acreage value, says: “Tt is, however, proper to add that right-of-way values, including estimates for damages to property not taken, or excess cost that railroads are compelled to pay in order to acquire right-of-way property needed by them for railroad use, have been recognized by some courts, and some railroad commissions, and such excess cost was held to properly constitute part of the DETERMINATION OF THE VALUE OF REAL ESTATE 207 right-of-way valuation for rate purposes. In Shephard us. Northern Pacific Railway Co. et al 184 Fed. 763, it is said the evidence was conclusive ‘ that every railroad company is com- pelled to pay more than the normal market value of property in sales between private parties for the irregular tracts it needs and acquires for rights-of-way, yards and station grounds. . . . The measure of the value of real estate is its market value for its most available use.’ ”’ California Railroad Commission on the Right-of-Way Value. — In discussing the valuation of a railroad right of way, the California Railroad Commission says (Stockton Terminal and Eastern Railroad. Decision No. 618): “ After ascertaining the market value of the property at the time of its acquisition, the department (engineering department) also ascertained the market value as of June 30, 1912, and then multiplied that value by 1.5. This multiple was applied for the reason that the investigations of the department throughout the State show that on an average it costs one and one-half times the normal market value of abutting property to acquire rights of way in country districts by purchase or condemnation for rail- road purposes. In the absence of more definite information as affecting this particular railroad, this average multiple was used.” The same commission again refers to and approves the use of this multiple in the matter of ascertaining the value of the property of the Nevada County Narrow Gauge R.R. Co. (Decision No. 1384). CHAPTER XI THE VALUE OF A WATER-RIGHT AND OF RESERVOIR AND WATERSHED LANDS Value of Irrigation Water. — When water is used for irrigation, it makes the intense cultivation of the soil possible. It aids in producing crops which can be marketed at prices not subject to regulation except by the law of supply and demand. The availability and use of the irrigation water modify the character and increase the amount and consequently the value of the crop. These elements may thus add an increment of value to the irrigated land. Under such use the value of the water at the field and, by comparison with the cost of development, its value at its source can be determined. Water and water-rights in districts where water is used for irrigation acquire, in con- sequence, a recognized market value depending upon the appre- ciation of the land that results from irrigation, upon the value of the crops harvested and upon the cost of developing and making available the irrigation water. Payment for Water-Rights. — Ordinarily when water is to be taken from a stream for uses which decrease or otherwise modify the natural flow of the stream below the point of diver- sion, the riparian rights of lower land owners are thereby affected. The diversion cannot be made in such cases without making compensation to the riparian owners for the damage to their property which results from the taking, except, of course, when such owners sleep upon their rights, virtually admitting too small a damage to make it worth while to attempt to recover compensation. To the extent of the cost of extinguishing the riparian rights and possibly of securing other water-rights whose use is secondary or which for any reason should be merged in one holding, there 208 THE VALUE OF WATER-RIGHTS is then — a public utility being under consideration — an invest- ment to be assumed in that intangible element, the water-right. Sometimes by reason of local development and high values of riparian lands and an already established use of the stream flow for power, the cost of settling with the riparian owners and of eliminating adverse use of the water may be large. At other times the situation is such that equally good rights to use water may be secured without any cost except the cost incident to the construction of the project features and the acquisition of the necessary lands and rights of way. Water-Rights have Value. — The fact that in the first case it will have to be conceded that the owner of the public utility is entitled to have the cost of the water-richt which he holds made a part of the rate-base and that at least to the extent of cost (reasonable and actual proper cost being assumed), this water- right has or should be made to have value, justifies the public in concluding that the other water-right which has cost nothing should have a similar value, whether the same be made a part of the rate-base or not. Water-rights, then, are to be regarded as having market value. When the water is developed and is actually being put to use or when the need of putting the water to beneficial use is proximate, the existence of such value is easily recognized. When an investment has been necessary to quiet title to adverse rights and to meet other expense of securing the water-right, the propriety of including its cost in the rate- base is unquestioned. Water-right Value in the San Joaquin and Kings River Canal Case. — The Supreme Court of the United States in “ San Joaquin and Kings River Canal and Irrigation Co. vs. The County of Stanislaus” (233 U.S. 458) in reference to the fundamental principle of taking the value of water-rights into account when rates are to be fixed, says, in its decision reversing the decree of the lower court: “By a statute of March 12, 1885, the boards (of County Supervisors) are authorized to fix these rates for their several counties, but so that the returns to the parties furnishing the 20Q 210 VALUATION, DEPRECIATION AND THE RATE-BASE water shall not be less than 6 per cent upon the value of the ‘ canals, ditches, flumes, chutes, and all other property actually used and useful to the appropriation and furnishing of such water.” The rates, when fixed are binding for one year and until established anew or abrogated. . . . The question before the court has been narrowed to a single issue. If the plaintiff is entitled to 6 per cent upon its tangible property alone, it is agreed that the order must stand. But if the plaintiff has water-rights that are to be taken into account, the rates fixed will fall short of giving it what it is entitled to and must be set aside. ov “Tt is not disputed that the plaintiff has a right as against riparian proprietors to withdraw the water that it distributes through its canals. Whether the right was paid for, as the plain- tiff says, or not, it has been confirmed by prescription and is now beyond attack. It is not disputed either that if the plaintiff were the owner of riparian lands to which its water was dis- tributed it would have a property in the water that could not be taken without compensation. But it is said that as the plaintiff appropriates this water to distribution and sale it thereby dedicates it to public use under California law and so loses its private right in the same. . . . “Tt seems unreasonable to suppose that the Constitution meant that if a party instead of using the water on his own land, as he may, sees fit to distribute it to others, he loses the rights that he has bought or lawfully acquired. Recurring to the fact that in every instance only a few specified individuals get the right to a supply, and that it clearly appears from the latest statement of the Supreme Court of California (Palmer vs. Railroad Commission, Jan. 20, 1914 (47 Cal. 201)), that the water when appropriated is private property, it is unreasonable to suppose that the constitutional declaration meant to compel a gift from the former owner to the users and that in dealing with water ¢ appropriated for sale’ it means that there should be nothing to sell. (See San Diego Water Co. vs. San Diego, 118 Cal. 556, 567; 50 Pac. Rep. 633; 38 L. R. A. 460; 62 Am. St. Rep. 261; Fresno Canal and Irrigation Co. vs. Park, 129 Cal. 437, 443; 62 Pac. Rep. 87; Stanislaus Water Co. vs. Bachman, 152 Cal. 716; Leavitt vs. Lassen Irrigation Co., 157 Cal. 82.)” According to this decision the water-right must receive the same consideration as other property when rates are to be fixed. THE VALUE OF WATER-RIGHTS But the court does not attempt to settle the question relating to how a water-right is to be valued. California Railroad Commission on Water-right Values. — In the matter of valuing water-rights Commissioner Thelen, in writing the decision of the Railroad Commission of California in the San Diego case (Decision No. 146 5), sounds a note of warn- ing, when he says: “This case illustrates clearly the tremendous importance to the people of this State of the claim made by certain water com- panies and other utilities that the value which adheres to the water which they convey to their customers belongs to the utility, and that the utility is entitled to capitalize the full value of that water, entirely irrespective of its cost to the utility, and to collect a charge for water high enough to yield a return on such amount as the experts for the utility estimate to be the value of the water or of the water-right. I do not deem it necessary at this point to discuss the authorities both in the State and federal courts bearing on this question, for the reason that, according to press despatches this question has now been decided by the Supreme Court of the United States in the case of San Joaquin and Kings River Canal and Irrigation Co. vs. County of Stanislaus. The question of the amount of value to be allowed is, of course, a question of fact, the determination of which still rests in this Commission. I desire, at this time, to draw attention to the grave consequences which may follow if the theories of value of water-rights urged by various public utilities before this Commission are adopted. If it is true that the entire value of the water which a public utility secured by appropriation or otherwise belongs to the utility and that the public must pay rates on such value, it follows that, where there is only one source of water supply for a municipality, the water utility has the right to capitalize the entire life of the munici- pality. And, in any case, the utility will have the right to take for itself the entire increased value of land due to the placing thereon of this water, entirely irrespective of the fact that the people of this State have given to the utility the right to appro- priate the water and that the actual price paid for the water may have been absolutely insignificant as against the amount claimed by the utility.” 21 F 212 VALUATION, DEPRECIATION AND THE RATE-BASE The Free Grant of Water-Rights in Western States. — The right to appropriate flowing water and to put the same to bene- ficial use is given by law, in most of the Western states, to any one who will construct proper works for the development of the water and for its transmission to places of use. The water of the stream belongs to the public. The grant of the right to put it to some beneficial use is on a par with a franchise to construct a highway or to build a railroad. This right has value as a franchise has value when the earnings are sufficient to create a value. As in the case of a franchise, so in the case of the water-right, the cost thereof becomes a part of the rate- base in the event that investment and not value be made the starting point. Determination of the Water-right Value. — The courts and the rate-fixing authorities accepting the view of the public are showing a tendency to allow earnings which will give the water- right value. But neither the courts, nor public service com- missions, nor experts have yet agreed upon any method of determining the water-right value. The method of ascertaining the water-right value, in the case of water used to supply the needs of an urban population, by comparison with the ordinary cost of developing water in the same region in like amount, of like quality and under similar conditions of delivery has occasionally been applied but not with entirely satisfactory results. To illustrate, let it be assumed that the average ordinary cost of making water for domestic use available for distribution, in the region in which a water-right is to be valued, is 10 cents per 1000 gallons. This cost is here supposed to include interest on the investment and the outlay of whatever nature connected with operation. Let it be further assumed that the cost of making available the water which is to be valued has been found to be g cents per tooo gallons. It will readily be seen that under such circumstances a rise of 1 cent per rooco gallons in the average regional cost of water production would have the absurd effect of doubling the value of the water-right. F urthermore, the water-right of any supply whose cost of development exceeds THE VALUE OF WATER-RIGHTS } the average or ordinary cost would, under strict application of this test of value, prove to be a liability and not an asset. This, too, is an absurdity and condemns the method. Neither this method nor a comparison with the cost of devel- oping the next most available supply can be used as a dependable method for determining water-right values. In some sections of the country, as, for example, in portions of California, the demand for irrigation water has nearly, if not quite, reached the limit of supply. In such regions the depress- ing effect upon the value of water which results from large undeveloped available sources is no longer felt. The earnings that result from the use of the water have become the measure of its value and this value is consequently relatively high. The recognized value of water-rights in such sections has an effect upon the value of water-rights elsewhere and for uses other than irrigation. The value of water used for domestic pur- poses, similar general conditions being assumed, should not be less than that of water used for irrigation, and, if for this pur- pose it has a high value in one part of the state, — the question is asked, why not in another? Such considerations as these are not without effect upon the market value of water-rights. The fact should not be overlooked that the inclusion of a water-right value in the rate-base of a public service property, to the extent that this value exceeds cost, would be in the nature of an allowance to be regarded as part compensation for having undertaken the water development, and this compensation increment might reasonably be brought into some definite re- lation to the general cost of developing water in any region. Water-right Values in Relation to Cost of Works. — It has above been stated that the allowance of a fair reward for the successful development and beneficial use of water is legitimate. The making of a reasonable allowance, preferably based upon some definite percentage allowance on the ordinary regional cost of developing water or of developing hydro-electric power as the case may be, should be encouraged. If this principle were generally recognized, it would result in fixing with some 21: 214 VALUATION, DEPRECIATION AND THE RATE-BASE definiteness the value of water at its source and would remove much of the uncertainty that now obtains in relation to the value of water-rights. If thus determined, the value of the water-right will not be subject fo unreasonable fluctuation nor to too wide a range. Where the average regional cost of development, including everything necessary to make water available for distribution, is 1o cents per 1000 gallons and the allowance for water-rights is to be about 10 per cent of this amount, or 1 cent per tooo gallons, a change of 1 per cent in the cost of water development would only modify the value of the water at the source by 0.01 cent per 1000 gallons. A 10 per cent increase or decrease in the regional cost of development would be necessary to affect this value by o.1 cent. In other words, when, in any region, an amount is generally recognized as a proper allowance to be made for the value of the right to water at its source, or rather, when such value is to be created by a suitable allowance of earnings, this value will be fairly stable and will thereafter pass as the market value whether or not the cost of development is below or above the average. Strategic Value of Water-Rights. — In addition to the basic value at its source, a water supply may have additional value, due to an inherent advantage of quality and location and other circumstances that determine its development cost in comparison with the development cost of competing supplies. Such value is properly termed strategic value.” To illustrate, a riparian ownership which controls a water- power may be cited. The case may readily be conceived of a water-power, limited in amount, but completely controlled by the riparian owner. When such a source of power is to be valued in a region where the market for power is good, where, for example, the water-power will be delivered to a market in which it displaces a like amount of power generated by steam, the cost of the latter in comparison with the cost of the former affords a legitimate means of determining value, or, better stated, an upper limit of value. The valuation becomes a simple matter when, under such circumstances, the power is THE VALUE OF WATER-RIGHTS IS already fully developed and is in use or is being supplied to a market which takes it all. But when the power is undevel- oped, some consideration must be given to the uncertainty of achieving the expected results and due allowance must be made for the time that will have to elapse before a return from the sale of power can be realized. There will, of course, be cases in which an analysis of the cost of generating and delivering power will show the advantage to be with the power developed by steam. In such cases the hydro-electric enterprise may nevertheless be a legitimate one. It may have been initiated when the price of fuel for generating steam was such that the advantage of cost was temporarily with the water-power; or the margin in favor of the steam-power may be so small that the recognized advantage and economic value to society in conserving the energy which annually reappears in the water of the stream outweighs any financial disadvantage that may appear from a comparison with steam as a source of power, and justifies earnings that might not under other cir- cumstances be considered reasonable. Furthermore, if the market for the output of a hydro-electric installation has been established, there is no certainty that the market of a competing plant, at a different cost and sale price of power, would be the same. This is a circumstance which should be duly weighed in making the comparison. In any event, the owner of such utility should be recognized as engaged in a meritorious enterprise, deserving not only ade- quate protection, but also such reward for having developed the water-power and having made an investment for the benefit of the public as the circumstances may justify. Under this view, even when the water-right which makes the development of power possible would appear to be without market value at current fuel prices, it will be reasonable to allow to the owner, not alone a rate-base increment equal to the cost of securing the water-right, if there has been any such cost, but also, if this cost has been legitimate and reasonable, some excess allowance in the earnings, perhaps proportional to the amount of power - “ous 216 VALUATION, DEPRECIATION AND THE RATE-BASE developed rather than to the actual investment in works for developing and marketing this power. But this can only be done within limits or so long as the rates for the service remain reasonable. When it would require excessive rates, the owner must suffer the penalty of having made an untimely if not an unwise investment. Illustration of Strategic Value. — As an illustration of special water-right value the case of a water supply for general and domestic use which affords water of prime quality in limited amount may be taken, but which, when compared with other sources in use in the same community, has the advantage of proximity, elevation and reliability of service. Let it be assumed, for example, that such a supply was the first to come into use, that its water was distributed as required throughout the built-up section of a growing town, but that at length a time came when additional water had to be brought in by a second system from some remote source, and that at the time of the valuation the distributing pipes of each of the two systems cover practically the entire built-up territory. The original water-works may now be supplying only a small fraction of the aggregate amount of water being used. Undoubtedly under such circumstances, the charge for water by the two con- cerns would be the same or very nearly the same. The water from the newer works could not be supplied at a low enough rate to drive the earlier concern out of business. Without any reduction of rates, this original utility should hold its customers. There need be no falling off in the amount of water which it supplies, assumed to be the limit of its capacity. But, if, as assumed, the rates charged by the two concerns are the same, the relative amount of net earnings will be greater for the original than for the new water-works. If it costs the original concern 17.5 cents per thousand gallons to develop and market its water crop (interest on the investment included) and it is costing the new concern 20 cents to do the same, and if this larger cost has been taken into account in fixing the water rates, then the water-right and other intangible elements of value of THE VALUE OF WATER-RIGHTS 7 the original concern may reasonably be valued at ($200—$175) $25 per day per million gallons of daily delivery more than the water-right and other intangible elements of value of the new concern. This is interest on about $1 50,000, if 6 per cent per annum be made the basis of the calculation. If, in other words, rates are allowed which in the case of the new or main water-works system will create a water-right value of $50,000 per million gallons of daily delivery for the new water- works, then the value of the water-rights controlled by the orig- inal system may be about $200,000 per million gallons per day. In the case of a water-power, too, there may be a pronounced and easily recognized strategic value. The usual distinction is to be made, however, between the power development with an established market and that in which the power output is not yet in full demand. When there is no question about the market for the power, the problem will have to be solved on the basis of a comparison of the cost of utilizing the water-power as compared with power from other sources and this comparison may show more or less strategic value. Where there is no such strategic value, the water-right should be considered as a privilege similar to a franchise and should be treated accordingly. It must be remembered in this connection, however, and in any analysis of this character, that the advantage that one con- cern may have over another in the amount that net earnings exceed interest on the investment, is to be applied to all ele- ments of value in excess of the capital actually invested and can not always be assigned to water-rights alone. The Time Element in Valuing Water-Rights. — The water- right as thus far discussed is the right to put water to a continuing beneficial use without limit as to the time during which such right may be exercised. There will be cases of reversion of the right within a fixed time to the public which has made the grant thereof and there will be other cases in which a superior supply of water, later to be developed, may at some time throw the original source out of use altogether or leave it available for 21 218 VALUATION, DEPRECIATION AND THE RATE-BASE only inferior uses. Where a water-right thus limited in life is to be valued, the question not only arises as to its strategic value, but cognizance must be taken of the fact that the life of the right is limited and that it will not be a source of revenue for all time. The value of any water-right, in excess of cost, like the value of a franchise, results from earnings in excess of a fair interest on the investment. This value is, therefore, directly dependent upon the rates established by the rate-fixing bodies or, in the case of the restricted franchise, upon the rates allowed to be charged under such franchise. Large power is in the hands of the rate-fixing authorities to make or to destroy the value of water at its source and until a definite policy has been adopted by such authorities, there will continue to be more or less un- certainty relating to such value. The real value of property of this character will, for the present, remain somewhat specu- lative, particularly in cases where the development of the water or of a water-power lies in an uncertain future. This can hardly be otherwise because it is not yet certain that the tendency of today to allow something for the water-right, practically as com- pensation for making the development, will be adhered to. When it is fully understood that such an allowance will be made and when a definite limit is set to the amount of such an allowance, the valuation experts will be relieved of much em- barrassment. In the case of the established utility much of the difficulty ordinarily encountered when water-rights or franchises are to be valued as a basis for fixing rates will fall away if the method of procedure which the author recommends be followed and the invested capital and not present value be made the rate-base. Views of the Wisconsin Railroad Commission on Water- power Value. — The attitude of the Wisconsin Railroad Com- mission toward the determination of the value of a water-power by a comparison with the cost of steam power appears in the following quotation from the Commission’s decision in the case of the City of Beloit vs. Beloit Water Gas and Electric Co. (Wis. R. C. R,, Vol. 7, p- 247). THE VALUE OF WATER-RIGHTS J “It seems clear from the expression of opinions thus made and from the general practice of engineers and other men in valuing water powers that the saving effected by the use of the water power over steam power, especially, measures the values of the water power. Other methods of appraisal are used and have been mentioned by the witnesses in these proceedings, namely, rental value and market value. These latter methods, however, are quite often open to objections which destroy their reliability and it appears that it is almost always neces- sary to fall back upon the method of calculating the saving over steam power and then by capitalizing this saving, arrive at the total value of the water power. The Commission has com- mented upon this and other methods of determining the value of water power in earlier decisions: “ ‘From a purely commercial point of view this method of estimating the value of water-power rights may, in the main, be sound. But it is not so clear that this can be said for it when the question is regarded from the point of view of public policy. . . . it appears to deprive a locality of the natural advantages it might otherwise derive from being located near such water powers. If water-rights are private property under the law, then all the benefits which accrue from these rights would probably go to their private owners. If, on the other hand, water-power rights are public rights rather than private rights, then it would also seem that the public ought to share in any benefits that may be derived therefrom.” Ross ef al vs. Burk- hardt Milling and Electric Power Co. (Wis. R.C. R., Vol 3, P- 139, 147).” On the subject of water-power value the Commission says further in the case of City of Rhinelander vs. Rhinelander Lighting Co. (Wis. R. C. R., Vol. 0, P- 424): “ While calculations of the saving produced by the use of water-power instead of steam-power are of much importance in private and public undertakings in showing the financial feasi- bility of hydraulic construction, the title of the owners in utility business to the entire savings so produced has not been clearly demonstrated. Indeed, the respondent’s claims seem to go so far as to preclude the public from any share in economical methods of service and seem to place upon users of utility service the burden of maximum costs of operation.” 21C 220 VALUATION, DEPRECIATION AND THE RATE-BASE Valuation of Reservoir Sites in Relation to Water-right Value. — Passing now to the consideration of the value of reser- voir sites it may be broadly stated that, in some measure, any value thus or otherwise ascertained as appertaining to water- rights may serve as an aid in determining the value of water- shed and reservoir lands or of other lands whose use is neces- sary to make the development of the water possible. The value of such lands should not, however, be measured by the necessity of the community which needs the water. Their value is not what the community can afford to pay for them; but they have at least the value which would be deter- mined by the market for similar lands devoted to other uses. They also have an additional value due to special adaptability for use in developing a water supply. It is owing to the desirability of bringing this excess value of reservoir lands into some relation to the value of the water whose development their ownership makes possible that it may sometimes be found desirable to make the value of the water- right a measure of the excess of value (sometimes perhaps only of the upper limit of the excess) of an assembled reservoir prop- erty over the value of the land for other purposes. While this is not an established practice, it is one which appears to have some merit. It is to be understood that the excess of the value of reservoir lands over similar lands not available for reservoir use as here considered is apart from and in addition to the value of the water-right. Where the water development requires only a few acres of ground, as in the case of artesian supplies, particularly if the land remains available for other uses, or when the topographic situation is unusually favorable, a small fraction of the value of the water-right might prove to be an adequate allowance for special adaptability. Value Multiple Applied to Reservoir Lands. — In such special cases some use might be made of a value multiple such as has become customary when rights of way are to be secured for railroads and canals which are acquired usually at some increase THE VALUE OF WATER-RIGHTS over ordinary values, i.c., over the value of grazing and farm lands crossed by the railroads and canals. In the case of rail- roads the excess is generally so per cent to 200 per cent. This would probably also be a fair assumption in the case of canal rights of way. In the case of reservoirs the value of the reser- voir site as compared with that of other land of similar location and quality may go to much higher limits, but not enough data are at hand to justify an attempt to give reliable averages. Where the site is large and the use one that may not prove highly remunerative, due to remoteness of location, high cost of con- struction, scant rainfall on the watershed or other modifying causes, such as the availability of alternative reservoir sites, a bare allowance to the owner for forced abandonment of his holdings may represent the limit of what any prudent purchaser would pay. In other cases a multiple of 5 or even more may not be unreasonable. When there is also a strategic value due to relatively large earnings that will result, perhaps, from rates that have been or that must be so fixed that they will yield a fair return on some other less favorably situated property, then there will be an excess of value determinable from the large present or pro- spective earnings, and a part of this excess would naturally be allotted to the person who owns the reservoir site, the rest thereof going to the party who actually makes the water de- velopment. Certain Increments of Reservoir Land Value. — It is gener- ally recognized that the problem of valuing reservoir lands is one of the most difficult that can be presented to the engineer. None of the facts relating to the availability of a reservoir site taken by itself determines its market value. But every such fact must have some effect upon the minds of an intelligent public and therefore influences the market value. Tracts separately owned which must all be combined under one ownership to be available for use as a reservoir will have less value in separate ownership than after being assembled in one holding. The value of reservoir lands will be less if there 221 222 VALUATION, DEPRECIATION AND THE RATE-BASE are other similar reservoir properties available for alternative use. The time when the utilization of the property is a neces- sity, if this time can be definitely or even approximately fixed, will affect its market value. The value will be higher after actual construction has demonstrated that a reservoir will hold water than before. If there have been any judicial determina- tions of the market value or of the value for rate-fixing purposes of the property to be valued or of similarly situated or otherwise comparable property or if valuations thereof have been made by authorities charged with the regulation of rates or by other public authorities, all such determinations will have an effect upon the market and would be given consideration by a prudent purchaser. They are also, therefore, proper elements for con- sideration by an appraiser. The cost of the lands In a site already acquired is a factor that should be given due weight with proper allowance for the circumstances attending the pur- chases. Appreciation or depreciation that may have taken place subsequent to such purchase may also have to be given consideration. ~The value of a parcel of land which is required in connection with others to make a reservoir site available is, as above stated, worth less by itself than it will be when united with other tracts into the one holding which makes the development possible. While the individual tract is reservoir land and due to this fact may have acquired a market value in excess of the value which it would have if not located in a reservoir site, this excess value would be estimated by a prudent purchaser at less than the excess value which it acquires when brought into the same ownership as all the rest of the lands which make the storage of water possible. Atihow much less it should be valued can- not be stated with any degree of confidence for general guid- ance. And yet it may tentatively be suggested that the party who assembles the property should get the benefit of at least one half and, in many cases, much more than this proportion of the excess of its value, in the constructed reservoir, over its value for ordinary uses. THE VALUE OF WATER-RIGHTS 2:3 Effect of Various Factors on Reservoir Value. — Too much weight is sometimes attached to the influence of the cost of developing a water supply upon the market value of the land which is to be acquired to make the water development possible. Whether this cost be great or small, the custom prevails of allowing the owner of the water-works to recover, in the earn- ings, the cost of operation including replacement requirements and interest on the cost of structures. Whenever, therefore, the necessity of using the land is unquestioned, the cost of develop- ing the water should have but little effect on the market value of the reservoir land. The amount of the water made marketable is, on the other hand, a circumstance which will have greater or less effect on this value, depending upon the value which will be allowed in the rate-base for the developed water-right. There are cases, too, in which the nearness of a storage site to the place of use may give it special value, due to the fact that it adds to the reliability of the service and, finally, there will be cases in which the property to be used for water storage or already in use as a reservoir has acquired greater value for residential or other purposes than, by any fair line of reasoning, could be determined for its use in developing or storing water. When this is the case, the market value of the reservoir land (always to be distinguished from the amount at which it is included in the rate-base) is determined by the other uses to which it might be put. If such a reservoir is a necessity and no other equivalent structure can be substituted for it, the appraisal of market value would be fixed by these other uses. If on the other hand it is possible to substitute for the reservoir some other structure located elsewhere, and costing less though of equivalent service value, then in the case of the constructed reservoir the time will have come when its use should be dis- continued or in the case of the reservoir site, not yet in use, the project plans should be so modified as to eliminate the reservoir. It may be well to repeat that when dealing with water not yet developed, proper allowance must be made in all appraisals 2 ls 4 224 VALUATION, DEPRECIATION AND THE RATE-BASE of water-right and of reservoir and watershed values for the probable lapse of time before the water will actually be in use. Watershed Land Value. — When storage reservoirs for water for domestic use are involved and the value of the watershed lands is to be determined, it would be legitimate to give consid- eration to the modification of the cost of operation which might result from the ownership of these lands. When such ownership would result in safeguarding the quality of water so that filtra- tion and other treatment to make the water attractive and wholesome would become unnecessary, some light will be thrown on the value to the water works owner by the added cost that would be incurred for a purification of the supply if the water were in danger of pollution due to the use of lands in the water- shed for human habitation or for other purposes that would de- tract from the wholesomeness of the runoff waters. Considera- tion would certainly be given by a prudent purchaser who is weighing the desirability of acquiring watershed lands to this matter and, therefore, this is properly an element to be con- sidered in determining the value of watershed lands whether already in use or required for early use. In this connection consideration would be given: first, to the degree of protection which will result from such ownership, because, after all, the ownership may not be an absolute insur- ance against the necessity of some treatment, such as filtration, sooner or later; second, to the sentimental value attaching to any drinking water not subject to the danger of pollution in comparison with a water known to have been polluted but made wholesome by suitable treatment; third, to the time in the future when the expenditures for filtration and other treatment will begin; fourth, also to any protection which the ownership of the watershed would give against an adverse use of the waters originating therein, and against their diversion from the water- shed and, finally, to any other benefits that might result from such ownership, such as uses not incompatible with the devel- opment of the water supply. Frequently, of course,’ the value of watershed lands, owing to THE VALUE OF WATER-RIGHTS 3 their use for farming purposes and owing to the inclusion of densely populated areas, is so high that their ownership for the protection of the quality of the runoff waters is entirely out of the question and they do not then come under consideration in the determination of the value of the opportunity to make a water supply available. Notes relating to Some Water-right Values in California. — The following relating to the cost and value of certain water- rights in California is from the testimony of engineers who appeared before the Master in Chancery in the proceeding entitled “ Spring Valley Water Company ws. The City and County of San Francisco ”” which was on trial from July, 19135, to May, 1916. Mr. G. G. Anderson in his testimony referred to the value of water-rights in southern portions of California as determined from the value of the shares of stock in the various mutual irrigation water companies, and he says ‘‘ care was exercised in the analysis of individual cases to limit the values of these water-rights to terms of the right to divert and use only, exclud- ing all interest in attached lands or ditch systems or any assets other than actual rights of diversion and use.” He cites: Per million gals. per day Duarte Mutual Co. near San Gabriel. . . . . Salted ee $154,800 Covina Co. near San Gabriel. .......... vod. 117,057 Del Monte Co. near Pomona. . .......... TES 98,220 Canyon Water Co. near Pomona. . . . . . . miata et 104,490 San Antonio Co. near Ontario. .......... py 144,738 Bear Valley Co. near Redlands. ........... 90,248 Mill Creek Co. near Redlands. .............. 02,880 Gage Canal Co. near Riverside. ........... 77,400 Temescal Co. near Corona. ....... . als a alae. § 96,750 The foregoing values Mr. Anderson states “attach to the service for the particular purpose (irrigation) which entails delivery of water during the irrigation season or ordinarily 240 days per annum, rarely does the season extend to 270 days, and the service during the limited period does not, in all cases, yield full efficiency on the water-right,” 22¢ 226 VALUATION, DEPRECIATION AND THE RATE-BASE For the irrigation plants in the Santa Clara Valley Mr. Ander- son develops values ranging from $31,442 to $67,724 per million gallons of daily supply from gravity systems, over periods up to a maximum of 115 days per annum; and $167,709 to $242,786 for pumping systems. He also finds that the original cost to the Spring Valley Water Company of acquiring water-rights on both sides of San Francisco bay (about 1865 to 1913) averaged nearly $38,000 per million gallons per day, of water delivered to the inhabitants of San Francisco on the date of valuation, Dec. 31, 1913. By a different analysis and with some allowance for uncertainties Mr. Chas. H. Lee testifying in the same case finds this cost to have been about $48,000 per million gallons per day. Mr. F. C. Herrmann calls attention to the purchase by the Pacific Gas and Electric Company from the Livermore Water and Power Company of rights to about one million gallons of water per day at about $100,000 in 1913. The water-rights involved in this transaction are for the Mocho and Positas Creeks near Livermore, Cal. He also refers to a number of sales of springs and wells with small yield and to the following sales in southern portions of California: In condemnation proceedings by the City of Sierra Madre the value of water for domestic use was placed by the court at $270,760 per million gallons per day. Near Alhambra, in 1892, Richard Garvey bought from De Barth Shorb about 390,000 gallons of water per day at $64,595 per million gallons per day. At Montecito, Mr. Knapp bought 12,900 gallons of water per day a one-third right in the Warm Springs tunnel, "at $386,000 per million gallons per day. The value of water fixed by the California Railroad Commis- sion in the Glendale case, in addition to the allowance for structures was $154,720 per million gallons per day. While each specific instance of a sale of water-rights, as cited by Mr. Herrmann, should be considered in the light of all cir- THE VALUE OF WATER-RIGHTS 27 cumstances attending each such sale and of the specific needs of the purchaser in each case, these sales, nevertheless, have some effect upon the market value of water-rights showing as they do what a purchaser may, under certain circumstances, be willing to pay for water. Both Mr. Herrmann and Mr. Anderson were witnesses for the plaintiff in the Spring Valley case. Mr. Chas. H. Lee appearing for the defendant, that is for San F rancisco, added the following estimates of net water-right values: 1. Culture exclusively citrus (Southern Cal.): Per million gals. per day Lugonia Water Co. near Redlands. . . . . ER rT $154,000 San Antonio Water Co. near Ontario. . . . . . . Ta I, . 142,800 Del Monte Irrig. Co. near Pomona. . . . . . an A 00,000 Temescal Water Co. near Corona. ......o a6 sued an | 69,600 Gage Canal Co. near Riverside. .................. , 73,500 Redlands Water Co. near Redlands. . SESE A 8 52,400 San Dimas Irrig. Co. near San Dinas... LO, 51,500 2. Citrus and diversified crop (Southern Cal.): Per million gals. per day Santa Ana Irrig. Co. near Redlands. . . terrace veel $43,500 Alta Mutual Water Co. near Riverside. . SR rm mtn rg EE, 42,500 Thermal Belt Water Co. in Santa Clara River Valley ........ 42,500 Riverside Water Co. at Riverside. ......... ..... 14,700 Los Nietos Ditch Co. near Whittier. . Sil Artal 13,200 South Side Improvement Co. in Santa Clara River Valley. . . 2,860 3- Diversified crops, no citrus (Southern Cal.): Per million gals. per day Banning Water Co. near Banning. ................. $37,400 Moneta Water Co. near Redondo. . . ....... Ss : 23,200 McKenzie Ditch Co. near San Bernardino. . | Sis 13,200 Stout Ditch Co. near Redlands. ........... .. re 12,100 Puente Water Co. near Puente. ........... leis WL 2,400 Arroyo Ditch Co. near Downey, i... 2,300 Little Lake Irrig. Co. near Norwalk. /.0 sy A Ty 1,000 For more northerly portions of the State of California where water is more abundant and where the demand does not yet approach the limit of possible development, Mr. Lee lists the following: art 4 L 228 VALUATION, DEPRECIATION AND THE RATE-BASE Culture exclusively citrus: Per million gals. per day Lemon Cove Ditch Co. on Kaweah River. ................ $25,400 Rosedale Water Co. on Tule RIVer. .. aie vive « sivsisluisleleiainlos 23,200 Citrus and diversified crops: Per million gals. per day South Tule Independent Ditch on Tule River. ............. 5,070 Diversified crops, no citrus: Per million gals. per day Bishop Creek Ditch'in Owens Valley... LLL UL LL LLL, 3,100 Clark Colony Water Co. in Owens Valley........... 0 3,100 MeNally Ditch Co. in Owens Valley... 0 ih 3,100 Owens River Canal Co. in Owens Valley. ............. ; 3,100 Roberts DitchiCo. near Colusa... LL LLL EE DEER As ; 1,160 Watson Ditch Co. near Visalia... LL. on nal .. . 2,560 EvansiDitch!Co. near Visalia... Lo Lh . 2,012 Murphy Slough Assoc. on lower Kings River......... 1,040 Rawson Ditch'in'Owens Valley. .........L............ . 1,040 Consolidated Peoples Ditch on lower Kings River. ......... 870 OakesiDitchiCoinear Visalia. Lo. SL 580 Poplar Ditch Co. onTule River... fs iLL, 21% Mr. Lee cites also a few canal companies for whose water- rights no value is demonstrable from the market value of stock in the canal company. These were omitted from the above enumeration. The above figures are not presented to show the value of water in regions where society already demands full utilization, but rather to show that with the demand for a higher use of water which must come as the pioneer region gradually changes to a densely populated territory, the value of the water-right in any such country as that under consideration, where nature has set a limit to the available supply, must go up. CHAPTER XII THE ACCOUNTING SYSTEM Purpose of the Accounts. — It is not proposed to take up the matter of accounting in connection with public utility enter- prises any further than to indicate its purpose and to refer briefly to certain instructions in relation thereto which have been issued by public service commissions. The accounts should show clearly and in sufficient detail the facts relating to the investment, to operating expenses and to income. The natural division is therefore into two groups, the one relating to the investment, the other to income and operat- ing expenses. The accounts relating to investment are designed to show the investment in the property which is devoted to public use. These accounts should be kept in such form that the additions and betterments from year to year will be clearly apparent. They will include not alone the actual cost of all physical prop- erties but also any amount paid for franchises or for water- rights and rights of way. The income accounts are those which are designed to show, for each year, the amount of money earned for services rendered or for commodity delivered and the cost of rendering the service or furnishing the commodity. They will include the returns from outside investments and other sources on the one hand and on the other every expenditure necessary to render the ser- vice or to supply the commodity including taxes, insurance, rents and the like. The net balance of the operating and in- come accounts is profit or loss. Construction Account, Interstate Commerce Commission. — In the general instructions of the Interstate Commerce Commis- sion relating to the accounting system of railroads, construction 220 230 VALUATION, DEPRECIATION AND THE RATE-BASE is defined as including all processes connected with the acquisi- tion of the original road and equipment, road extensions, addi- tions and betterments. The following is from these instructions: « Costs shall be actual money costs to the carrier. When a portion of the funds expended by the carrier has been obtained through donations by the states, municipalities, individuals or others, no deduction on account of such donations shall be made in stating the costs. Contributions for joint expenditures should not be considered as donations. The carrier’s proportion only of the cost of joint projects, such as construction of jointly owned tracks and elimination of highway crossings at joint expense, shall be included in these accounts. “ The charges to the accounts of this classification shall be based upon the cost of the property acquired. When the con- sideration given for the purchase or the improvement of property the cost of which is chargeable to the accounts of this classifica- tion is other than money, the money value of the consideration at the time of the transaction shall be charged to these accounts, and the actual consideration shall be described in the record in sufficient detail to identify it. The carrier shall be prepared to furnish the Commission, upon demand, the particulars of its determination of the actual cash value of the consideration, if other than money. «Tt is intended that the accounts for fixed improvements and equipment shall include the cost of construction of such prop- erty. The cost of construction shall include the cost of labor, materials and supplies, work-train service, special machine ser- vice, transportation contract work, protection from casualties, inquiries and damages, privileges, and other analogous elements in connection with such work.” Treatment of Depreciation and Replacement, Interstate Com- merce Commission. — The attitude of the Interstate Commerce Commission with reference to the depreciation and replacement of property appears from the following instructions: “ When a unit of property other than land or equipment — such as a section of road, side or yard track, shop or power plant machine, building, or other structure — is retired from service and replaced with property of like purpose, the ledger value of the retired property shall be credited to the appropriate THE ACCOUNTING SYSTEM I: accounts of this classification at the time that the property is retired from service. The amount of this credit shall be charged concurrently as follows: “ An amount equal to the credit balance in the accrued depre- ciation balance-sheet account with respect to the property thus retired shall be charged to that account and the remainder (less salvage and insurance recovered, if any), together with the cost of demolishing the property, if demolished by or for the carrier, shall be charged to the accounts in Operating Expenses appropriate for the cost of repairs of the property before retire- ment. The accounting for the salvage shall be in accordance with the disposition made of the material recovered. “ If, however, the property retired and replaced with property of like purpose is of minor importance , such as a small roadway building or other small structure, and is replaced in kind with- out betterment, the cost of the replacement shall be charged to operating expense accounts, and no adjustment made in the road and equipment accounts. “If so authorized by the Interstate Commerce Commission, the carrier may charge to Profit and Loss any extraordinarily large item representing the cost of property retired and replaced, instead of charging such item to Operating Expenses. The carrier shall file with the Commission a statement of the cost and a description of the property retired and the reasons which, in its judgment, indicate the propriety of charging the cost of such property to Profit and Loss. “The provisions of this section are applicable in accounting (at the time of retirement) for the cost of property abandoned, even though the new property has been actually installed pre- viously to the date of the demolishment of the abandoned prop- erty. “ When the renewals to be made to an important building or other structure will constitute the major portion of its value when renewed, the property, when taken out of service, shall be considered as retired and accounted for as provided above, and for the purposes of this classification the renewed property shall be considered as an addition, and the appraised cost thereof shall be included in the accounts of this classification, considera- tion being given to the second-hand portions remaining therein. In no case shall the charge for the renewed property exceed the cost (at current market prices of labor and material) of new property of equal capacity and equal expectation of life in serv- 23] 232 VALUATION, DEPRECIATION AND THE RATE-BASE ice, less a suitable allowance on account of the second-hand parts remaining therein. « When a unit of property other than land or equipment — such as a section of road, side or yard track, shop or power plant machine, building, or other structure — is retired from service and not replaced, the ledger value shall be credited to the appropriate property accounts at the time that the property is retired from service. The amount of this credit shall be con- currently charged as follows: “ An amount equal to the credit balance in the accrued depre- ciation balance-sheet account with respect to the property thus retired shall be charged to that account, and the remainder (less salvage and insurance recovered, if any), together with the cost of demolishing the property if demolished by or for the account of the carrier, shall be charged to the appropriate profit and loss account. The accounting for the salvage shall be in accordance with the disposition made of the material recovered.” Retirement of Land, Interstate Commerce Commission. — In the matter of land retired from use the Commission says: “ When any land, the cost of which is included in the accounts of this classification, is retired, the ledger value shall be credited to account ¢ Land for transportation purposes.’ If the land is retained by the carrier, its estimated value shall be charged to balance-sheet account ‘Miscellaneous physical property,” the necessary adjustment of the difference between the ledger value and the estimated value on account of the loss in the property due to its retirement from transportation service shall be made through Profit and Loss. If sold, the difference between the ledger value . . . and the amount received for the land shall be adjusted in Profit and Loss.” Engineering Account, Interstate Commerce Commission. — Relating to engineering on the construction of a railroad, the Commission says: « This account shall include the pay and expenses of engineers, assistants, and clerks engaged in the survey and construction of new lines and extensions, or in making additions to and better- ments of the carrier’s road, including wharves and docks. “ When employees . . . are engaged in the maintenance of the road, their pay and expenses while thus employed shall be charged to Operating Expenses. THE ACCOUNTING SYSTEM 233 “ Expenditures for tentative or preliminary surveys shall be carried in a suspense account until it is determined whether or not to continue the work. If the project is continued, expendi- tures for all surveys in connection therewith shall then be trans- ferred to this account, and, if abandoned, to Operating Expenses, Income, or Profit and Loss, as may be appropriate.” Interest during Construction, Interstate Commerce Commis- sion. — The Interstate Commerce Commission in the instruc- tions relating to “ interest during construction ” says: “ When any bonds, notes, or other evidences of indebtedness are sold, or any interest-bearing debt is incurred for acquisition and construction of original road and equipment, extensions, additions, and betterments, the interest, accruing on the part of the debt representing the cost of property chargeable to road and equipment accounts (less interest, if any, allowed by depositaries on unexpended balances) after such funds become available for use and before the receipt or the completion or coming into serv- ice of the property so acquired shall be charged to this account. “ When such securities are sold at a premium the proportion of such premium assignable to the time between the date of the actual issuance of the securities and the time when the property acquired or the improvement made becomes available for serv- ice shall be credited to this account. “This account shall also include such proportion of the dis- count and expense on funded debt issued for the acquisition of original road, original equipment, road extensions, additions, and betterments, as is equitably assignable to the period between the date of the actual issuance of securities and the time when the property acquired or the improvement made becomes available for the service for which it is intended. The proportion of dis- count and expense thus chargeable shall be determined by the ratio between the period prior to the completion or coming into service of the facilities or improvements acquired and the period of the entire life of the securities issued. “This account shall also include reasonable charges for in- terest, during the construction period before the property be- comes available for service, on the carrier’s own funds expended for construction purposes.” Application of Accounting Principles to the Unlimited Life Method. — Under the Unlimited Life Method of procedure, 234 VALUATION, DEPRECIATION AND THE RATE-BASE which is a new suggestion and which is not contemplated in the foregoing instructions, but which is the one that should find preference for all complex public utility properties made up of a large number of individual items, there will be no depreciation to write off. It will be unnecessary to estimate accrued depre- ciation except when the transfer of the property is involved or a valuation is to be applied to individual articles. The current replacement requirement, however, will have to be estimated; but the estimate need be only approximate. The replacement fund will not be available for the retirement of capital. Neither will it be available for betterments or additions to the property. If it grows too rapidly, if the accumulation in it becomes un- necessarily large, the current replacement requirement may have been over-estimated; if it is depleted there may have been an underestimate of the replacement requirement. Excessive accumulation in the replacement fund should be checked by reducing the amount annually set apart for the fund. In the accounting system, the cost of cach article as it goes out of use is written off the books and each article which replaces a discarded article is entered as a renewal and is treated practi- cally as though it were new construction. Its cost is offset by the amount written off for the discarded article and the replace- ment fund is depleted by this cost. The capital investment account remains unaffected unless the cost of the new article is greater or less than that of the discarded article. The excess cost, if any, should not come out of the replacement fund but from new capital. The deficiency, if any, represents a reduc- tion of the invested capital. The accounting system under the Unlimited Life Method of procedure, as will be seen from the above statements, is much simpler than that for procedures which take cognizance of the accrued depreciation and of the constantly changing present value of the physical elements. The replacement account, if the Unlimited Life Method be adopted, will be credited with all expenditures that are made for the renewal of items which can be conveniently individualized THE ACCOUNTING SYSTEM 235 and which serve or are expected to serve for a number of years, and it will be charged with the amount annually set apart out of earnings for replacements. This account should be kept separate from repair accounts although there is no fundamental difference between the replacement of a broken spoke in a wheel and the replacement of a discarded generator. It is funda- mentally immaterial whether the replacement relates to single lengths of pipe, to broken window panes and the like or whether they are large as in the case of the dismantled steamboat. The only difference lies in the classification of the accounts. In either event funds for the replacement must be made available at the proper time. It is in the making of suitable provision for the replacement of the individualized items that expert advice should be sought in order that a proper distinction may be made between the apparent and the real profits of the busi- ness. Without a proper analysis, an apparent profit has, too frequently, been found to be in fact a loss. Application of Accounting Principles to Other Methods. — Under any method of procedure, other than the Unlimited Life Method, the difficulty is presented of dealing with articles which do not serve throughout their full probable life terms and with articles which remain in service beyond these terms. In the one case the cost of an article may have to be carried for complete amortization long after the article has gone out of use. In the other case an article with many more years of usefulness should be rated as of no value. Accountants have found methods to overcome these difficulties but the book- keeping which is involved becomes complicated. When a public utility is established and its existence is justi- fied by all attendant circumstances, the owner has reason to assume that the prospective business will prove profitable. There will usually, however, be a certain time during which his operating expenditures will exceed the revenue produced by the property. This time may extend over a period of years. Due consideration must be given to such facts as this as well as to the estimates of the prospective business when the cost of a 236 VALUATION, DEPRECIATION AND THE RATE-BASE commodity or of a service is to be ascertained and its sale price is to be fixed. The cost records should be so kept that they will give all needed information relating to past financial history as well as to the current cost of operation. Any reduction in the value of an operative property such as may result from an advance in the art of the manufacture of its output or due to decrease in value of real estate and like causes, may result in an operating loss. In the case of a public service corporation where the investment is of real concern, such possible reduction of value is one of the elements covered by the hazards of the business and should be forestalled or should in the course of time be amortized by the excess of earnings over and above earnings on ordinary safe investments. Any increase in value, no matter what it may result from, belongs among the earnings. Despite the rulings which have been had on this point by competent authority, it would seem preferable not to include appreciation in the rate-base but as elsewhere suggested to permit earnings that will give the owner a limited share in the general prosperity of the community. CHAPTER XIII THE VALUATION OF MINES AND OIL PROPERTIES General Statement Purposes of the Valuation. — Valuations of mines and oil properties as in case of other properties are needed for many purposes, the most general being, (1) the purchase or sale of such properties or portions thereof, (2) the information of owners or others interested in the property as a guide to the proper opera- tion thereof or to the financial operations connected with such operation and (3) the determining of a basis on which taxation can be figured. The methods used to accomplish purposes (1) and (2) are closely associated and in many cases identi- cal, but the proper method or methods for determining what the basis for taxation shall be, as shown later, must differ from valuations for other purposes. Limitations upon Accuracy. — Because of the impossibility of fixing definitely the economic value of the mineral deposit, the extent of which may be indeterminable, valuations of mining and oil properties must be less definite than the valuations of industrial and public utility properties, the value of whose physical elements, at least, can usually be determined with considerable accuracy. In underground metal mining, the development is in many instances kept just a short distance in advance of productive operations. This is sometimes due to the irregular nature of the ore bodies, but generally can be explained as a result of the method of financing mining properties. This is particu- larly true in small operations where the money earned is used to carry the expense of the development and the necessity to raise additional funds for extensive development is avoided. 237 238 VALUATION, DEPRECIATION AND THE RATE-BASE This is not always true of extensive mining properties repre- senting large investments. The Utah Copper Company in the United States and the Braden and Chicaquamata copper prop- erties in Chile have ore bodies blocked out sufficient for 45 to 70 years of operation. This extensive development facilitates the valuation of these ore bodies. It should be noted, however, that two mines having equal ore reserves might be valued at very different figures because one may promise a future beyond its reserves while for the other there may be no hope of further production when the reserves in sight are exhausted. The difficulty that is met in estimating the value of the mineral deposit is apparent also at oil properties when only a number of wells sufficient to develop enough oil to supply the existing market and to provide for a limited period in advance are drilled. Because of the usual great depth of oil wells, the sinking of new bores becomes an item of large expense and the development to a considerable extent of the holdings of an oil producing company might financially embarrass an otherwise profitable concern. Placer gold deposits (hydraulic and dredging) in most cases are thoroughly prospected by pits or drill-holes and the value ascertained before mining operations are commenced. The drift placer mines of the Western United States form an exception and it is in most cases extremely difficult if not impossible to determine the value of such deposits. Methods Commonly Employed in Valuation Enumeration of Methods of Valuation. — Numerous methods of valuation have been employed and these have been modified by such variations as have suited the views of the valuating engineer or valuating body. That this has resulted in con- fusion is shown by recent court decisions. The engineer or valuer who does not definitely state the methods used by him in obtaining his valuation of the property seems to be the most likely to have his estimate supported by the findings of the court when appeal has been taken. THE VALUATION OF MINES AND OIL PROPERTIES 239 Among methods that have been used the following are the most important: (1) Valuation by empirical methods. (2) Valuation based on market value. (3) Valuation based on royalty value. (4) Valuation by capitalizing profits. (5) Valuation by estimation method. (1) Valuation by Empirical Methods. — An important ex- ample of an empirical method is the so-called * foot-acre ” valuation of coal measures. A certain value per foot-acre of coal has been established in a certain district and the value of any property is based on this unit disregarding the fact that thin beds of coal are not worth as much per acre-foot as thick beds. Another empirical method is that under which a value is placed on a mineral property of so many times the annual proceeds or the annual profits regardless of the actual expecta- tion of life of the mine. It is needless to say that this method is used only for taxation purposes. (2) Valuation based on Market Value. — A method of valuation of coal lands based on the use of the results of sales of neighbor- ing properties has been found acceptable to the courts. The attempt is made to fix the actual sale value of a coal property by examining the price at which other property similar to that under consideration has been sold. This method is derived from existing methods of real-estate valuation and from an engineer’s standpoint is acceptable only when checked or sup- plemented by a valuation on some other basis. Such checks may demonstrate that recent sales were not made at the actual value of the properties sold. Further than this no recent sales of similar properties may be available for purposes of com- parison. (3) Valuation Based on Royalty Value. — The royalty value method of appraising the value of mining properties makes use of the established royalty value per ton. This method of 240 VALUATION, DEPRECIATION AND THE RATE-BASE valuation has been applied to some extent in coal regions. Because coal becomes more valuable from year to year the value of a leasehold will increase. The annual profits exceed the royalties by continuously increasing amounts and a valua- tion based on the average royalty payments in a district cannot be a gauge of the actual values, particularly districts where the leases have been in effect for some length of time. In addition to the value of the mine or colliery determined from royalty values, the leasehold itself has a value which increases as the value of the mineral product goes up and the actual value of the property must be the summation of these two values. As the leasehold value is determined by subtracting the valuation based on royalty values from a valuation of the property, itself, by some other method, it is evident that the royalty value method cannot be independently used to determine the value of the property. (4) Valuation by Capitalizing Profits. — By this method the valuation is based on a capitalization of the net annual profits. It requires an estimate of the remaining life of the property but does not take into account the fact that incompetent manage- ment may so deplete the profits that a valuation with these as a basis may not approximate the actual value of the property in competent hands. This method should only be adopted when estimated profits instead of actual profits are used as a basis. It is then appli- cable in the case of oil properties and other deposits the extent of which is indeterminable. If the life of adjoining or neighbor- ing properties has been proven, an approximate basis may be had for estimating the life of the property which is to be valued. The depths to which mineralization extends in neighboring mines often is used to determine the expectation of a prospect when such information supplements the geological features of the deposits. (5) Valuation by Estimation Method. — This method is adopted by mining engineers in the valuation of mineral prop- erties when these are to be bought, sold or financed. Deter- THE VALUATION OF MINES AND OIL PROPERTIES 241 mination of all the elements that have a bearing on the values is necessary. The estimated profits capitalized furnish the foundation for a valuation of the ore bodies or deposits. These profits are dependent on the sales value of the product, the geological structure of the deposit, the cost of mining (present and future), the cost of surface treatment, and other factors. In fixing the value of coal lands use can be made of the foot- acre ” method of valuing coal lands provided account is taken of the fact that a foot-acre of coal in a thin vein is not so valuable as it is in a thick vein. The sales of adjoining properties will be of assistance to the engineer in fixing a value, particularly in case of coal lands which have not been explored but which con- tain the same beds and show geological conditions similar to properties that have recently changed hands. The © royalty value ”” should not be ignored and when properly determined furnishes a valuable check on the valuation. When account has been taken of the risks of operation, the geological features of the deposit and the economics of the necessary surface plant, the total prospective estimated profit can be suitably discounted and a certain definite valuation placed on the property. In determining the present value of a property for which the profits have been estimated, it is necessary to remember that certain fixed charges such as replacements, sinking fund payments (paid or not paid), etc., are to be deducted before the profits are capitalized. A mining property to be a good investment must promise to an investor the return of his capital in addition to interest on the capital at a rate commensurate with the risk he takes in investing in such a property. What the risk will be should be determined by the investor before he makes the investment. Comparison of the proposed investment with certain standard investments such as government bonds, railroad bonds and real- estate mortgages should be made. Proper Rate of Interest. — The proper rate of interest on mining investments has been and still remains the subject of much discussion among engineers. A reasonable solution of 242 VALUATION, DEPRECIATION AND THE RATE-BASE the problem has not been advanced and it is the belief of the author that it is not possible to determine a rate of interest that would apply equally well to all mining investments. The risk incurred by investing in a property that has been slightly developed is much greater than the risk in the case of a well- prospected ore body even when the mines contain similar ores and will be operated under similar conditions. Then again the average risks in copper mining differ from the average risks in gold mining and so on. Mr. H. C. Hoover has tabulated the risks of mining as follows:* “1. The risk of continuity in metal contents beyond the sample faces. “2. The risk of continuity in volume through the blocks estimated. “ 3. The risk of successful metallurgical treatment. “4. The risk of metal prices, in all but gold. “5. The risk of properly estimating costs. “6. The risk of extension of the ore beyond exposures. “#7. The risk of management.” Several of these risks are found in industrial enterprises (Risks 4, 5 and 7). The risks of continuity of ore body and of ore values are peculiar to the mining industry. The limited market for the mineral products and the effect of the volume of the output on the prices that can be obtained increases the risk that capital must take. The problem of obtaining proper metal- lurgical treatment is an important one particularly when start- ing operations at new properties. The fact that the mineral constituents of the ore may change as greater depths are reached and that the previously satisfactory flow sheet may no longer realize the percentage of extraction on which the profits were based cannot be ignored by the investor. The interest return that might be attractive to an investor in a proven district might not be sufficient to attract capital in a district where the mines are still prospects and where the depth of the mineraliza- tion has not been tested. * H. C. Hoover, “Principles of Mining,” 1909. THE VALUATION OF MINES AND OIL PROPERTIES 243 It is a fact that industrial enterprises because of additional risks demand greater interest returns than Government bonds and it seems reasonable that mining investments taken as a class should call for a greater rate of interest than industrial enterprises. This claim for a higher rate of interest is opposed by such an authority on mine valuation as Mr. J. R. Finlay * who can be quoted as follows: “ Ihave generally assumed that 5 per cent was a normal inter- est — or discount rate. If that is so, it is a fair figure to use in a mine valuation, which should be nothing but a candid inquiry into the present value of expected profits.” If Mr. Finlay’s statement is correctly understood, he is willing to ignore the risk that these prospective profits may be dimin- ished or may entirely be cut off before the estimated life of the property has been accomplished. If it is true that at any min- ing property risks exist over and above the risks existing in so-called “safe” investments, then a 5 per cent discount or interest rate is not sufficient to induce sane investment. Mr. Finlay’s 5 per cent interest rate, as applied to the iron mines of Michigan in his appraisal made for the State Tax Commission in 1911, was changed by that Commission to a 6 per cent basis in 1913. Other authorities have gone on record as advocating higher interest rates and in this connection the following will be found of interest: Mr. J. H. Curle | states that a suitable mining investment must fulfill the following requirements: “ 1st. The development in the bottom must be good; “2nd. The mine must pay 10 per cent per annum; “ 3rd. There must be 60 per cent of the price of the shares in sight.” Mr. Hoover in his admirable work on mine valuation says: } * J. R. Finlay, “Valuation of Iron Mines,” Trans. A.LM.E., Vol. 45, P- 295. t J. H. Curle, “The Economist,” London, Sept. 15, 1903. I H. C. Hoover, “Principles of Mining,” 1909. 244 VALUATION, DEPRECIATION AND THE RATE-BASE “ What rate of excess return the mine must yield is a matter of the risks in the venture and the demand of the investor. Min- ing business is one where 7 per cent above provision for capital return is an absolute minimum demanded by the risks inherent in mines, even where the profit in sight gives warranty to the return of capital.” Mr. G. A. Denny, an English engineer, says: “ A normal mining risk stated in terms of interest may be taken at 10 per cent per annum on the capital expended plus a rate for the redemption of capital.” John Hays Hammond { expressed his views on this question as follows: “ In many mines persistency of the ore deposits and, therefore, the reliability of the mines as dividend payers, justified the in- vestment upon a basis in some instances as low as 8 per cent, dividends to which, of course, must be added a certain per- centage to provide for the amortization of the capital. Gener- ally speaking, however, investments in mining securities are not to be regarded as attractive unless they return from ro per cent to 15 per cent in dividends, in addition to the profits to be set aside for amortization.” Price of the Mineral Product. — Because of wide fluctuations in the prices that minerals bring in the market, the use of the current market price of such a product in measuring the value of a mineral deposit is not proper for valuation purposes in general. No hardship would be forced on the owner or operator if, for taxation purposes, valuations were made annually based on the current price of the mineral produced. This method, however, results in a valuation fluctuating in amount from year to year and because of the constant changes required, does not seem to be practical. The “normal” price of a mineral may be defined as the aver- age market price over a certain definite period of years. Periods of time five or ten years in length are in general use. The * G. A. Denny, Mexican Mining Journal, July, 1910. t John Hays Hammond, Engineering and Mining Journal, Jan. 1, 1910. THE VALUATION OF MINES AND OIL PROPERTIES 245 “basic ” price represents the point at which the mineral produc- tion falls off to such an extent that a rise in price results. Mr. Hoover in his “ Principles of Mining ” states that safety lies somewhere between the “basic” and “ normal” prices. No such limitation should be placed on the exercise of the judgment of the valuating engineer, as this assumption cannot hold good during the years following protracted periods of finan- cial depression such as the hard times of 1893 to 1898. The “normal ” price of many minerals estimated on a 10-year or 20- year average basis was for a considerable period of time following this depression less than the actual value of the mineral. For illustrative purposes certain tables of statistics giving the production and average prices of four important metals (copper, lead, silver and zinc) from 1880 to 1914 are given at the close of this Chapter. Curves have been plotted which illustrate the relative increase in the production of these metals from year to year and also the changes in the average annual price. (Fig. 4 to Fig. 7.) For comparison normal curves of production and price (based on ten-year averages) have been plotted assuming that the average figure for production and price are applicable midway of the ten-year period. By continuing these normal curves to date on the assumption of a five-year future history for the metal, a present “ normal ” price can be obtained that will be as close an approximation as can be made. Valuations for Purchase and Sale. — When a valuation of a mining property is needed because of a contemplated change in ownership, the most satisfactory method of valuation is the straightforward one involving the determination of the value of the ore body on the basis of its production past, present and expected. Such a valuation includes an estimate of the probable life or expectancy of the property under the actual or an assumed rate of production, an estimate of the price that the mineral product will bring in the markets of the world and an estimate of the cost of producing the mineral. This method requires the use of all available information as to geology, actual operating costs, 246 VALUATION, DEPRECIATION AND THE RATE-BASE adjacent developed properties, recent sales of same, determina- tion of the ‘“ normal” price of the mineral, recent sales of metal or of ore at the property, determination of the proper rate of interest to be used as a basis for capitalization, and the like. The rate of production that is properly brought under consider- ation must be determined from consideration of the fact that the operating costs per ton decrease as the capacity increases, while the fixed charges increase when the cost of the installation is increased. It may be found that the rate of production actually in use is not that which brings out the full value of the property and an assumption of a proper rate should be made in determining the profits that can be expected. In the case of cer- tain minerals having a limited market, the output is controlled by market conditions which must be considered in determining the rate of production. Valuations for Owner’s Information. — Valuations made for the purpose of informing the owner as to the condition of the property, although made in a similar way to those for purchase and sale purposes, may be limited by the special purpose for which they are required. During the operation of a property it may be desirable to determine from time to time the present value of the property, taking into account the new underground developments, im- proved methods of ore treatment and changed market condi- tions. A desire on the part of the owner to ascertain on what basis he might, with advantage to himself, join in coSperative operations with adjacent properties, may lead to a valuation. This often occurs in the case of oil lands in small holdings that for reasons of economy can only market their product by co- operative means. The rental of coal lands and other deposits that contain large mineral bodies to other operators requires a determination of the “ royalty ” that should be charged and this should be based on an actual valuation and not on the average royalty in current use in the district although this value may be used for a check. THE VALUATION OF MINES AND OIL PROPERTIES 247 Valuation for Taxation Purposes. — Whether it is desirable from an economic standpoint to tax the ore bodies in the pos- session of mining companies is an open question that has been hotly debated by engineers and economists. Different methods of taxation have been suggested: (1) Taxation based on surface improvements only. (2) Taxation based on estimated value of the ore body and surface improvements. (3) Taxation based on foot-acre” or “royalty” value and on empirical methods of valuation. (4) Taxation based on annual production or gross proceeds. (5) Taxation based on annual profits or net proceeds. Probably the earliest popular method of taxing mining properties was to tax only their surface improvements. It was not considered advisable to tax an industry that was of such economic value to a community. Also because of the risks of the business it was deemed necessary to make mining investments as attractive as possible to the capitalist and not to hamper operations, particularly in the early stages, when an enterprise was just getting on its feet. The history of the mining industry in this respect is similar to that of public utilities, which have anticipated and facilitated the growth of population in the territory served. Just so long as the operations were conducted at a risk the public showed no desire to interfere or to assume responsibility, but once the investments have be- come firmly established and are earning a reasonable interest on the capital investment regulation of the utility with its accompanying embarrassments has been commenced and the practice of allowing the company a return on its depreciated “fair ” value and not on its investment has sprung up. In the case of the mining properties it became apparent that the large coal, iron and copper operations after a successful struggle for existence had become profitable and represented a very large portion of the business of certain communities. Taxa- tion above a mere tax on surface improvements was proposed and has become an established practice in many states. 248 VALUATION, DEPRECIATION AND THE RATE-BASE Valuation of Mines for Taxation in Various Localities In a general way some methods of valuing mining property for taxation purposes will now be outlined. Alabama, California, Towa, New Jersey, New York, Oregon, Washington, and West Virginia appraise mining property in a similar manner to real estate and other property. They have no laws pertaining to the valuation of mining property. This method requires a perfunctory valuation of the surface improve- ments and of the ore body, the latter in some cases being entirely ignored. Michigan, Minnesota and Wisconsin assess their mining prop- erties on a basis of the estimated value of the ore body and the surface improvements giving weight to all the elements that enter into value. In Michigan the present system was introduced by Mr. J. R. Finlay in 1911. Data are compiled from the reports of mine operators in sworn statements. Then an inspection is made by the State Geologist and his assistants to estimate the reserves and check up other data. The State Tax Commission passes on the figures and after a public hearing the final results are reported to the local assessors. The valuation is based on four elements — ore reserves (developed and prospective), average annual profits (five-year average), life or expectancy, and the rate of interest. The developed reserves consist of ore blocked out above the bottom levels. Prospective reserves con- sist of the expected extension of the ore bodies downward or laterally beyond existing workings. The average annual profits are estimated from a five-year record when such exists. Undeveloped properties are judged by the operations of other mines. The expectancy of a property is taken at the ratio of the estimated reserves to an average five-year shipment. The life of the undeveloped mines is estimated by comparison with adja- cent operations. The interest rate is now 6 per cent for both principal and sinking fund. It was 5 per cent and 4 per cent respectively in 1grr when Mr. Finlay had charge. The criti- THE VALUATION OF MINES AND OIL PROPERTIES 249 cism of this system is that the values of the ore bodies cannot be accurately determined, that by using annual profits as a basis a premium is placed on inefficient operations, that the life cannot be determined with any degree of certainty and that the rate of interest is too low, making the present esti- mate of value too high. It has several times been proposed to introduce a tonnage tax in Michigan. Recently the State Grange proposed to invoke the Initiative in order to obtain a tax bill proposing a levy of cent per pound on copper and 10 cents per ton on iron ore. This method of taxing would penalize the concern that was mining with only a small margin of profit and would tend to unnecessarily hamper the mining industry in the State. Minnesota has the engineers of the State Tax Commission measure up the tonnage of ore underground and then an ad va- lorem tax on 50 per cent of the present indicated value is levied. Mineral lands that are not productive are taxed. A tax of 4 to 43 cents per ton has been proposed on stock piles. In Wisconsin the 1913 Legislature passed a law assessing mining properties or mineral lands upon the estimated value of the ore underground. A report based on production profits, etc., was made by W. L. Uglow, engineer for the State Tax Commission, but his recommendations were greatly altered by the Commission. It was found necessary to reduce the figures for developed properties and to entirely cut out the estimates on undeveloped properties. The system he adopted might be called a semi-empirical method which is based on figures from a theoretical zinc mine. His theoretical or ‘hypothetical ” mine was the result of combining the figures from several actual operating properties. The assumed life was taken as four years which is the average as determined from the previous experience of the district. Mr. Uglow’s method of ascertaining the value of a mine as applied consisted of multiplying the annual profit by the factor 2.43 which is the figure obtained by using the “ hypothetical ” mine and assuming that profits do not fluctuate from year to year. He claims as advantages that his method 250 VALUATION, DEPRECIATION AND THE RATE-BASE is based on actual profit and average life and that it bases the assessment on a multiple of the profits rather than on the market value of the mine. Pennsylvania taxes its coal lands under the acts of 1841 and 1842 which require the taxation of “ every subject of taxation at the actual value thereof.” The foot-acre method of assess- ment was in general use until 19o7 when a big jump in value was made. Appeal to the state courts resulted in decisions which declared the ¢ foot-acre” and “ royalty ” methods un- satisfactory and dependence is now placed mainly on recent sales in the vicinity to determine the market value of a property. Although fairly satisfactory for real estate appraisals this method cannot be applied with equal success to lands whose coal deposits, of indeterminate extent, in many instances give them value. Further than this recent sales in the vicinity may be scarce and the resulting standard of value because of this fact very un- satisfactory. Arizona and Colorado tax mining properties on the basis of production. Arizona divides mining properties into two general classes, productive and non-productive. Productive properties include those which yield net proceeds during the year, after deducting cost of active operation, cost of transportation, cost of market- ing, smelting and refining, and expenses for betterments and repairs. The return of the capital cannot be considered as part of the cost nor can the salaries of those not continuously en- gaged in the enterprise within the state be included as an element of expense. The assessed value is arbitrarily taken as one-eighth of the gross value plus 4 times the net value of the annual output plus the value of the surface improvements. Non-producing mines are taxed in the same way as other real property in the State. Colorado determines the net proceeds by deducting the actual cost of extraction, after eliminating unnecessary expenditures and the actual cost of transportation to place of sale, from the gross value of the annual production (the sum actually obtained THE VALUATION OF MINES AND OIL PROPERTIES 251 by the owner). In 1915, the assessed value was fixed at 25 per cent of the gross annual proceeds or the net annual proceeds whenever this exceeds 25 per cent of the gross proceeds. Im- provements are assessed at the same rate as other property in the vicinity is assessed. It is claimed in Colorado that this law permits the owner of a large idle group of claims to pay no greater tax than a prospector actually working a single claim. Idaho, Montana, Nevada, New Mexico and Utah tax the net proceeds of mining properties. In Idaho the net proceeds are used as a basis for the assess- ment. Improvements are assessed at full cash value. The ground of undeveloped claims is taxed on the prices paid to the U. S. Government when they were purchased. Montana bases its mine tax on the net proceeds. The surface is assessed at the price paid to the U. S. Government ($5 per acre for metal mines and $2 per acre for coal). If the sur- face is more valuable for other purposes, it is assessed at the market value of such property. Surface improvements are taxed at market or local value. Nevada assesses all patented claims at $500 unless it can be proved that over $100 worth of work has been done during the year. Improvements are assessed at local value. A tax is levied on the net proceeds of all operating mines. By deduct- ing such charges for operation, transportation and reduction or sale of output as the State Tax Commission permits, from gross value of the production, the net proceeds are estimated. No deduction for office expenses other than those of operating offices are permitted. The salaries of mine officials are limited. The investment in surface plant is not depreciated nor is the redemption of any investment in mine ground or prior develop- ment permitted. By an agreement between the Tax Commis- sion and operators, future levies were to be made only on 6o per cent of the net profits or the same percentage which is applied in assessment of other property. During 1913, this percentage has been raised to 70 per cent by the Tax Commission. New Mexico has placed its mine taxation in the hands of a 252 VALUATION, DEPRECIATION AND THE RATE-BASE State Tax Commission. The owners or lessees of mines are ordered to furnish annual statements supplying the Commission with the necessary data to determine the net proceeds. Surface improvements are taxed as other like property. Unproductive patented mining claims are assessed and taxed on a reasonable valuation as undeveloped mineral lands in addition to their surface value whatever it may be. The law for the taxation of mining property was drawn up by the attorney of one of the large mining companies in New Mexico and is believed to be satisfactory to the mining interests. Utah has a system for assessing on the basis of the net proceeds but the State Board of ;Equalization does not allow deduction for interest, taxes, insurance, legal expenses, etc., so the mines are really being taxed on more than their net proceeds. Mexico prior to the Carranza regime placed an annual surface tax of 6 pesos per pertenencia (100 meters square) on all claims of less than 25 pertenencias in size. On each pertenencia in excess of 25 the annual charge is only 3 pesos. A state or federal tax on output could be levied not to exceed 13 per cent of the assay value. The tax on reduction plants was 0.6 per cent of the valuation but other improvements were not taxed. When ore was exported unrefined it was taxed 33 per cent of the assay value but when it was refined in Mexico the export tax was only 22 per cent of the assay value. Since the de facto government has been controlled by Car- ranza, an annual tax has been established at the rate of $6 per hectare on a property of not over ro hectares, $7.50 per hectare on the acreage in excess of 10 hectares and below 20 hectares; $0 per hectare on that from 20 to 50 hectares; and $12 per hectare on all above 50 hectares. Recent developments in Mexico are such that it cannot be stated with definiteness what is the method of mine taxation. German South-West Africa. — British consular reports state that the mines of German South-West Africa were taxed by an empirical method. The tax amounted to the difference be- tween 66 per cent of the gross value of the output and 70 per cent THE VALUATION OF MINES AND OIL PROPERTIES 25 3 of the cost of operating. This amounts to no tax when the profits are 6 per cent or less, to 10 per cent tax on gross produc- tion when the profits are 20 per cent of the gross, to 31 per cent when the profits are so per cent and so on up to the limit of 66 per cent of the gross production when the operating expenses approach zero. Propriety of Taxing Mining Property. — The question of the propriety of taxing mining properties is an important one. In states such as Michigan and Minnesota where mines make up a large proportion of the industry of the state it is necessary that mining properties bear a large share in the maintenance of the government which exists largely for their protection. In the states just mentioned a closer approximation of the value of the ore underground is possible than in states where the mining interests are largely concerned with precious metals. This should not be construed to mean that the methods of assess- ment now in vogue in the former should be considered the proper ones. There is no doubt that taxation of mines in any form must retard to some extent the development of the mining industry which is of such economic value to the country. It also must be granted that in certain communities the mining interests are so large that it is only proper that they pay their share of the governmental burden. Injustice can be avoided only by the exercise of caution when mineral lands are to be taxed. That taxation may run riot has been shown in Minnesota in the case of mines located within the boundaries of municipalities. In Buhl, Minnesota, the 1913 municipal tax levy was $12 5,000 or $125 per inhabitant. The town had 172 voters and had over 100 persons on the pay roll during the year. Only 1} per cent of the assessment was paid by the inhabitants and ¢82 per cent by the Mining Companies. In Keewatin the levy amounted to $374.10 per inhabitant. The township of Stutz in 1914 spent more than $goo for every voter. By court order some of these levies have been modified but they show what extremes are possible. It is understood that the per 254 VALUATION, DEPRECIATION AND THE RATE-BASE capita expenditures of municipalities have now been limited to $25 per inhabitant by the State Legislature. The general principles of mine taxation are not comparable with those controlling the taxation of unimproved real estate which is held idle waiting for the unearned increment. Mining properties may be allowed to remain idle because there is no present market for their product at a price that will permit a profit but they cannot be held for any length of time as an investment waiting for a chance to make a large turn because under ordinary circumstances no important permanent increase in value is to be expected. When large increases in the price of minerals take place, new substances at more reasonable prices are apt to be supplied to do the same work. Water power takes the place of mineral fuels. Oil takes the place of coal in certain localities where coal is high and so on. Improvements in the methods of production as well as in- creased production have resulted in decreased prices of the output rather than in increased returns. Furthermore as com- pared with farming and other manufacturing industries mining is not as attractive a field as it formerly was and in another decade will probably not be as attractive as it is at the present time. Mr. T. A. Rickard, in a recent paper before the International Engineering Congress, points out that a mine is not an invest- ment but is a speculation. He writes: “ The act of mining cannot be applied on scientific principles until two basic ideas are fully comprehended: (1) A mine is a wasting asset and (2) mining is a speculative business. To treat a mine as an investment, and to appraise it on that basis is to ignore the cumulative facts of to-day and of other days. Min- ing is a speculation that can be wise or foolish according as a man recognizes the inherent risk and takes his chances ac- cordingly.” Taxation of certain deposits such as coal-beds, oil fields, etc., on the basis of the present value of future production tends to increase the current output and might easily lead to the de- structive working of such deposits. if vigorously enforced, e.g., THE VALUATION OF MINES AND OIL PROPERTIES 255 the abandonment of thin beds of coal or the failure to take care of the water in the oil well. The same is true but probably not to the same extent of other minerals. The unfair taxation of precious metals will result in the hampering of the organization and the financing of promising prospects or the shut down of properties that are running very close to the margin of no profits. The following quotation from Mr. T. C. Bonney * emphasizes the difference between real estate and mineral lands: “ The mineral store of each district and of the whole earth is practically limited in quantity, be it gold, or any other metal, be it coal or any fuel. The formation of a fresh supply is a process so slow that, for all practical purposes, it may be excluded from consideration. . . . Hence the store, sooner or later, must be exhausted, now in this country, now in that. In agriculture, provided manures can be obtained, the land seems never to lose its productive power. The mine or quarry, once worked out, has played its part for good in the economy of the earth.” Conclusion Relating to Taxation of Mines. — In conclusion, it may be stated that the fairest way to tax mining properties of any class would be on their annual profits, modified by the regulating body in the case of wasteful or careless operations, capitalized at a rate of interest commensurate with the average mining risk for that class of property. By repeating these valuations at frequent intervals no hardship will be thrown on the property whose profits are on the downward grade. When it is found impossible to estimate the life of the property involved with definiteness as is usually the case in the mining of precious metals, empirical or semi-empirical methods of valuation must be adopted. Such method as establishing a taxable value equal to a percentage of or a multiple of one year’s net or gross pro- ceeds would probably be preferred to the use of an estimated market value by the mining companies. The percentage or multiple used should be fixed so as to distribute the taxes in the proper proportion between mine owners and other taxpayers. The effort to tax non-productive properties cannot be endorsed * T. G. Bonney, D.Sc., F.R.S., Dictionary of Political Economy, 1910, p. 768. 256 VALUATION, DEPRECIATION AND THE RATE-BASE except in cases where it can be clearly demonstrated that deposits economically available do exist. Methods of Valuing Oil Properties In the Appalachian oil fields, oil properties have been valued on the basis of the daily production of the wells measured after the output has reached a settled stage. The valuation is so fixed as to permit the purchaser to recover his capital in 5 to 10 years and to obtain a reasonable return on his investment. It is stated that the average sale price of producing lands varied from $800 to $1000 per barrel-day a few years ago. In Illinois, many properties changed hands during the early stages of the operations at a rate that would insure the return or amortization of capital within 18 months. This was before the life of the wells had been given a practical test. Two large valuations of oil properties have been made in California since 19oo and the methods that were adopted are of particular interest to the valuation engineer. In 1910 the Kern River oil-field was valued because of the in- tended consolidation of several separate holdings within the field. Because of the object of the investigation only values bearing comparison with one another were required. The values of all the properties involved were expressed in terms of the value of a certain selected tract of oil land located in the approximate center of the field. Concentric circles drawn about the center of the field were used to express the relative value of individual tracts as affected by their distance from the center of greatest productivity. A measurement of the productivity of all the producing wells was made covering a month’s time, thus deter- mining the production at that time and experiments were con- ducted on samples of the oil-bearing strata to determine the amount of oil that could be recovered from a known volume. The results were used as a measure of the extractable oil which could be pumped from the oil strata, the volume and area of which could be estimated. A safety factor was introduced by assuming that only one-half of the‘oil measures would be pro- THE VALUATION OF MINES AND OIL PROPERTIES 257 ductive. Subsequent experience indicates that this safety factor was not sufficient. A method of oil land valuation, which has been applied more recently, is that adopted by the engineers in valuing the proper- ties which market their product through the Independent Oil Producers Agency, which valuation had in view the merging of a number of companies in one large organization or corporation. The method used was based on the determination of a pro- duction curve for each property. A study of the history of producing wells has given basis for the assumption that the wells in a field constantly decrease in production at a rate the changes of which can be plotted in curves and, using these curves as a basis, old wells, new wells and wells not yet drilled can all be taken into account in estimating the future production of the oil lands. The total operating expenses have been estimated from existing records and the prospective future net receipts have been discounted in obtaining the present value of the prop- erties. Amortization of all capital except the salvage of sur- face improvements has been assumed to take place in ten years. ‘ History” is also prerequisite to this method and attention should be called to the fact that, because of the inaccessibility of the reservoirs of oil, the more extensive the record of previous operations, the more satisfactory will be the valuation no matter what method may be adopted. PRODUCTION AND PRICE OF COPPER, SILVER, LEAD AND ZINC IN THE UNITED STATES Plates and Tables Accompanying Chapter on Valuation of Mines and Oil Properties Figures 4 to 7, and Tables 15 to 18 which directly follow this page deal only with four of the principal metals, copper, silver, lead and zinc. The statistics given are based on the best available data and the figures are believed to be sufficiently accurate to justify their use by valuating engineers who have in hand problems in which these metals have a part. The figures submitted for the United States prices and pro- duction are those of the United States Geological Survey. 258 VALUATION, DEPRECIATION AND THE RATE-BASE Other available sources were found to be less complete and no discrepancies sufficiently large to question the reliability of these figures could be located. The world production of these metals has been taken from the annual reports of the U.S. Geological Survey supplemented by the annual statements of the Director of the U. S. Mint, Henry R. Merton & Co. (Limited) of London, and the Metallgesellschaft and Metallurgische Gesellschaft, A.-G., Frankfort-am-Main, Germany. TABLE 15. COPPER IN THE UNITED STATE ANNUAL PRODUCTION (Based on smelter returns and prices at New York City) (1880-1914) Production. Por odut of Averageannual Price received Year. world . ; price at N. Y. for Lake copper. Pounds. | Total value. produstion 1880 60,480,000 $ 11,491,000 174 $o.190 $o.195 1881 71,680,000 12,176,000 19.5 o.170 0.180 1882 91,646,000 16,038,000 22.7 0.175 0.180 1883 117,152,000 18,065,000 2601 0.154 0.154 1884 145,222,000 17,790,000 30.0 oL122 0.131 1885 170,963,000 18,293,000 34.1 0.107 0.110 1886 161,235,000 16,528,000 33.4 0.102 0.108 1887 185,227,000 21,116,000 36.9 0.114 0.120 1888 231,271,000 33,834,000 39.7 0.146 0.152 1889 231,246,000 26,908,000 40.1 0.116 0.120 1890 265,115,000 30,849,000 44.0 0.116 0.150 1891 295,812,000 38,455,000 47.2 0.130 0.125 1892 352,972,000 37,977,000 50.2 0.107 OILS 1893 339,786,000 32,055,000 50.1 0.094 0.105 1894 364,867,000 33,141,000 51.6 0.091 ake a Caden 1895 385,913,000 38,012,000 52.3 0.098 ETE 1896 460,061,000 49,457,000 54.4 0.107 SE 1897 494,078,000 54,080,000 572 oO TOONEE . Vs i a ae 1898 526,513,000 61,865,000 54.7 on 117 re] eal a 1899 568,667,000 101,223,000 54.8 0.178 a 1900 606,117,000 98,494,000 55.6 0.162 0.166 1901 602,073,000 87,301,000 51.8 0.145 0.150 1902 659,509,000 76,569,000 53.5 0.116 0.119 1903 698,045,000 91,506,000 53.2 ©. 131 0.133 1904 812,537,000 105,630,000 55.8 0.130 0.132 1905 888,784,000 137,762,000 57.5 0.155 0.156 1906 917,806,000 177,596,000 57-5 0.103 0.191 1907 868,996,000 173,799,000 54.7 0.200 0.184 1908 942,571,000 124,419,000 56.0 0.132 0.134 1909 1,092,952,000 142,084,000 58.4 0.130 0.133 1910 1,080,160,000 137,180,000 56.8 OL. 127 0.130 I9II 1,097,233,000 137,154,000 56.0 0.125 0.128 1912 1,243,269,000 205,139,000 55.0 0.165 0.164 1913 1,224,484,000 189,795,000 55.7 0.155 0.154 1914 1,150,137,000 152,968,000 ae 0.133 0.136 THE VALUATION OF MINES AND OIL PROPERTIES 259 TABLE 15. COPPER IN THE UNITED STATES (Continued) NORMAL PRODUCTION AND PRICE (Normals for ten-year periods) (1880-1914) Production. : T= _ _ Normal production, poor! peice. (inclusive). Pons Velue pounds. 225). 1880-1889 1,466,122,000 $ 192,239,000 146,612,200 $o.131 1881-1890 1,670,757%7,000 211,597,000 167,075,700 0.127 1882-1891 1,894,889,000 237,876,000 189,488,900 0.126 1883-1892 2,156,215,000 259,815,000 215,621,500 0.121 1884-1893 2,378,849,000 273,805,000 237,884,900 o.115 1885-1894 2,598,494,000 289,156,000 259,849,400 0.III 1886-1895 2,813,444,000 308,875,000 281,344,400 0.1I0 1887-1896 3,112,270,000 341,804,000 311,227,000 0.110 1888-1897 3,421,121,000 374,768,000 342,112,100 0.110 1889-1898 3,716,363,000 402,799,000 371,636,300 0.108 1890-1899 4,053,784,000 477,114,000 405,378,400 0.118 1891-1900 4,394,786,000 544,759,000 439,478,600 0.124 1892-1901 4,701,047,000 593,605,000 470,104,700 0.126 1893-1902 §5,007,584,000 632,197,000 500,758,400 0.126 1894-1903 5,365,843,000 691,648,000 536,534,300 0.129 1895-1904 5,813,513,000 764,137,000 581,351,300 0.131 1896-1905 6,316,384,000 863,887,000 631,638,400 o.137 1897-1906 6,774,129,000 992,026,000 677,412,900 0.146 1898-1907 7,149,047,000 I,III,745,000 714,904,700 0.155 1899-1908 7,565,105,000 1,174,299,000 756,510,500 0.155 1900-1909 8,089,390,000 1,215,160,000 808,939,000 0.150 1901-1910 8,563,433,000 1,253,846,000 856,343,300 0.146 1902-1911 9,058,593,000 1,303,699,000 905,859,300 0.144 1903-1912 9,642,353,000 1,432,269,000 964,235,300 0.149 1904-1913 10,168,792,000 1,530,558,000 1,016,879,200 0.151 1905-1914 10,506,392,000 1,577,896,000 1,050,639,200 0.149 260 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 16. SILVER IN THE UNITED STATES ANNUAL ProDUCTION (1880-1914) Annual production. Average Year. Por centroid commercial Troy ounces. Total value. Falut pet ounce: 1880 30,318,700 $34,717,000 40.6 $1.15 1881 32,257,800 37,657,500 40.8 1.13 1882 36,196,900 41,105,900 41.9 114 1883 35,732,800 39,618,400 40.1 T.0% 1884 37,743,800 41,921,300 46.3 1.1% 1885 39,909,400 42,503,500 43.6 1.07 1886 39,694,000 39,482,400 42.5 0.99 1887 41,721,600 40,887,200 42.9 0.98 1838 45,792,700 43,045,100 42.2 0.94 1889 50,004,500 46,838,400 41.7 0.94 1890 54,516,300 57,242,100 43.2 1.05 1801 58,330,000 57,630,000 42.5 0.99 1892 63,500,000 55,662,500 41.5 0.87 1893 60,000,000 46,800,000 36.4 0.78 1894 49,500,000 31,422,100 30.1 0.63 1895 55,727,000 36,445,500 33.2 0.65 1896 58,834,800 39,654,600 37-5 0.68 1897 53,860,000 32,316,000 33-6 0.60 1898 54,438,000 32,118,400 32.2 0.59 1899 54,764,500 32,858,700 32.5 0.60 1900 57,647,000 35,741,100 33.2 0.62 1901 55,214,000 33,128,400 31.9 0.60 1902 55,500,000 20,415,000 34-1 0.53 1903 54,300,000 29,322,000 32.4 0.54 1904 57,682,800 33,456,000 35.% 0.58 1905 56,101,600 34,222,000 32.6 0.61 1906 56,517,900 38,256,400 34.2 0.68 1907 56,514,700 37,299,700 30.7 0.66 1908 52,440,800 28,050,600 25.8 0.53 1909 54,721,500 28,455,200 25.8 0.52 1910 57,137,900 30,854,500 25.8 ©.54 I9II 60,399,400 32,615,700 26.7 0.53 1912 63,766,800 39,197,500 28.4 0.615 1913 66,801,500 40,348,100 yr neg 0.604 1914 72,455,100 40,067,700 al 5 in eet 0.553 THE VALUATION OF MINES AND OIL PROPERTIES 261 TABLE 16. SILVER IN THE UNITED STATES (Continued) NORMAL PRODUCTION AND PRICE (Normals Based on ten-year periods) (1880-1914) : od Production. Normal prod Normal price ji ly : 0 iy raat Gen-year aver- Pounds. Value. : 1880-1889 389,462,200 $407,776,700 38,946,220 81.045 1881-1890 413,659,800 430,301,800 41,365,980 1.04 1882-1891 439,732,000 450,274,300 43,973,200 1.025 1883-1892 467,035,100 464,830,900 46,703,510 0.995 1884-1893 491,302,300 472,012,500 49,130,230 0.96 1885-1894 503,058,500 461,513,300 590,305,850 0.915 1886-1895 518,876,100 455,455,300 51,887,610 0.88 1887-1896 538,016,900 455,627,500 53,801,690 0.845 1888-1897 550,155,300 447,056,300 55,015,530 0.813 1889-1898 558,800,600 436,129,600 55,880,060 0.78 1890-1899 563,470,600 422,149,900 56,347,060 0.75 1891-1900 566,601,300 400,648,900 56,660,130 0.703 1892-1901 563,485,300 376,147,300 56,348,530 0.67 1893-1902 555,485,300 349,899,800 55,548,530 0.63 1894-1903 549,785,300 332,421,800 54,978,530 0.605 1895-1904 557,968,100 334,455,700 55,796,810 0.60 1896-1905 558,342,700 332,232,200 55,834,270 0.595 1897-1906 556,025,800 330,834,000 55,602,580 0.595 1898-1907 558,680,500 335,817,700 55,868,050 0.60 1899-1908 556,683,300 331,749,900 55,668,330 0.595 1900-1909 556,640,300 327,346,400 55,664,030 0.59 IQOI-IQIO 556,131,200 322,459,800 55,613,120 0.58 I902-IQTI 561,316,600 321,947,100 56,131,660 0.575 1903-1912 569,583,400 331,729,600 56,958,340 0.58 1904-1913 582,084,900 342,755,700 58,208,490 0.59 1905-1914 596,857,200 349,367,400 59,685,700 0.585 262 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 17. LEAD IN THE UNITED STATES ANNUAL PRODUCTION (Based on smelter returns and prices at New York City) (1880-1914) Annual production. yest ; i RTT Pounds. Total value. 1880 195,650,000 $ 9,782,500 2.7 $o.050 1881 234,170,000 11,240,160 24.4 0.048 1882 265,780,000 12,624,550 26.2 0.049 1883 287,914,000 12,322,719 20.3 0.043 1884 279,794,000 10,537,042 29.1 0.037 1883 258,824,000 10,469,431 26.4 0.039 1886 261,258,000 12,200,749 24.3 0.046 1887 201,400,000 13,113,000 24.9 0.045 1888 302,838,000 13,399,256 24.8 0.044 1889 312,794,000 13,794,235 26.0 0.039 1890 287,260,000 12,668,166 21.6 0.045 1891 357,108,000 15,534,198 26.4 0.043 1892 347,308,000 13,892,320 22.7 0.040 1893 327,964,000 11,839,590 23.3 0.037 1894 318,662,000 9,942,254 23.4 0.033 1895 340,000,000 11,220,000 23.8 0.032 1896 376,000,000 10,528,000 25.3 0.030 1897 424,000,000 14,885,728 26.8 0.036 1898 444,000,000 16,650,000 25.9 0.038 1899 421,000,000 18,945,000 29.9 0.045 1900 541,648,000 23,561,688 29.0 0.044 1901 541,400,000 23,280,200 27.6 0.043 1902 540,000,000 22,140,000 27.3 0.041 1903 564,000,000 23,520,000 28.0 0.042 1004 614,000,000 26,402,000 20.4 0.043 1905 604,000,000 28,690,000 29.0 0.047 1906 700,306,000 39,917,442 33.7 0.057 1907 750,198,000 39,760,494 35.0 0.053 1908 621,524,000 26,104,008 27.0 0.042 1909 726,638,000 31,245,434 32.6 0.043 1910 778,422,000 34,250,568 32.2 0.044 1911 811,726,000 36,527,670 33.1 0.045 1912 830,790,000 37,385,550 32.4 0.045 1913 872,860,000 38,405,840 34.4 0.044 1914 1,025,588,000 39,997,932 AR 0.039 THE VALUATION OF MINES AND OIL PROPERTIES 263 TABLE 17. LEAD IN THE UNITED STATES (Continued) NORMAL PRODUCTION AND PRICE (Normals for ten-year periods) (1880-1914) Production. y Ten riods : Normal price Ty = Mion, pounds. | (ten-year aver. Pounds. Value. : 1880-1889 2,690,602,000 $119,483,500 269,060,200 $o0.044 1881-1890 2,782,212,000 122,369,200 278,221,200 0.044 1882-1891 2,905,150,000 126,663,200 290,515,000 0.044 1883-1892 2,986,678,000 127,931,000 298,667,800 0.043 1884-1893 3,026,728,000 127,447,900 302,672,800 0.042 1885-1894 3,065,596,000 126,853,200 306,559,600 0.041 1886-1895 3,146,772,000 127,603,800 314,677,200 0.041 1887-1896 3,261,514,000 126,003,100 326,151,400 0.039 1888-1897 3,394,114,000 127,703,800 339,411,400 0.038 1889-1898 3,535,276,000 130,954,500 353,527,600 0.037 1890-1899 3,643,302,000 136,105,300 364,330,200 0.037 1891-1900 3,897,690,000 146,998,800 389,769,000 0.038 1892-1901 4,081,982,000 154,744,800 408,098,200 0.038 1893-1902 4,274,674,000 162,992,500 427,467,400 0.038 1894-1903 4,510,710,000 174,572,900 451,071,000 0.039 1895-1904 4,806,048,000 191,132,600 480,604,800 0.040 1896-1905 5,060,048,000 208,602,600 506,004,800 0.041 1897-1906 5:394,354,000 237,992,000 539,435,400 0.044 1898-1907 5,720,552,000 262,866,800 572,055,200 0.046 1899-1908 5,898,076,000 272,320,800 589,807,600 0.046 1900-1909 6,203,714,000 284,621,200 620,371,400 0.046 IQ0I-IQI0 6,440,488,000 295,310,100 644,048,800 0.046 1G02—-IQI1 6,710,814,000 308,557,600 671,081,400 0.046 1903-1912 7,001,604 ,000 323,803,200 700,160,400 0.046 1904-1913 7,310,464,000 338,689,000 731,046,400 0.046 1905-1914 7,722,052,000 352,284,938 772,205,200 0.046 204 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 18. ZINC IN THE UNITED STATES ANNUAL PRODUCTION (Based on smelter returns and prices at St. Louis) (1880-1914) Annual production. Year. = En. ts Tegel Pounds. Total value. 1880 46,478,000 $ 2,277,432 0.1 $o0.055 1881 53,600,000 2,680,000 9.3 0.052 1882 67,530,000 3,646,620 iT.x 0.053 1883 73,744,000 3,311,100 15.2 0.045 1884 77,088,000 3,422,707 11.8 0.044 1885 81,376,000 3,539,856 12.4 0.043 1886 85,282,000 3,752,408 1257 0.044 1887 100,680,000 4,782,300 14.7 0.046 1888 111,806,000 5,500,855 13.3 0.049 1889 117,720,000 5,791,824 15.7 0.05 1890 127,366,000 6,266,407 16.4 0.055 1891 161,746,000 8,033,700 19.9 0.05 1892 174,520,000 8,027,920 20.8 0.046 1893 157,664,000 6,306,560 18.7 0.04 1894 150,656,000 5,288,026 17.8 0.035 1895 179,372,000 6,278,020 19.4 0.036 1896 162,998,000 6,519,920 17.4 0.039 1897 199,960,000 8,498,300 20.4 0.041 1898 230,798,000 10,385,910 22.3 0.046 1899 258,102,000 14,840,865 23.9 0.058 1900 247,772,000 10,654,196 ass 0.044 I90I 281,644,000 11,265,760 25.0 0.041 1902 313,354,000 14,625,596 26.0 0.048 1903 318,438,000 16,717,995 25.2 0.054 1904 373,404,000 18,670,200 26.9 0.051 1905 407,698,000 24,054,182 28.0 0.059 1906 399,388,000 24,362,668 2517 0.061 1907 447,490,000 26,401,910 27.5 0.059 1908 381,498,000 17,930,406 23.9 0.047 1909 460,450,000 24,864,300 27.0 0.054 1910 504,958,000 27,267,732 27.6 0.054 1911 543,242,000 30,964,794 27.6 0.057 1912 647,814,000 44,699,166 30.3 0.069 1913 674,504,000 37,772,224 30.8 0.056 1014 686,836,000 35,028,636 RC ER WTR 0.051 THE VALUATION OF MINES AND OIL PROPERTIES 206 5 TABLE 18. ZINC IN THE UNITED STATES (Continued) NORMAL PRODUCTION AND PRICE (Normals for ten-year period) (1880-1914) Production. : : Normal Peden periods - Normal production. a. Pounds. Value. age). 1880-1889 815,304,000 § 38,705,100 81,530,400 $o.047 1881-1890 896,192,000 42,694,100 89,619,200 0.048 1882-1891 1,004,338,000 48,047,800 100,433,800 0.048 1883-1892 1,111,328,000 52,428,100 111,132,800 0.047 1884-1893 1,195,248,000 55,424,600 119,524,800 0.046 1885-1894 1,268,816,000 57,289,900 126,881,600 0.045 1886-1895 1,366,812,000 60,028,000 136,681,200 0.044 1887-1896 1,444,528,000 62,795,500 144,452,800 0.043 1888-1897 1,543,808,000 66,511,500 154,380,800 0.043 1889-1898 1,662,800,000 71,396,500 166,280,000 0.043 1890-1899 1,803,182,000 80,445,600 180,318,200 0.045 1891-1900 1,923,588,000 84,833,400 192,358,800 0.044 1892-1901 2,043,486,000 88,065,500 204,348,600 0.043 1893-1902 2,182,820,000 94,663,200 218,282,000 0.043 1894-1903 2,343,594,000 105,084,600 234,359,400 0.045 1895-1904 2,566,342,000 118,456,800 256,634,200 0.046 1896-1905 2,794,668,000 136,233,000 279,466,800 0.049 1897-1906 3,031,058,000 154,075,800 303,105,800 0.051 1898-1907 3,278,588,000 171,979,400 327,858,800 0.0525 1899-1908 3,429,288,000 179,523,900 342,928,800 0.052 1900-1909 3,631,636,000 189,547,300 363,163,600 0.052 190I-IQIO0 3,888,822,000 206,160,800 388,882,200 0.053 1902-1911 4,150,420,000 225,859,800 415,042,000 0.054 1903-1912 4,484,380,000 255,933,400 448,438,000 0.057 1904-1913 4,840,446,000 276,987,600 484,044,600 0.057 1905-1914 5:153,878,000 293,346,000 513,387,800 0.057 266 VALUATION, DEPRECIATION AND THE RATE-BASE COPPER 1880-1914 : pRNAL AVER GE : rer. Lb.) |_so18 I 3 Xi $0.18 ~ 0.16 0.16 o | A014 W| 0.14 IRL - o 0.12 0.12 Q & 0.10 | 0.10} | 0.0% | 0.08] Pound- 1200009¢ 11000 0€ ¥* Co 3000016 16000000“ I 4000000" | 2000000° 3. 4. SILVER 1880-1914 $1.40 | ‘ TT CRE i 8 ry IE EED fs 1.2000 [F& ie ; gz | | 5 [| 0.90 20.80 I | 0.50] A 0.60 1 4 0:50 . . Yo Ounce ro 0 000 | 60 000 00 | 50 00° “0.000 40 000 Ls || tA (00 000 | — (50 000 Gr ft ey FiG. 5. THE VALUATION OF MINES AND OIL PROPERTIES 267 LEAD 1880-1914 _ seh = 7 go Res | i 0.04 #7 1& i 80. yt 4 0.07 fo | Produstic in Pound [700 A 500 - an~ F106. 7. 268 VALUATION, DEPRECIATION AND THE RATE-BASE BIBLIOGRAPHY Valuation of Mines and Oil Properties “The Valuation of Metal Mines,” by T. A. Rickard, International Engineering Congress, Oct., 1915. “Principles of Mine Valuation,” by J. R. Finlay, Columbia School of Mines Quar- terly, Jan., 1913. “The Valuation of Mines,” by J. B. Kendall, Mining Magazine, Nov. 21, 1914. “Valuation of Mining Shares,” by Newton B. Knox, Mining and Scientific Press, Vol. g6, p. 773. “Appraisal of Mining Properties of Michigan,” State Board of Tax Commis- sioners, IQII. “Study of Method of Mine Valuation and Assessment,” Wisconsin Geological and Natural History Survey, 1914. “Principles of Mine Taxation,” by E. B. Kirby, Engineering and Mining Journal, Oct. 28, 1011. “Mine Taxation,” by Heath Steele, Engineering and Mining Journal, Aug. 29, 1914. “Initial Report of Nevada Tax Commission, 191 3-1914,” Nevada Tax Commission. “« Assessment of Mines, 1915,” Nevada Tax Commission. “Suggestions Regarding Mining Investments,” John Hays Hammond (address before Financial Forum, N. Y.), Engineering and Mining Journal, Vol. 89, p- 8. “Safety of Judicious Mining Investments,” by J. Parke Channing, Engineering and Mining Journal, Vol. 89, p. 211. “The Classification of Public Lands,” by G. O. Smith and others, Bulletin No. 537, United States Geological Survey. “The Cost of Mining,” by J. R. Finlay, McGraw-Hill Publishing Co., 1909. “Principles of Mining,” by H. C. Hoover, McGraw-Hill Publishing Co., 1909. «Valuation of Mines and Mineral Lands,” by H. M. Chance, Trans. A.LM.E., 1904, Abstract from same, Engineering and Mining Journal, Vol. 78, p. 515. «Valuation of Coal Lands,” by H. M. Chance, Trans. ALM.E., Vol. 47, p. 111. «Valuation of Public Coal Lands,” by G. H. Ashley, Bulletin No. 424, U. S. Geo- logical Survey. “The Valuation of Anthracite Mines,” by R. V. Norris, International Engineering Congress, Oct., 1915. “Evaluating Coal Properties in Western Canada,” by R. W. Coulthard, Inter- national Engineering Congress, Oct., 1915. “Mine Taxation,” by H. M. Chance, Proceedings American Mining Congress, Oct., 1013- «Taxation of Coal Lands,” by R. V. Norris, Proceedings American Mining Con- gress, Oct., 1913, also Colliery Engineer, Feb., 1914. “Ore Valuation of Gold Mines,” by C. B. Horwood, Trans. A.LM.E., Vol. 39, p- 68s. « Appraisal of Michigan Mines,” by J. R. Finlay, Engineering and Mining Journal, Sept. g to Oct. 14, 1911. (Serial.) THE VALUATION OF MINES AND OIL PROPERTIES 269 “Valuation of Iron Mines,” by J. R. Finlay, Trans. A.I.LM.E., Vol. 45, p. 282. “Observations on the Appraisal of the Iron Mines of Michigan,” Engineering and Mining Journal, March 6, 1915. “Michigan Iron Ore Reserves and Method of Appraisal for Taxation,” by R. C. Allen, Mining and Engineering World, Sept. 12, 1914. “Iron Mine Assessments in Minnesota,” by D. E. Woodbridge, Engineering and Mining Journal, Vol. 84, p. 967. “Valuation of Oil Lands and Properties,” by M. E. Lombardi, Trans. International Engineering Congress, Oct., 1915. “The Valuation of Oil Lands,” by Wm. Forstner, Mining and Scientific Press, Nov. 4, 1011. “Examination of Petroleum Properties,” by Chas. Janin, Mining and Scientific Press, Vol. 101, p. 269. “Valuation of Oil Wells,” Mining and Scientific Press, Vol. 104, p. 284. (Editorial.) “The Valuation of Mining Areas on the Rand,” by W. F. Wilkinson, T.I.M. and M. Vol. 18, p. 348 — 6 pages. “Valuation of Oil Wells in the Appalachian Fields,” Mining and Scientific Press, Feb. 17, 1912. “Petroleum Mining and Oil Field Development,” by A. Beeby Thompson, Lon- don, Lockwood, 1910. (“Production and Life of Oil Fields,” pp. 83-88.) “The Oil Fields of Russia and the Russian Petroleum Industry,” by A. Beeby Thompson, C. Lockwood & Son, 1904. (“Valuation of Oil Properties,” pp- 382-4.) “Present Conditions in the California Oil Fields,” by M. L. Requa, Trans. A.IM.E., Vol. 42, p. 837. “Estimating Productive Capacity of Oil Lands,” by R. P. McLaughlin, Western Engineering, July, 1914. “Estimation of Oil Reserves,” by C. W. Washburne, Bull. A.I.M.E., Feb., 1915. “Factors in Cost of Oil Production,” by Wm. R. Jewell, Mining and Scientific Press, July 8, 1911. “Depreciation as applied to Oil Properties,” by P. W. Henry, Bull. ALM.E., Jan., 1915. “Comparative Costs of Rotary and Standing Drilling,” by M. L. Requa, Bull. AIM.E,, Feb. 1915. CHAPTER XIV THE STANDARD OF VALUE (Note: In this chapter there is presented the substance of an address delivered by the author in February, 1920, before the Commonwealth Club of California. He was at that time President of the Club.) During the world war and the years immediately following, it was brought home to millions of people in this country and abroad, that there is something radically wrong with the function- ing of the generally approved and accepted monetary systems of all civilized countries. The rapid decline of the purchasing power of the money unit, whether the same is called pound, dollar, franc, lire, mark, ruble or yen, has been one of the immedi- ate results of the world war. This has set the masses to wonder- ing and to thinking. They are astounded at the sudden very considerable shrinkage in the value of long-time credits and the country’s best thought is directed toward finding a remedy. Credits in the sense in which here used should be considered to mean the right to obtain a specified, definite sum of money at some future time. There has been shrinkage of the real value, not only of the bond which was bought before the war, its value being measured by the desirable things which the money which it commands will buy, but also, in every wage and salary which was not increased in full correspondence with the increase in the cost of living. When employment is accepted at an agreed wage or salary it is ordinarily understood that the wage or salary will continue either for a fixed term or for an indefinite time in the future. In either case time is an element which enters into the transaction, and whenever any considerable length of time must elapse before the transaction is complete the parties thereto are, in a sense, speculating. They stand to gain or lose in direct proportion to the change in the purchasing power of the dollar (the dollar representing any money unit) during the time in- volved in the transaction. 270 THE STANDARD OF VALUE 271 To illustrate: In the first six months of 1919 the dollar in the United States was worth on an average only forty-three per cent as much as during the ten-year period, at the beginning of this century, 1900 to 1909. This statement applies to the gold dollar, its value being measured by the amount of the multipli- city of things (in proportion to their consumption by the nation) which it will buy. This great fall in value was due to the new economic conditions resulting from the war, such as inflation of currency, war debts and high taxation. The bond holder had sacrificed at that time, if measured in the desirable things which money will buy, more than one-half of that portion of his wealth which he held in long-time credits. But he was not the only loser. The salaried class had likewise been hard hit during the same period. Salaries, more particularly those of men and women in the public service of school teachers, of post office employees, of firemen, of policemen and public officials and also those of clerks, and of the whole class of salaried professional men — not to forget the clergy — had remained comparatively stationary. It is this salaried class, dependent as they ordi- narily are upon their immediate earnings to meet their family requirements, which had to stint itself. Here was found a real sacrifice with a resultant reduction in the standard of living, temporary to be sure, which was almost universally accepted as a necessary sacrifice for the welfare of the country. The owners of real estate and the wage earners were among those who were least affected in the years during and immediately following the war by the decline of the purchasing power of the dollar. The real estate owner found that property values — measured by the dollar — had gone up, though not perhaps in the same proportion as the value of the dollar had gone down. The wage earner, well organized, kept close watch of the increase of cost of food and other necessities and made demands from time to time for increase of compensation, which to the extent of their reasonableness, gauged by the increased cost of living, he was bound to secure in the long run. He was, moreover, not back- ward in asking for all that circumstances would allow. Statis- 272 VALUATION, DEPRECIATION AND THE RATE-BASE tics compiled by the United States Department of Labor show, for example, that near the peak of the high prices after the war the cost of living was about 125 per cent greater than the average cost of living during the ten years 1goo to 19og, while wages at that time were 109 per cent greater than the wages during the same base period. A comparison of the changes in the cost of living covering the period 18go to 1919 shows the remarkable agreement between the cost of living and the wage scale and shows how quickly a change in the cost of living is followed by a change in wages. (See diagram, Fig. 8.) The main trouble in connec- tion with this matter is the fact that the change is not automatic, that the wage earner usually has to fight for each increase and that the employer throws every difficulty in the way when he finds that an increase of wages is in order. The question naturally presents itself whether means could not be found to eliminate the speculative feature from contracts involving a future transfer of money ownership from one person to another. Is it desirable, or necessary, in other words, to specify the dollar as the unit of value when a deferred payment is involved? The money unit is a definite quantity of some metal such as gold or silver of prescribed fineness. This unit is defined by the government and is commonly, almost universally, ac- cepted as a standard of value. It, however, falls far short of being a satisfactory standard, though admittedly a convenient one. Itisnot,in fact, a standard at all, or at best only a momen- tary standard. It lost, even in our country, as above stated, more than one-half of its value during the five years of the war, and is still now (1926) far below its pre-war value. Value ex- presses the measure of the desirability of anything in comparison with other desirable things, and this value can only be deter- mined and expressed by making such a comparison. Money is desirable because it can be exchanged for other things which are necessary or are desired for human comfort or pleasure. In view of the defects of money as a standard, having value which changes in consequence of currency inflation or depletion, and from other causes, some other less variable standard of value to supplement bs + u vo Eg 3 2 5 } z o: F too C. byt c. = - 81 85a; > 02 : 3 ; 20 tS | = 2 9] Fic. 8. WAGES PER HOUR AND THE COST OF LIVING. The index numbers shown in this diagram have been calculated from the index numbers determined by the Bureau of Labor Statistics of the U. S. Department of Labor from the wholesale prices of a large number of commodities (now over 290 articles). N Being weighted averages they may be considered to represent the relative cost of living. Some portions of the curve showing wages os per hour were determined from wages in 192 occupations, others had to be determined from wages in but a few industries. The curve is offered subject to correction. 274 VALUATION, DEPRECIATION AND THE RATE-BASE money when functioning as a standard of value is desirable and to prevent such injustice as was done in Russia, in Austria, in Germany and even in France, and to a less degree in the United States and other countries, such a substitute must be found. This is not to be sought among the metals but rather among the things which in civilized communities are necessary to meet the wants of man. The ideal, and what would appear to be the natural, unit of this character, to supplement (not to replace) money, is that which, in any country, is made up of definite quantities of staples such as food and fuel, iron and each of the many other things which a family requires to live in ordinary comfort — each of these several things in fairly close proportion to the nation’s annual consumption thereof. The introduction of such a supplementary commodity unit into the industrial and business life of the country would be simple. Money would still be necessary and would continue to be used as a medium of exchange, as at present, in all ordinary transactions involving only a negligible time element. Purchase and sale transactions would be conducted as is now customary, cost being determined and the price fixed in terms of money. Alongside of such a norm the use of money would be subject to certain limitations, easily recognized, which should long ago have been prescribed Let the proposed unit, for example, be called a “ com ” (ab- breviated from com-modity unit) and let it be supposed that, to start with, the quantities of each of the 300, or more, things which the U. S. Department of Labor takes into account when it fixes the general commodity index number” have been determined, which, in the proportion of general consumption thereof, would at the average wholesale prices during the ten years 19oo to 1gog (incl.) have been purchasable for some round number of dollars, say $1000. One thousandth part of these several quantities considered collectively, may then be con- sidered “ one com.” Once fixed in this fashion and defined by congressional action, the “ com ”’ would remain a definite per- manent legal unit until modified — should such modification THE STANDARD OF VALUE } become necessary — by later congressional action. The real value of the dollar would, upon adoption of such a unit, there- after be expressed in coms or by inversion, as is now the practice, the number of dollars equivalent to a com, or to 100 coms, would be noted from day to day, from month to month and from year to year. (See diagrams, Figs. 9 and 10). All payments would be made as they are today in money, the amount of currency equivalent to any number of coms being ascertained by the simple process of multiplication. Is the com as a measure of value necessary? Is it practical? Although the first question has already been answered, a few more thoughts on this phase of the problem may be pertinent. Fair compensation for service rendered should never fall below the point a little better than just affording a reasonable living. Any condition which prompts the offer of service at less than this lower limit is only temporary; breeds discontent and ultimately results in economic revolution. Whenever proposed compensation for services is expressed in terms of money without further provision, as has heretofore been the universal custom, the agreement to pay carries no assurance of being continuously, that is, for an indefinite time in the future, sufficient to meet the above specification. It may be adequate at the time the agreement is entered into but who can foresee to what extent the value of money may change? In making such agreements something else besides the immediate adequacy of the wage or salary requires consideration. There have been times in the history of all civilized countries and there will be others, though, perhaps, never another as distressing as the one of recent years, when the prices of commodities were, are. or will be rising rapidly and the value of money was, is, and will be correspondingly lessening. There is, at such times, an increase in the money requirement of the family. The prevailing salaries and wages become inadequate. Something must be done. The employee demands relief. The employer, in such circumstances, reluctantly accedes to the demands of his employees and adds the resulting increase of cost to the sale price of his output. 278% a0 : = 240 230 ! k 230 N > 090 220 (@) 210 | 219 wl laf 90 iso = 80 | | 1g} i 60 | 160 te 150 > = 150 , 140 | 140 ‘ & 130 ; = 120 120! S 1110 Ba 110° 100 _ a 190 mst [290 o | _! af os eal J9 = 60 ola ol EE 40 : © ! 40 r= SEE al i i “ic.oelerOnsRY | | 30 2 lo |. | WSR. 0.4 { | hil mr JF pe | [| Ue mlelale Ella lslelele- ini mle ~Toiolal=lale]l=Tulelsls low hel 1 1 7 | EY 2 il Fic. . THE EQUIVALENT IN DOLLARS OF 100 COMMODITY UNITS. This diagram is based on index numbers determined by the Bureau of Labor Statistics of the U. S. Department of Labor, from the wholesale prices of a large number of articles (now more than 290) which taken collectively in the proportion of annual Con bi pa at the average prices of the 10 years, 19oo to 190g, have been used to establish a Commodity Unit — called for con- | g ¢ = <7 = < t= " 10: g§ » 4 d 60 & dd & & 8&8 07 ) - A Fic. to. THE NUMBER OF COMMODITY UNITS PURCHASABLE WITH ONE HUNDRED DOLLARS. D This diagram is based on the general index numbers for all commodities, as determined by the Bureau of Labor Statistics of the ~¥ U. S. Department of Labor. ~y 278 VALUATION, DEPRECIATION AND THE RATE-BASE But the generally accepted remedy, the granting of more pay, is at best only a temporary expedient. Scarcity of labor is not responsible for high prices. It may be assumed that there is and always will be an abundance of labor to produce and to distribute the things that man demands in order to live in comfort. High prices are themselves an ade- quate stimulant to the production in quantity of all varieties of things which are in demand. But the occasional periods during which there is a rapid advance of what is commonly called “ the cost of living >’ have the gradual but none the less certain effect of reducing the amount, despite their possible abundance, of the desirable things which the family can afford. The standard of living at such times gradually comes down when considered by averages for an entire nation. A rise in the cost of living is always sure to accompany or to closely follow an inflation of currency and will, naturally, prevail when countries are running heavily into debt — when, in con- sequence, taxes are high and the individual strives to earn more dollars than theretofore with the same output of effort, in order that the greater number of dollars wanted by the government for taxes, and required to meet his family requirements, shall be forthcoming. The value of the money unit measured in terms of commodities is at such times dropping down. Everybody wants more of the currency for every service performed. Wages must go up. All prices rise, and as they rise there is new de- mand for higher wages and salaries. Some one has said that the movement thus goes on in an endless circle. The illustration would perhaps be more apt if an ever widening spiral were sub- stituted for the circle. There has been no remedy for such conditions, heretofore, except as found in the succeeding periods of business depression such as have been recurrent during more than a hundred years with rather surprising regularity at intervals of about twenty years. At such times the over speculation incident to rising prices, frequently inflated, particularly of land, has passed its crest. Appreciation has been forestalled. New investments in land cease. Loans are THE STANDARD OF VALUE called in and cannot be paid. Government and other em- ployees are discharged. Public improvements are stopped. Taxes are reduced. The volume of business shrinks. Capital becomes timid. The value of the dollar goes up. Everybody by spending less and curtailing requirements below normal con- tributes his share to make matters worse. But hard times as a remedy for high prices, implying the reduction of the great mass of people to a condition in which means are lacking with which to buy the cheapening necessaries, are worse than the feverish condition of business activity at the other extreme when every one complains of high prices. Because of these possible extremes an adequate wage which is to persist for an indefinite time can not be satisfactorily defined in terms of money. Compensation must be fair alike to the employee and the employer. The latter will always make it his endeavor to secure services that are satisfactory at the lowest possible rate. The former will contend for a living wage and in the long run will accept nothing less. Agreements momentarily satisfactory to both parties may be reached; but there is no certainty, so long as money is named as the consideration, that during the period which the agreement is to cover — generally an indefinite future — the compensation will always buy as much shelter and clothing, and food, fuel, education, transportation and recreation as it would at the time when it was agreed to be fair and adequate. This element of uncertainty, this specula- tion in futurities, can be successfully eliminated, as has already been stated, by reference in all such agreements to the * com instead of the “ dollar.” Turning now to the question as to whether it would be practical to introduce the com to serve alongside of the money unit, the following possibilities, subject to more or less modification during the transition period, may serve as illustrations. Take first an industrial establishment such as a factory with an output which is placed on the market at the fair average cost of production plus a profit. The labor item, rents and perhaps, too, the cost of borrowed capital, would in this case be computed 270 280 VALUATION, DEPRECIATION AND THE RATE-BASE in coms, other items in dollars. That increment of cost which is expressed in coms would be converted into dollars according to the prevailing money equivalent of the com which would be ascertained at intervals of a month or more, and the sale price would be modified from time to time to the extent that the vari- able money equivalent of the com affects the cost of production. The retail merchant would have no greater difficulty than at present in marking his goods. He would pay his clerks in coms, perhaps his rent also, and based on the proportion of the cost which is incurred in coms and the fluctuating number of dollars in a com he would, from time to time, add to or take from his listed prices. Ordinarily the change in the value of the dollar would be so slight that within the time that goods are on his shelves no re-marking would be necessary. The capitalist, too, would soon learn how to take advantage of the protection which a commodity unit would afford him. Why should he not, in making a loan, express the amount thereof in terms of coms instead of in terms of gold coin. He would have loaned rooo coms instead of $1130 in 1910 and when his capital was returned he would have gotten back 1000 coms which in terms of money might then have been equivalent to more or less than $1130 according to whether the value of the dollar had gone down or up. Under our present system as al- ready stated every promise to pay a definite number of dollars at a future date involves a speculation in the rise and fall of the value of the dollar. Thus, for example, the bond holder, no matter how dependable his securities, finds that during the five years 1914 to 1919, the bonds which he held shrank to less than one-half of their original real value (from 87 coms per $100 to 43). He may be as well off in dollars as he ever was, but the part of his wealth in credits, measured by the desirable things which his dollars will command, was nevertheless taken from him to the extent of more than one-half. Money in this period was made more abundant, and was made to flow more rapidly. More units thereof are even now required to accomplish any particular purpose than before the war. If such credits, bonds, THE STANDARD OF VALUE for example, as the capitalist holds, were in commodity units (coms) the government would have no power by inflation or otherwise to destroy the accumulated wealth of the individual unless he were foolish enough to hoard dollars. All govern- ments of countries which are heavily in debt naturally favor a decline of the value of the money unit because this decline carries with it a reduction of the tax burden. Our national debt of $20,000,000,000 or more with the dollar now at two- thirds of its pre-war value, is no greater burden for the nation to carry than $13,000,000,000 would have been before the phenomenal shrinkage of the purchasing power of the dollar. If all things were managed fairly, every one should be earning a number of dollars inversely proportional to the purchasing power of the dollar. The use of the com would bring this about. For the capitalist, however, who finds his bonds and other securities shrinking in value, there has been no general relief. His sacrifice has been real and he must expect no protection so long as he sub- mits to the prevailing custom. He, too, however, would hereafter get protection, as already stated, if some plan were adopted of expressing value in terms of commodity units. The banker would continue to deal in money as he does today except, however, that he would have recourse to the more stable unit of value, the com, when he lends money for a period of such dura- tion that the value of the money unit may materially change before the loan becomes due.* Rents, salaries and wages could be specified in coms instead of in dollars. In the case of the government employees whose prospective compensation in dollars must be forecast for a year, means would have to be found if this compensation be expressed In coms to make the tax levy adequate. The money equivalent of the commodity unit during the quarter preceding the fixing * As an example of how this may be done it may be noted that the employees of the Philadelphia Rapid Transit Co. are now being paid on a scale of wages con- trolled by a Commodity Index Number and that the Rand Cardex Companies have recently issued securities in the form of stabilized bonds, under the terms of which the commodity index number will determine the number of dollars per annum which the money invested in the bond will earn. 281 282 VALUATION, DEPRECIATION AND THE RATE-BASE of the tax levy should, in this case, be acceptable as a sufficiently close approximation of its money equivalent throughout the ensuing year. In such event the salary permanently fixed in coms would be convertible throughout each year into money at the equivalent sum thus determined. Similar provision could be made, too, when rents and the like are to be covered in annual budgets. Public utility rates might be established as at present, but with the proviso that at intervals of a year these rates would auto- matically increase or decrease in some relation to the change in the value of money as measured by the com. It may be noted that under such a system of evaluating rela- tive desirability of things and services, each country would proceed independently. The commodity unit could be adapted to the local standard of living. The commodities which taken collec- tively will best represent value, in the sense of desire to possess, would, in each country, be selected with a view to their inclu- sion in quantities bearing a fair relation to their proportional contribution to the requirements of the family and the indi- vidual. As already stated, money as a medium of exchange, when the commodity unit comes into general use, will be as necessary as heretofore. The commodity unit will take a place on the list of the many things subject to price quotation. Would it not be possible, may be asked, to let the com supplant the dollar, there- by accomplishing what Prof. Irving Fisher would bring about — the stabilization of the dollar? This would involve, as Professor Fisher points out, the acceptance of a variable weight of gold as the money unit. Legislation would be required and complicated government control, the successful accomplishment of which does not appear to be within easy reach. Nor, as already pointed out, is it necessary. Alongside of a commodity unit, whether legally recognized, or not, money would be used as it is used, today, and would always be specified in transactions which are unaffected by the time element. But money would no longer function as the standard of value to determine the amount of a THE STANDARD OF VALUE z future obligation. Whenever the time element enters into a transaction as in making a loan, or in entering into a lease, or in agreeing upon a salary or wage, which is expected to continue for an indefinite time, the money unit would be supplanted by the commodity unit, by the com, because of the undoubted greater stability of the value of the latter; but, ultimately, payment would still be made in money. Having thus attempted to show that a value unit is conven- iently at hand, and that its general adoption is practical, it remains to show that its introduction and use in ordinary trans- actions and particularly where compensation for services is in question need not be deferred until Congress has acted, nor even until further studies have been made by the Department of Labor or any other branch of the government on which the definition and description of the commodity unit is to be based. The data at hand are quite sufficient to serve in the interim. The general commodity index numbers as ascertained and com- puted by the Department of Labor would afford a sufficiently close approximation for immediate purposes. It may safely be assumed that any index number based on the prices of numerous commodities, preferably always including food and clothing, will show the general trend of prices, and, also, this being the main point, that even though the price change for the individual articles may not always have been weighted in the exact proportion of the nation’s consumption of each, the final result as expressed in the index number will be a sufficiently close index of the cost of living. It will, therefore, be safe to say that the index number based on all commodities (over 300 as used by the Department of Labor) gives a sufficiently close approxi- mation for all practical purposes to the changing value of the dollar when this value is measured by the ‘“ com ” as herein defined and suggested. If the commodity unit as defined be adopted and the ““ com ” be accepted as a measure of value, the average purchasing power and therefore the average value of $100 and of 100 coms in the ten-year period goo to 1909 would have been identical and the com at the time that this chapter 283 284 VALUATION, DEPRECIATION AND THE RATE-BASE was first written (February, 1920), would have been equivalent in value to about $2.30. It would now (May, 1926) be equiva- lent to about $1.70. To the foregoing a brief historical reference may be of interest to show the quick response of prices of commodities to changes in the amount of currency in circulation. That currency in- flation increases the cost of living has already been noted. It will now be of interest to compare the volume of currency in circulation in the United States from time to time, with the cost of living as shown by the index numbers based on the wholesale prices of commodities. Thus, for example, in the five years preceding the civil war, roo coms would have been equivalent to $103. At the same time there were about $14 of currency per capita in circulation. At the close of the civil war in 1865 the per capita currency circulation had been increased to nearly $21 and the equivalent of roo commodity units had gone to $185. The 50 per cent inflation of currency was accompanied by an 8o per cent increase in the cost of living. (See diagram, Fig. 11.) In the five years, 1910 to 1914, preceding the recent war, the currency circulation was about $34 per capita; it had reached $51 in 1918. The money equivalent of 100 coms had in the same period gone from 114 to 225. A 50 per cent increase in the per capita amount of currency in circulation has been accompanied by a 97 per cent increase in the cost of living which is, however, probably considerably more than can reasonably be ascribed to inflation of currency. In the years following the civil war the per capita currency circulation gradually fell from $20.57 to a minimum of about $15.32 in 1878. During this decline of 25 per cent in the per capita circulation prices fell 46 per cent, from $185 per 100 coms to about $100 in 1878. These facts are not offered to establish any definite relation between the amount of money in circulation and the cost of living, but they do show what seems to be axiomatic, that the per capita increase or decrease in the amount of money in circulation must be reflected in the shifting prices of commodities and that, rrr 2 : ¢ . k o w 3 : QO lea] £ 3 t= _ . 15 et Fi. 11. PER CAPITA CURRENCY CIRCULATION AND THE COST OF LIVING. © The line marked ‘“ 100 commodity units” is based on the index numbers for all commodities as determined by the Bureau of Labor oo Statistics of the U. S. Department of Labor. The lower broken line represents the per capita circulation in dollars. ” 286 VALUATION, DEPRECIATION AND THE RATE-BASE therefore, the government has been in position to lighten the nation’s debt and tax burdens by the simple expedient of pro- viding means for the inflation of the currency — a recourse heretofore frequently resorted to, regardless of the fact that such a procedure is grossly unjust and inequitable. The only method thus far pointed out which will enable the individual to protect himself against such price changes as result from sudden changes in the volume of currency in circulation, and other causes, lies in the official sanctioning of the use of a commodity unit substantially as here set forth. The com will, thereupon, become quite as acceptable as the dollar, even though it never be made the basis of currency as a money unit. A suggestion that recourse should now be had to a commodity unit for the purpose of stabilizing salaries and wages has been prompted by the abnormal recent changes in the purchasing power of the dollar. The plan of utilizing a commodity unit as a norm is not, however, claimed to be new. The author has only attempted to define a particular practical commodity unit for this country, immediately available, and has given it a name to emphasize its distinction from money. It will perform that function of money for which money is least adapted, namely to serve as a standard for deferred payments. The use of the commodity unit for this purpose has long ago been proposed and has been quite fully discussed by economists in the light of pre- war conditions. The advantage, and, it will hardly be going too far to say, the necessity, of employing the multiple standard when the deferred payments are in the form of salaries and wages is not yet generally recognized, obvious though it must be, to every student of the question, that the dollar standard is inade- quate, while the com running with the cost of living would be fair and adequate. There is nothing, as above shown, that will prevent agree- ments immediately being made in which the com, as here defined, or based directly on the accepted Commodity Index Number, may be used to supplement the money unit. It will only be neces- sary to distinctly specify that the com, however defined, shall be THE STANDARD OF VALUE 287 used to determine the money equivalent which the transaction involves. Wages, salaries, rent and loans can all be defined in terms of coms coupled of course with the mutual understanding that some standard commodity index number shall, for the time being, be used in determining the amount of money which is equivalent to one com or to one hundred coms. After the commodity unit has once been legalized by congressional action it will automatically take its place alongside of the dollar. Both the com and the dollar will then perform separate and supple- menting functions. The com will best and most reliably measure value. Money will serve, as it does at present, as the medium in which value can most conveniently be expressed, when an im- mediate and not a future transaction is involved. It will always be used, too, at the consummation of every transaction in which the com has been used in defining the measure of an obligation. Note: The information on which the diagrams are based relating to wages per hour and to the purchasing power or value of the dollar as shown in Figs. 8, 9, 10 and 11 from 1890 to 1919 will be found in the publications of the Bureau of Statistics, U. S. Department of Labor. The following were consulted: For wages per hour, 18go to 1918, see Bulletins 129, 134, 150, 218, September 1898, July 1900, and Monthly Labor Review of March 1919, and for wages in all industries, 1840 to 1891, see Report of Senate Committee on Finance 1893, cover- ing Wholesale Prices, Wages and Transportation. For the cost of living as represented by index numbers, 18go to 1919, see Monthly Labor Review of September, 19109. For the cost of living as represented by index numbers, 1850 to 1891, see Report of the Senate Committee on Finance 1893, on Wholesale Prices, Wages and Trans- portation. For the per capita circulation in the United States, 1850 to 1893, see “Gold Production and Future Prices” by Brace, and also Statistical Abstract of U. S. covering the years 1893 to 1918. CHAPTER XV ELEMENTS DESERVING SPECIAL CONSIDERATION WHEN RATES ARE TO BE FIXED (Note: This chapter is substantially as it appeared originally in the author’s “Public Utility Rate Fixing,” now out of print.) A — Obsolescence Obsolescence Cannot Be Predicted. — An appliance, ma- chinery or a process of manufacture in use by a public utility may under efficient management at any time be replaced and super- seded by a better device or process. When this is the case more or less property is usually discarded, which, under the conditions as they prevailed when this property first came into use, should have served for many years longer. Obsolescence has forced its abandonment. The knowledge that obsolescence may shorten the term of usefulness of a machine or of portions of any plant used in the public service has prompted valuation experts and the rate-regu- lating authorities to attempt estimates of the allowances which should be made in the earnings to cover the prospective aban- donment of property due to this cause. The last word has not been said in the discovery of new forces in nature and their adaptation to human requirements. It is the belief of many engineers, for example, that the internal com- bustion engine will put the old types of marine engines of ocean freighters on the scrap heap, and yet the older type under gradual development to its present high state of efficiency has maintained itself for more than a hundred years. The use of oil in place of coal, not alone as a producer of gas but also as fuel in the production of steam, has caused appliances and machinery to be abandoned which would otherwise have continued in service. No one today can be sure which of two 285 ELEMENTS DESERVING SPECIAL CONSIDERATION 289 extremes is most likely to prove true, whether, for example, the last word has been said in the manufacture of gas and there will be no further abandonment of standard gas making appliances and processes, or whether, due to exhaustion of sources of oil, or due to other causes, there may not be found some new substitute for oil or for the gas itself which will render some of the most modern appliances of the day obsolete in the near future. Past experience in the matter of abandonment of property, due to obsolescence, is not a dependable guide to what may happen in the future. In this respect there is a difference be- tween the failures from this cause and those which result from the wear and tear of use and from the somewhat less regular failures through accidents incident to human frailty, fire and similar causes. In the one case the basis for a satisfactory pre- diction is lacking. In the other the probability of events occur- ring in the future can be predicated with some confidence upon what has occurred in the past. There is a difference, too, between replacements made as the result of obsolescence and replace- ments due to failure from other causes. In the case of obsoles- cence the replacement is made with some device which betters the service — the output costs less, or the service is made more reliable or the quality of the output is improved, while in the case of ordinary replacements or renewals the betterment of service is not a necessary incident. Treatment of Obsolescence and Replacement Compared. — It is proper to charge the rate-payer with the cost of replacement when property fails from ordinary causes and to let the earnings, therefore, cover a replacement increment during the useful life of any item of property and to base the charge on the ordinary replacement requirement as determined for such property. Not so, however, in the case of obsolescence. This will be made plain by the following considerations: There would be no obsolescence if the improved machinery or the new process which takes the place of that which is being replaced did not result in advantage to some one. If the obso- lete property has been treated as though its failure could have 200 VALUATION, DEPRECIATION AND THE RATE-BASE been correctly foreseen and as though funds for its replacement had already been collected from the rate-payers, it may still ap- pear on the books as an element of some remaining value, due to insufficient collections for its complete retirement. If this apparent remaining value were ignored, and rates were estab- lished as though the abandoned property had never been in use, the rate-payer would at once get the full benefit of the innovation and the owner would have made a sacrifice of capital which he could perhaps have avoided by being a less efficient manager and holding to the older, less efficient plan of operation. Let it be known that the usual procedure will be to forecast failures by obsolescence and to amortize the capital in such properties which become obsolete on the basis of assumed average conditions, which means inadequate amortization in many cases, and there will no longer be any inducement to the owner to improve the efficiency of his plant. He will conclude that it will be safest not to use new inventions or to introduce new processes so long as a sacrifice of capital is thereby involved. He might, in making an innovation, find that he had on his hands abandoned property, the cost of which has not only not been fully returned to him but concerning the further amortization of which the established rules of rate-regulating bodies may give no ade- quate assurance. Obsolescence Should Affect Rates After, not Before, the Event. — It seems self-evident that when the introduction of a new invention, whether the same applies to a machine or to a process, reduces the cost of operation, the resulting advantage should go to both the owner of the utility and the rate-payer. But it is also true that in such event there will be no hardship imposed on the rate-payer if the benefit of reduced cost of pro- ducing the output does not come to him immediately. A rea- sonable procedure would therefore be, in all such cases, to allow the rates to remain as they would have been without the new process (unless a reduction would result in increased demand and greater net profit to the owner), at least long enough to amortize so much of the original plant as is thereby rendered useless and, ELEMENTS DESERVING SPECIAL CONSIDERATION 201 thereafter, to so adjust rates that, for a suitable period of time, the benefit of the reduced cost will be shared on a fair basis by the owner and the rate-payer. Any treatment less favorable to the owner of a public utility would discourage the introduction of innovations if they involve further investment of capital and would make for inefficient rather than for efficient management. The owner must not be expected to consent to an increase of hazard without an increase of profit. The practice of attempting to foresee obsolescence and of burdening the rate-payer before the failure by obsolescence with the charge that is necessary to amortize the capital which obso- lescence renders useless, is not alone unwise but unjust. It is not fair to the rate-payer because those who pay rates before the betterment is made should not be made to pay for the advantage which will come to those who pay rates after the betterment has been made; it is not fair to the owner because while apparently increasing his earnings it will act, as do all high charges for service, as a deterrent upon the extension of business and because there will be cases where by error in the estimate of time allowance for obsolescence the owner will be called upon to make a sacrifice when, due to obsolescence, property is abandoned, which cannot be offset against the advantage that may come to the owners of other utilities who benefit by an allowance for something which, in their case, never happens. The obsolescence will, in many cases, occur before any adequate provision to meet it has been made. B — Losses From Fortuitous Events Amortization of Losses from Fortuitous Events. — Losses of magnitude which result from floods, earthquakes, volcanic eruptions and the like and in general losses against which the owner cannot insure, belong to a class of sacrifices which, like those due to obsolescence, should be made good to the owner of the utility after the event, by the public, that is to say, by the rate-payers. Such losses cannot be forecast. They should not fall entirely on the owner of the utility. In some fashion and to 292 VALUATION, DEPRECIATION AND THE RATE-BASE a fair extent, they should, in the course of time, be amortized out of earnings. As a rule no provision for other than ordinary risks is made in the allowed rate of return. Consequently, after a catastrophe, for which the owner is not responsible, but which entails a large investment of new capital to rehabilitate a public utility plant, there should be some provisions for amortizing the loss. It will, in such event, be better to let the amortization take place within a reasonable time rather than to carry an equiva- lent sum in the rate-base as though it were a permanent, though unproductive, interest-bearing investment. It will perhaps be claimed, by some, that such losses should not be differentiated from the ordinary losses due to unforeseen causes, and that whatever hazard is involved in any enterprise has unqualifiedly been assumed by the owner of the utility. Under such a theory the allowance for hazard should at all times be liberal enough to compensate the owner for the chance which he takes of at some time suffering material loss. He would be compelled to take the gambler’s chance and the rate-payer should stand the higher rate. Under such a practice there would be an owner here and there who would suffer large loss, while the great majority of owners, escaping the great catastrophes, would get what really should be paid, in the exceptional case, to the unfortunate owner. Under such a treatment of this matter, the tax for the risk would fall upon those who are paying rates before a catastrophe occurs, as well as upon those who receive service from the rehabilitated works. The more logical procedure would be to relieve the rate-payers from the burden of making the in- adequate provision for catastrophes which may never occur and letting the loss that actually results from a catastrophe be met out of future earnings. The usual provision for meeting losses which result from such fortuitous events as are here under dis- cussion, is inadequate. The owner does not, as in the case of losses which must be made good by assurance companies, get the full benefit of the allowance for risk which is distributed in small measure or is at least supposed to be distributed among all public utility owners and is supposed to be collected in the earnings. ELEMENTS DESERVING SPECIAL CONSIDERATION 203 The owner’s share in this risk allowance is only a proportionate one, while the loss, when it occurs, cannot be distributed to the other utilities of the country which escape such loss, but falls in its entirety upon the one utility that may be affected thereby. In recognition of the fact that most utilities escape such losses, the usual allowance in the public utility rates for the element of risk is small and probably in most cases negligible. The allow- ance for management, for business hazards, together with the allowance for participation in the general prosperity of the country, in short the profit allowance, would probably in few, if any, cases be materially reduced, if this element of risk were entirely eliminated. In all cases in which this interpretation of the present-day procedure is substantially true, it would be unfair to an owner whose public utility plant sustains material damage by flood, by earthquake or by other fortuitous event, against which insurance is impossible, to let the entire loss fall upon him with- out recourse. That such losses should in some way ultimately fall upon those who are served by the utility seems self-evident. The most equitable procedure would be to let them be borne both by the rate-payers before the event as well as by the rate-payers of the future. But as they cannot be foreseen the practical alter- native would seem to be to let them fall in their entirety on the rate-payers of the future as would be the case if the utility were publicly and not privately owned. In the case of a business not subject to regulation the oppor- tunity to make up for past losses exists if larger profits can be made by charging what the traffic will bear. Owners of public utilities should be allowed to recoup their losses, if this can be done without making rates unreasonably high. C — Hazard, Management and the Unearned Increment The Allowance for Hazard, for the Unearned Increment and for Management Should Not be Based on Value. — All rate- regulating authorities are devoting much thought and study to 294 VALUATION, DEPRECIATION AND THE RATE-BASE the establishment of a proper basis of calculation when the rates to be charged by public utilities are to be fixed. The highest court has said that value must be the starting point and the attempt is therefore generally made to comply with this apparent requirement of the court. The result is the use of a rate-base conforming to ‘ present value ” or to some- thing that may be called present value, even though in attempt- ing to use value as the rate-base it is occasionally found neces- sary to read new meanings into the word value. After this value has been ascertained in some fashion the owner of the utility is allowed to earn a return thereon, usually somewhat in excess of what would be a fair interest return on money for investment in enterprises of like character. When there is included in the rate-base thus established an allowance for “ going value,” the interest return allowed and earned on this increment of value together with earnings to cover the excess of the rate of return over the ordinary interest rate, is the owner’s compensation for hazards and for management and may also cover some participation in the prosperity and increas- ing values of the property in the community which is served by the utility. If the allowance for hazards has been correctly estimated, the owner will in the long run get little or no advantage therefrom, because this allowance will be offset from time to time by losses or sacrifices of various kinds. The allowance for par- ticipation in the general prosperity is not always recognized as being due to the owner for the reason that a part thereof, under the prevailing system of using value as the basis of the calcula- tion, makes its appearance in the increase of real estate values and in the increasing values resulting from the gradual but recognized rise in the price of materials and the rise in the wage scale. And yet every utility helps to create the general pros- perity. It adds to the unearned increment of the vacant lot and unused field as well as to that of the lot or field whose owner is a rate-payer. Some share of this prosperity should go to the utility, even when its property items do not include appreciating real estate. But, even when the earnings cover fair allowances ELEMENTS DESERVING SPECIAL CONSIDERATION 295 for hazard and for the unearned increment, the obligation of the public to the owner of the utility is not yet fully discharged. There should be compensation for management. It is not enough to allow the bare salaries of those who are entrusted with the management and operation. The owner is entitled to some- thing more. He has brought into being and has placed at the service of the community, an effective organization, the stability and efficiency of which is guaranteed, as in the case of a corpora- tion owner, by the character, judgment and business experience of a board of directors selected by the stockholders. The exist- ence of the corporation, the business ability of its directors resulting in the energetic control of its affairs, the cash contribu- tion by stockholders, the successful operation of the enterprise, or, in the case of the new venture, the implied guarantee of success, afford the basis for making loans and extend the ability of the public to enjoy transportation facilities or electric service, or gas and water supplies that might otherwise long be out of reach by reason of the limited borrowing capacity and lack of business ability of municipal organizations. Volume of Business to be Considered. — That there should be something in the earnings as compensation for management can hardly be questioned. There will, however, be difficulty in bringing the same into a satisfactory relation to the rate-base. This is equally true of the allowance which should be made for the participation in the general prosperity and is true to a less extent of the hazard allowance. All of these elements which should be covered in the earnings are more closely related to the volume of business than to the capital invested in the enterprise or to any rate-base built up from “ value.” It happens occasionally that a public utility concern does a large volume of business on a small investment. Some of the express companies belong in this class. The case may readily be conceived, of such a concern which rents its office facilities and operates under contract with railroad and steamship companies and which, outside of its trucks and other vehicles for local de- livery, has made no investment of any moment. It would be 200 VALUATION, DEPRECIATION AND THE RATE-BASE in vain in such a case to attempt a regulation of rates based solely upon a fair return upon the invested capital. The whole field must be brought into view. The volume of business transacted is, in such a case, equally as important an element for considera- tion as is a rate-base when a limit is to be set upon the earnings. An express company, as here assumed, has no appreciating property. Its share in the unearned increment of the country should be brought into some relation to the amount of service which it renders, that is, to the volume of its business. The compensation for management likewise is intimately related to and should be figured with the volume of business as the starting point. It would, of course, be quite as feasible to start with the total cost of operation instead of with the gross annual receipts when determining what should be allowed for management and what should be allowed to cover participation in general prosperity, but the gross income as a basis has obvious advantages. Book- keeping will be simplified and the control is more readily effected. The annual cost of operation will be more difficult to ascertain and will show greater relative fluctuations than the annual gross income, and for the same allowance in the earnings, the per cent of the annual gross income will be less than the per cent of the operating cost, thus resulting in greater stability of the percent- age allowance when once fixed. From the standpoint of the public, there can be but little question that the compensation for management should, as here suggested, be brought into fair relation to the volume of business instead of making its appearance in the interest allowance on an arbitrarily established or assumed * going value.” No basis has yet been discovered for estimating “ going value ” except capitalization of net profits. When, therefore, ¢ going value ” deduced from the opinion of experts, supported chiefly by assump- tions, as distinguished from cost of developing business, is in- cluded in a rate-base, the procedure must appear illogical to the rate-payer and will always remain subject to attack, both as to principle and amount. The alternative procedure which is now ELEMENTS DESERVING SPECIAL CONSIDERATION 297 suggested and which is novel, should appeal to all concerned as logical and in accord with the common practice in ordinary business affairs of allowing commissions based on the magnitude of the involved transaction. To summarize: — No argument seems to be required to prove the owner’s right to compensation for management. This compensation cannot be brought into any definite or satisfactory relation to what the author believes should be designated as the natural rate-base, being the legitimate invest- ment, usually determined from recent investment and cost of reproduction including an allowance for cost of developing business but without deduction of depreciation, because the amount of business bears no definite relation to the amount of capital invested. If this compensation is brought into some relation to value (including in value the going value of the concern), then the reasoning will be in a circle and the proceeding will be illogical and absurd. It will always be fair to both the owner and the rate-payer to let this compensation be brought into a proper relation to the gross income. The owner's share in the general prosperity of the community, under the customary procedure of the rate-regulating authorities, is recognized in those cases in which the utility plant includes property which is appreciating in value. There may be some unearned increment, in addition thereto, concealed in the allow- ance for “ going value ”” and in a rate of return in excess of the cost of borrowed money, but so long as one concern gets the unearned increment in large amount, due to increasing values of real estate and other concerns apparently get none, the system will be at fault. The participation in general prosperity should, therefore, also be brought into relation to the volume of business and not to a rate-base. The business hazard is contingent in part on the amount of 298 VALUATION, DEPRECIATION AND THE RATE-BASE capital which the owner has invested and in part on the cost of operation. The allowance for hazard if considered apart from obsolescence and from losses due to fortuitous events, which should ultimately fall on the public and not on the owner, will ordinarily be small, and, if expressed in figures at all, can be readily brought into relation to the volume of business. It is not logical to bring it into relation to value which may be made up largely of intangibles. It is not logical either to bring it into definite relation to the natural rate-base. Hazard, too, there- fore, had best be brought into some relation to the volume of business. D — Volume of Business Public Utility Rates and the Volume of Business. — In pre- senting the following ideas relating to the profit which the public utility should earn, the writer disclaims any intent to appear as an advocate of limiting the profit which the owner of the public utility can make at reasonable charges for the service rendered or the commodity furnished. When the owner succeeds by efficient management in keeping operating expenses low he is entitled to a suitable reward. His treatment by those who are charged with regulating rates should be such that efficient man- agement will be encouraged and not discouraged. The sugges- tions which follow should be considered in the light of these qualifying statements. The compensation to which the owners of public utilities are entitled for management and business hazards, or, speaking broadly, the profit to which they are entitled, cannot be brought into any definite, universally applicable relation to the capital invested in such enterprises. Another element, the volume of business, deserves consideration in this connection. That there should, in the case of every legitimate public utility, be some profit will be admitted. This profit will appear as an excess of earnings, present and prospective, over a fair allowance for the use of the money invested in the utility, pro- vision having first been made for operating expenses and replace- ELEMENTS DESERVING SPECIAL CONSIDERATION 290 ment requirements. It has been customary heretofore to use value as the starting point when rates are to be fixed with in- clusion of some allowance for “ going value.” The general practice also prevails of introducing into the calculation a rate of return on the so-called “ fair value ”’ of the property, higher than ordinary interest rates. Without giving special considera- tion to the question of compensating the owner for management and of allowing him to share in the general prosperity of the community, which prosperity he has helped to create, a way has thus been found to permit the utility to yield some profit. Under such procedure there will be cases, however, in which the profit will be very large and may be an onerous burden upon the rate- payer, as in the case of certain utilities in which the amount of invested capital is large when compared with their annual gross income and particularly if the ultimate profit is swelled by the increasing value of large holdings of real estate. And there will be other cases in which the profit may be small and inadequate under reverse circumstances, when the volume of business is large in comparison with the invested capital. As an example of the first kind, certain water supply enterprises on the Pacific Coast might be cited. These not only require the investment of relatively large amounts of capital but in connection with some of them large areas of land are held for reservoir and re- lated purposes. As an example of the second kind, certain express companies which operate under contract with other transportation companies and which do a large business on a small investment of capital have already been cited. Profit in Relation to Volume of Business. — The proposition has, therefore, been submitted as above noted, that the equit- able arrangement would be to bring the profit, covering com- pensation for management, for hazard, and for participation in general prosperity, into some definite relation to the volume of business, that is, into some fixed relation to the amount of annual gross income. When the procedure is followed of applying the interest return to a rate-base determined from the amount of capital legiti- 300 VALUATION, DEPRECIATION AND THE RATE-BASE mately invested, including cost of developing the business, cost of franchises, water-rights and the like, but without deduction of accrued depreciation, a reasonable profit allowance should not be difficult to determine. If the interest allowance on the rate- base be just sufficient to cover the cost of borrowed money, due regard being had to the effect of legitimate discounts and com- missions, then certain additions to earnings, perhaps about as below set forth, would be fair and proper, this being in lieu of a higher interest rate and of interest on the additions to invested capital, which it has been customary to make for going value, or other intangible values, but which really result from the capi- talization of profit. It will be found simpler and more satis- factory to reverse the usual procedure by determining what the annual profit should be, instead of starting with a set of intangible values which after all result from the capitalization of an ill- defined arbitrary subdivision of this profit. The following profit allowances are tentatively suggested and remain subject to mod- ification to fit local conditions. When the gross income is $ 10,000 about 15% $ 1,500 per year AEE # 100,000 “14.5% T4500 Tee FORE Ly 0 i 500,000. 13.590 G7, Soo“ S IEEE eC eele ot i 1,000,000% © ive 595 T25,000, le Sih IE 7 3,000,000 “10% 200,000/1¢¢ Ee He “ i 5,000,000% 0% ATO,000, 1) 1150 A # “8 10,000,000 8% 800,000 “at EE RE ¢ & 20,000,000 7% 1,400,000 _ “IL GeO Ee 5 5 40,000,000 6% 2,400,000" “WF JIRA 4 “ 100,000,000 5% 5,000,000 ‘ « The allowances, here suggested as additions to the interest return on the natural rate-base, are those which appear reason- able under ordinary conditions. They should be considered subject to modification to fit any particular case and they may not be adequate when it happens that the cost of output has been materially reduced by the introduction of a new invention which may be the result of efficient management and skillful operation, and the use of which may entitle the owner of the utility to larger profit for a time at least than he would expect under ordinary circumstances. ELEMENTS DESERVING SPECIAL CONSIDERATION 391 E — Going Value Going Value in the San Francisco Water Rate Case. — Refer- ring to going value as an element deserving consideration when “value” and ‘ rate-base” are treated as synonymous the standing Master in Chancery, Mr. H. M. Wright, in his report (August, 1917) on the value of the properties of the Spring Valley Water Company,* says: “ Such additional value, if it is to be recognized here, is ob- viously not of a separate element in the plant, as is a conduit or a reservoir, but of the plant as a whole; an intangible value, a characteristic of the unified business structure, inhering in every part. We are here concerned, however, to estimate this value, if possible, as if it were a separate thing. “ Going value and development expense are not synonymous. One is value; the other is cost, either actual, where the form of value is actual investment in plant, or hypothetical, or repro- duced, where the present valuation is by present market value, or reproduction cost.” That there is always difficulty in estimating ‘ going value ” for inclusion in the rate-base is clear from this general statement and has been universally recognized. The Master quotes Judge W. W. Morrow, who in Bonbright 2s. Geary (D. C. Ariz. 1903) 210 Fed. 44, 54, 56, in an opinion awarding a preliminary in- junction, said that a going value should be allowed but that, though often presented to him, he had never been able to deter- mine a proper amount upon the evidence submitted. He quotes Judge W. C. Van Fleet of the District Court of Appeals, San Francisco, as saying: “All that we are agreed upon is that upon principle there should be a greater value attachable to a going concern than one which is merely in its initiative and not enjoying the benefit of patronage.” The law as interpreted by the courts requires that value be made the basis of the calculation when the sufficiency of the * Spring Valley Water Co. vs. City and County of San Francisco (rate case). 302 VALUATION, DEPRECIATION AND THE RATE-BASE charges for service or for the output of a public utility is in question, and it is for this reason that the embarrassment plainly evidenced by these quotations has resulted. In the Spring Valley rate case already referred to the Master refers to the difficulty of determining going value when he says: “It is the intangible nature of the going value which makes it difficult to prove. . . . A large part of the aggregate wealth of the world is intangible, without separate market value or ascer- tainable reproduction cost. In Adams Express Company us. Ohio, 166 U. S. 185, the Supreme Court sustained the taxation of an express company upon an assessment of property largely in excess of the value of tangible property. The intangible property is at one place ascribed to franchises, and in another to good will; the name is not important.” Justice Brewer, in delivering the opinion of the Supreme Court in this case, uses the following language in discussing intangible property: “ To say that there can be no such intangible property, that it is something of no value, is to insult the common intelligence of every man. . . . This is eminently a practical age; courts must recognize things as they are and as possessing a value which is accorded to them in the market of the world.” In the light of such opinions by our highest tribunals, universal recognition of the fact that a business may have going value is to be expected. Whether or not it is logical or wise to include such value in the rate-base of a public utility is another question elsewhere considered. Determination of Going Value. — How can this value be measured? This is the problem for immediate consideration and it may as well be stated at the outset that no acceptable solution thereof has yet been offered. In comparing two business enterprises alike in all respects except that the one already enjoys a fully developed business while the other has just emerged from the construction stage and is about to begin operation, a difference in value is readily recog- nized, and the appraiser of the first, which is already a going ELEMENTS DESERVING SPECIAL CONSIDERATION 303 concern, would naturally be inclined to take the view that the advantage which it has over the second can be measured by the cost of developing the business and that this cost in the absence of other satisfactory standards may be accepted as an index of the “ going value.” This appears so plausible that many economists and engineers have adopted a procedure based on this reasoning for estimating going value. They have recognized, however, that while cost of developing business can be treated as an investment of capital, it would not always be fair to accept the actual cost in each individual case as representing a proper allowance in the rate- base for cost of development. If this were done it would be equivalent to placing a premium upon inefficiency because the actual cost of development would naturally be greatest in the case of the property which has been least efficiently managed. To obviate this difficulty recourse has been had to the reproduc- tion method with an attempt to visualize and estimate the cost of development which would be incurred if under present-day conditions a plant had to be reproduced. In the application of this method of determining the advantage expressed in terms of money which the going concern has over another exactly the same, and in the same market, but with business not yet estab- lished, it is necessary to assume that some definite time will elapse between the completion of the system and the full develop- ment of the business as commanded by the concern whose * going value ” is to be appraised. It does not seem to the writer any simpler or more satisfactory to thus, on the judgment of the expert, make an assumption of the time that would be required to establish a business than it would be on the basis of actual experience in the same line of business, in the locality involved and elsewhere, to form an opinion as to what would be a proper allowance for the cost of development. In any business which is already established, an analysis may be desirable of the various elements that make up the intangible values of the property. In such cases some such procedure as that of estimating the cost of re-establishing the business under 304 VALUATION, DEPRECIATION AND THE RATE-BASE present-day conditions may be of service in segregating ‘ going value.” But when earnings are to result from rates yet to be fixed the case is somewhat different, and the question will arise whether the relation between cost of development actual or hypothetical, however ascertained, is a safe guide to the “going value’ which should be created by the profits of the business in excess of interest on the invested capital. Intangible values of whatsoever nature result from high earnings. They include not only “ going value,” but also in some cases water-right values and whatever may be included in such terms as ‘ franchise value,” ‘ good-will,” and the like. Such values do not exist unless the rates are higher, as the writer has elsewhere pointed out they should be, than would produce net earnings equaling the return ordinarily expected from money loaned for use in similar enterprises. The difficulty of using a hypothetical reproduction of an existing utility property, as a means of estimating the cost of developing the business, is apparent from the following considera- tion. The comparative plant is assumed to be an exact repro- duction of the existing plant. There is no competition between the two plants. It might be assumed that the moment that the comparative plant is completed, it will be in full service at the same earning power as the established plant. There would then be no appreciable development period. If such a period is admitted it implies a lack of completion of the comparative plant or the development period should be measured only by the time that it would take the consumer to put himself in position to avail himself of the service. The market in such a comparison is assumed to be at hand. The expert who resorts to this method of estimating going value will give his judgment wide latitude, and his conclusions are not apt to be convincing. Cost of Establishing Business is Not Going Value. — It is well to bear in mind, however, that if a community which is served by a public utility had undertaken the establishment of this utility as a public enterprise it would have been subject to the same and perhaps greater costs in developing the local business ELEMENTS DESERVING SPECIAL CONSIDERATION 305 than the costs which were incurred by the owner of the property. The losses in the early years, on the same chances that there would be loss, would have confronted the public as it confronted the private enterprise. The cost of establishing business is, therefore, an element apart and while perhaps in some measure and under a multiplication of facts relating to many enterprises, the cost of establishing business may be some guide to what the normal going value should be, it will be more logical to treat this cost either as a part of the capital legitimately in the enterprise, or taking the other extreme, as a business loss to be amortized out of earnings within a reasonable time. While the costs of establishing the business, including early losses and expenditures for unsuccessful work, are not a direct measure of going value, they are, nevertheless, in so far as they were legitimate, of that class of expenditures which should, as already stated, come back to the owner of the property sooner or later. The mere knowledge that this is the case, or the prob- ability that the owner will some time recover them, adds value to the property. To add them in the exact amount shown by the cost records in any particular case would not, invariably, be a fair procedure. The owner who builds with care and under the best expert advice, and who pushes his work forward as rapidly as the market to be served will justify, and who enters immediately upon a profitable business without any lean years, is entitled to a reward for his able management and the success of his enterprise. The “ going concern value ” of a plant con- structed under such favorable circumstances is as great as the ‘ going concern value ”’ of other plants of a similar character but burdened perhaps with large expenditure for unsuccessful work and for the development of business. The combined experience of all utilities of similar character should in the long run establish the addition which should be made to the earnings, either to amortize a fair allowance for this class of expenditures in a reasonable time or to provide an ade- quate return thereon if treated as investment or as an increment of the value of the going concern. In the light of this conclusion 300 VALUATION, DEPRECIATION AND THE RATE-BASE it would not be fair in the individual case to treat all losses during lean years and all unproductive expenditures during the con- structive period, such as water tunnels or wells that produce no water, structures that are abandoned, damage by fire and flood, earthquake or war, as additions to value or as additions to a rate-base. These are losses and if occurring after operation has commenced are naturally treated as the reverse of earnings. They cannot with propriety be added to the valuation of the physical properties, though it may be eminently proper on ac- count thereof to estimate the cost of reproduction liberally. In some form they should be taken into account in fixing rates. It is rarely practicable to determine such losses and unproductive expenditures with accuracy. These expenditures and losses may be large and yet they may generally be regarded as having been incurred under competent advice. It should ordinarily be assumed, in other words, that it could not be foreseen that what turned out to be unproductive work would have no value. The easy way to deal with such expenditures is to add them to the rate-base valuation, giving them a name and treating them as a measure, in part at least, of intangible values. While this may appear reasonable when the amount involved is small, or not beyond what the sum of human experience would seem to indi- cate as fair, the other case can readily be foreseen, as already explained, in which this would not be so. To lay down a rule that actual losses whether during construction or in the early years of operation, are to be treated as elements of value is never logical. It should be noted, too, that there is a clear distinction to be made between the expenses ordinarily classed as “ overhead ” and “ development cost.” The overhead expense is an expense incurred during construction and is naturally and logically made a part of the cost of construction. The development cost is an additional outlay during operation, which is necessary to main- tain and operate the property during the time when the receipts for commodity furnished or for service rendered are insufficient to meet operating expenses including a fair interest return on the invested capital. ELEMENTS DESERVING SPECIAL CONSIDERATION 307 “ Going Value ” the Result of Earnings. — It is apparent from what has above been stated that * going value ”’ and the value of physical properties are elements apart; between which, in other words, there is no definite relation. ‘ Going value ” then is not dependent upon the capital which is invested in any property. And yet ‘“ going value ”’ grows with the business enterprise. It is subject to appreciation. This suggests that when once the “going value” is determined which efficiently managed enterprises of various kinds should ordinarily have, this value can be brought into some relation to the volume of business. This thought has heretofore been advanced by the author and by others who are contending that it would be fair to allow a ‘‘ going value ” about equal to one year’s income to be created by adequate earnings. On this point the late Mr. Leonard Metcalf, a consulting en- gineer of large experience in valuation matters, in the recent Spring Valley Water Company rate case, said: “In terms of gross annual revenue, development expense is found to be approximately equal to one year’s gross revenue as of the date of valuation, in the case of ordinary waterworks properties of medium and small size, and between one and one and one-quarter times the gross annual revenue in the case of the larger properties — the cumulative interest during construc- tion charges incident to the long period of construction involved in the building of the larger works being accountable for the difference.” Bearing on this same subject the author, in a paper read in 1912 before the American Society of Civil Engineers, said: “ The most logical course to be pursued, and the one which is always open to the appraiser ”’ (rate-fixing authority) “is to use the best available means for determining the amount of capital which is properly invested, then to determine what the earnings should be to yield an ordinary return on the investment thus ascertained, and then to increase these earnings by an arbitrary ” (reasonable) ‘“ amount, which may vary within wide limits, not only to compensate for past losses and for the hazard during construction and operation, but also as a compensation for management.” And again: ‘“ Any addition to the rate of 308 VALUATION, DEPRECIATION AND THE RATE-BASE return . . . if there is certainty that it will be earned, is the real basis for the intangible values as they would be taken into consideration by a purchaser.” Along the same line of reasoning Mr. Allen Hazen, also of the highest standing among consulting engineers who have devoted attention to valuation matters, in the rate case already referred to, says: « When a business is established and going and earning a certain revenue, it is normally worth to the investor what that income amounts to, capitalized on a rate of return on other in- vestments of equal security, and that rate of return is normally less than the amount which a company has to have the chance of earning, if it can, in order to induce capital to go into an enter- prise of that kind; in other words, if you want to build the Calaveras works, and you want people to put their money into the enterprise on a chance of earning some rate of return without any guarantee that they will earn it — simply on a chance — we have to make that chance 7 per cent, we will say. Now, when the Calaveras works are built, and if the enterprise is successful and it earns that 7 per cent on what it has cost, and is estab- lished, then the man on the street will capitalize that income at 6 per cent and the plant is worth one-sixth more than it cost.” The Master in Chancery in this case upon reviewing the testimony of Mr. Hazen, of which the above is but a brief extract, then goes on to show what going value would be created if various rates of return appropriate for a going plant and a like plant ready to begin business were assumed. It is with some satis- faction that the author makes note of these facts and of the endeavors by others to lay a basis in the earnings for “ going value,” because they confirm his conclusions that this basis lies there and that capitalization of the earnings or value should not be used as a rate-base. (See preceding pages.) May we not conclude, then, that in the case of the public utility which is subject to regulation, its intangible values arise from some allowance in the earnings, in excess, by some pre- determined amount, of earnings which would just yield an ordi- nary rate of interest on the actual capital reasonably and properly ELEMENTS DESERVING SPECIAL CONSIDERATION 300 invested. When the sum of all intangible values is thus deter- mined (by capitalization of a part of the earnings) it will matter little what name is used to designate them. But the increment of earnings in excess of the ordinary interest rate on investments in safe going concerns should be so fixed as to cover also any amortization made necessary by obsolescence, or loss by fortui- tous events, and to cover whatever allowance is to be made as compensation for management and as a share in general pros- perity, possibly in lieu of appreciation. When the limitation of this excess by rate-fixing authorities is under consideration, it can probably be more nearly standardized by bringing it into some definite relation to volume of business, as already fully explained, than in any other way. The fact should not, however, be overlooked that compensa- tion for management and for hazard must be deducted from net income before the same can be capitalized to find value. It will suffice to say in this connection that no new owner would de- prive himself of the benefit of compensation for management by paying to the former owner anything for the privilege of assum- ing the management. Were he unwise enough to do this he would be making a financial sacrifice which would nullify the com- pensation. Likewise in the case of hazard. The assumption by a new owner of a hazard for which some properly ascertained return is in prospect has no capital value. CHAPTER XVI THE RATE-BASE AND DEPRECIATION IN RECENT DECISIONS OF THE U. S. SUPREME COURT The following references to decisions of the U. S. Supreme Court in recent years, that is, since the publication of the first edition of this book, will give some idea of the present attitude of the Public Service Commissions and of the courts toward the problems involved in rate-fixing. Although not always clearly expressed in words the purpose to protect legitimate investment is clear. The time does not appear to be far off when all the Rate-Fixing Commissions will cut loose from the attempt to make © fair value” their starting point and will recognize the fact that they must take legitimate investment into account, and protecting this must also allow the public utility owner an income sufficiently large to create the “ going concern ” and other intangible values and to compensate him for hazard and manage- ment. The courts will then still have the opportunity to deter- mine whether the resulting rates are confiscatory or not. The demonstration made by the author of the fact that it may fairly be assumed that public utility properties ordinarily have unlimited life has been strongly fortified by the decision in the case of the New York and Queens County Gas Company os. Newton (269 Fed., p. 277) in which the District Court (1920) and later the Supreme Court approve the report of the Special Master who discusses present value and depreciation in the following language: “ In determining that the complainant’s property has a fair present value of at least the amount of the complainant’s actual investment therein as found by me, viz., at least $1,655,887.04, I have made no deduction for what is termed ‘ depreciation,’ in whatever way calculated. Under any basis of determining present value, the complainant’s property is now worth at least the amount of such investment therein, and the sound rule of 3I0 THE RATE-BASE AND DEPRECIATION S51 law and policy seems to require the allowance of a reasonable return upon at least that sum. “ Upon the present trial, it was insistently urged upon me by some of the defendants that there should be deducted from the cost of the property (irrespective of whether ‘original,’ ¢ pre- war,” or ‘ present reproduction ’ cost be under consideration) an amount claimed to represent so-called ¢ accrued theoretical de- preciation,” based upon an assumption of ‘life expectancy ’ for a gas plant and equipment and the estimated or known number of years since the same was erected or installed. From the testimony given upon the trial, I was strongly impressed that, in respect of a very large proportion of gas property, there is no ascertainable ‘life expectancy.” The withdrawal of such prop- erty from service comes about from inadequacy or obsolescence, which cannot be forecast in terms of years or even satisfactorily guessed at. “ Certain parts of operating machinery and equipment are of course subject to the effects of use. The replacement of these wearing parts enters into the cost of repairs. As to the sub- stantial units of structures, apparatus, mains, and equipment, their withdrawal from the property accounts comes about from causes not attributable to the condition of the property itself, or any diminution in its operating efficiency, but varying utterly with the particular plant, time, local conditions, and service demands, and hence capable of being forecast only as the occa- sion for such change in plant or equipment becomes imminent. “ In other words, in order to keep abreast of improvements in the art of making and distributing gas when and as it becomes economically advantageous to do so, and to meet the growing demand of the public for service more adequately and economic- ally than would be possible through merely making additions and extensions to existing plant and equipment, larger or better and more economical and efficient units of plant and equipment are from time to time installed, to take the place of units which are still operating as efficiently as when first installed. The loss due to such supersession cannot properly be said to have accrued during the period the superseded unit was in service. It occurred when supersession took place. It became a proper charge against the economies to be realized therefrom. It furnished no basis for the imposition of an additional charge against the user of the superseded unit during the period of its useful service, over and above the higher cost of operating it. Such a charge could not be justified, either on the ground that the unit was losing poten- Pa 312 VALUATION, DEPRECIATION AND THE RATE-BASE tial life, or that the capital invested in it was being consumed, because neither is true. “In order to justify the deduction of ‘theoretical deprecia- tion,” I was asked in this case to assume that ‘a depreciation reserve ’ equal to the computed ‘ theoretical depreciation ’ had been collected from the public, and then to deduct from the company’s investment the amount of such assumed reserve. No such reserve had, in fact, been collected or accumulated by this company. The rate chargeable did not permit it, and there is no reason to believe that the Legislature, in prescribing the rate, ever contemplated it. As I have set forth in findings Nos. 32 and 27 of my report, and as I have elsewhere indicated herein, the complainant gas company has maintained its property and investment intact in the past, through renewals and replace- ments at an average actual cost of approximately .3 cent per 1000 cubic feet of gas sold, and no reason appears for believing that it cannot continue to do so on that basis. Even assuming that the statute permitted such a rate, to have imposed on the company’s consumers an additional burden nearly twice as great, representing a purely theoretical item of operating cost, merely to accumulate a useless reserve to justify a drastic deduction from investment in some ultimate proceeding as to rates, could not have been justified on any sound theory in the past, and cannot now be sustained as to the future. “In order to justify the assumption that a ‘depreciation reserve > was or should have been collected, defendants’ witness Hine testified in this case that such a reserve was necessary, ‘ so that when the property is retired for any cause whatsoever the fund can be charged with the cost of the property.” He testified, also, that the reserve should be in his opinion ‘ invested in the property,” and that when the funds were needed for renewals and replacements they would be provided °by issuing securities against construction work which had been done originally out of this fund, for the money laid aside for this fund, just to reimburse the treasury on account of these expenditures.’ This view seemed to me to disregard the obvious fact that, having deducted the amount of the reserve temporarily invested in property from that on which he proposed the company should be allowed to earn a return, he, to all intents and purposes, destroyed the earning power of such property, and investment; that therefore he could not issue any securities against such property, there being no earnings therefrom with which to pay interest on the securities: that the reserve could never thereafter be availed of THE RATE-BASE AND DEPRECIATION BT 3 for the purpose for which it was alleged to have been created and that it would be, in fact, as if it had never been created. Thus he not only failed to sustain his contention that a © deprecia- tion reserve ’ was necessary for the purpose which he alleged, but he proposed to treat the reserve as if he himself believed it to be both unnecessary and ineffectual, except for the purpose of justifying a deduction from the complainant’s investment. “It is obvious that the collection of an unnecessary reserve and its periodic deduction from the value of the property in service would operate to effect a piecemeal purchase, on the part of the public, of the property used by the utility in its service. In other words, it is really asking the consumer to pay for the plant, instead of paying a return on the investment. If such a consummation is desirable, of which there is no evidence, it should be effected openly, and not surreptitiously, under the guise of providing for so-called ¢ theoretical depreciation.’ “ Mr. Miller testified that, as of April, 1920, the expenditure of $6,144.07 for repairs, renewals, and replacements, would put the plant, structures, machinery, and equipment in condition substantially as good as when they were erected or installed. His testimony in this respect was not contradicted by that of any witness. This sum, however, does not, in my opinion, measure any impairment in the present value of the property used and useful in the gas business. It represents merely an unmatured obligation to maintain the property in efficient operating condition out of future earnings; the expert witness of both the complainant and the defendants agreeing that it was and is maintained in efficient and first-class condition. I there- fore have not deducted this or any other sum representing so- called ‘ accrued depreciation ’ from the amount found by me to represent the investment of the complainant in its gas property upon which it is entitled to have its rate such as to yield a reason- able return.” This is a strong presentation, too, in favor of the author’s con- tention that not value but the legitimate investment in the property, should be made the starting point or the basis of the calculation, when rates are to be fixed. It is of interest to note that in this case in the supplemental opinion, Learned Hand, Judge of the District Court (267 Fed., p. 231) expressed himself as follows with reference to de- preciation. 314 VALUATION, DEPRECIATION AND THE RATE-BASE “In the case of a public service company, where the authori- ties may always require the plant to be kept up to standard, there is an obvious advantage in declining to attempt a repeated adjustment between the actual renewals necessary and normal renewals, as would be necessary if the present prospect of such allowances were now discounted; it is the better practice to allow the plant to bear its own extra renewals and to insist that it shall always be kept up. Therefore it appears that, so far as concerns the future, the age of the plant should not be a function in the rate base.’ “ On the other hand, in computing the ‘rate base’ from the original cost, depreciation is of vital consequence. Practical men will prefer to ascertain the cost of a present plant by experi- ence, when they can, rather than by estimate, just as the master here has done. In so arriving at the cost of a present plant of equal capacity, it is clear that the original cost of the plant in question must be abated by depreciation, so far as that is re- flected in a loss of capacity. In such a calculation, however, there must figure past renewals as an offset to past depreciation, and, if in fact the capacity has remained the same, depreciation should not be a function of the ‘ rate-base ’ at all. In such a case the inquiry as to depreciation should be confined to changes in ¢ price levels.” In the matter of ascertaining “ current depreciation,” being that item of operating expense in its larger sense which had better be called the replacement requirement,” it is of interest to note that in the case of the Glaveston Electric Company vs. the City of Galveston tried before the District Court, S. D. Texas in 1921 and affirmed by the U. S. Supreme Court (272 Fed., p. 147) the lower Court in discussing depreciation said: « On the other hand when the matter of establishing the depreciation annuity is considered, the analytic process is em- ployed, and the sum total of the value of the plant is resolved into its constituent items, so as to select those making up the whole which are susceptible to depreciation. Under the in- fluence of this process it is clear that the overhead items must be discarded in arriving at the annual depreciation. “ That this disposition is sound as to such items as interest during construction, organization expense, law expenses, etc., admits of no doubt, because under no kind of theory could they THE RATE-BASE AND DEPRECIATION ls be supposed to be subject to depreciation, and what doubt might arise with reference to the propriety of including engineering charges in these figures is at once dissipated when it is considered that the property will not be constructed again as an entirety, but is to be kept up by annual renewals from time to time made, so that engineering, and other such overheads caused by the assembling of the plant, will not have to be provided against, because they will not again be incurred.” The definition here given of annual or current depreciation is identical with what the author contends should be called the annual replacement requirement. That the import of the latest decisions of the United States Supreme Court in rate cases is the protection of the legitimate investment will appear from a careful reading of the decisions in the Southwestern Bell Telephone Company case, in the Blue- field Waterworks case and in the Georgia Railway and Power Company case from which the following extracts should prove of interest. In the case of the Southwestern Bell Telephone Company vs. Public Service Commission of Missouri (262 U. S., p. 276, and L. Ed., p. 981) decided, May 21st, 1923, it was shown that the Commission had made an estimate of the actual cost of the property decreased by depreciation and had used this as the rate-base. The Court found fault with the Commission because of its disregard of the higher prices of labor and materials which prevailed at the time when the rates were fixed as compared with those which prevailed at the time the plant was constructed. “ Obviously, the commission undertook to value the property without according any weight to the greatly enhanced costs of material, labor, supplies, etc., over those prevailing in 1913, 1914 and 1916. As matter of common knowledge, these increases were large.” The principle is here clearly favored of giving consideration in a fair measure to the fluctuating value of the dollar. (See Chapter XIV.) On this subject of valuing physical properties at prices of labor 1c 316 VALUATION, DEPRECIATION AND THE RATE-BASE and materials other than those which prevailed at the time of original construction, the Supreme Court in the case of the Blue- field Water Works and Improvement Company vs. Public Service Commission of West Virginia (U. S. 262, p. 679; L. Ed. p. 1176) has this to say: “ The record clearly shows that the commission, in arriving at its final figure, did not accord proper, if any, weight to the greatly enhanced costs of construction in 1920 over those prevail- ing about 1915 and before the war, as established by uncon- tradicted evidence; and the company’s detailed estimated cost of reproduction new, less depreciation, at 1920 prices, appears to have been wholly disregarded. This was erroneous. “ The question in the case is whether the rates prescribed in the commission’s order are confiscatory and therefore beyond legislative power. Rates which are not sufficient to yield a reasonable return on the value of the property used, at the time it is being used to render the service, are unjust, unreasonable, and confiscatory, and their enforcement deprives the public utility company of its property in violation of the 14th Amend- ment. This is so well settled by numerous decisions of this court that citation of the cases is scarcely necessary.” In the Atlanta case, that is, Georgia Railway and Power Company vs. Railroad Commission of Georgia (U. S. 262, p. 625; L. Ed., p. 1144) some attention is given to the ‘‘ rate base ” the difficulty being indicated of laying down any definite rule for its determination. The Court says on this subject: “ The objections mainly urged relate to the rate base; and one of them, is of fundamental importance. The companies assert that the rule to be applied in valuing the physical property of a utility is reproduction cost at the time of the inquiry, less depreciation. The 1921 construction costs were about 70 per cent higher than those of 1914 and earlier dates, when most of the plant was installed. So much of it as was in existence Janu- ary 1, 1914, was valued at an amount which was substantially its actual cost or its reproduction cost as of that date. The companies claim that it should have been valued at its replace- ment cost in November, 1921,— the time of the rate inquiry; and that the great increase in construction costs was ignored in determining the rate base. THE RATE-BASE AND DEPRECIATION 7 “ The refusal of the commission and of the lower court to hold that, for rate-making purposes, the physical properties of a utility must be valued at the replacement cost, less depreciation, was clearly correct.” The court in these various decisions shows its embarrassment resulting from the attempt to use value and not the reasonable legitimate investment as the rate-base. The court fails, also, to indicate that intangible values in excess of investment are created by adequate rates and that such values cannot exist unless the rates produce a net income in excess of a fair interest rate on the legitimate investment. The legitimate investment is usually best determined on the basis of actual cost of recent investments and on the reproduction cost of older items at the best available approximation of current normal prices of labor and materials. In the determination of normal prices considera- tion should be given to the prices which have prevailed in years recently past (generally 2 to 5) and also to the causes, if they can be identified, of the recently past and current trend of prices. The fundamental requirements when rates of public utilities are to be fixed may now be restated as follows: The rates should produce an income adequate: 1. To meet operating expenses (here used in the narrow sense not including interest). 2. To amortize properly estimated unavoidable losses during the development period of the business (i.e., the cost of establishing the business). 3. To amortize losses from fortuitous events. 4. To amortize the remaining value of property discarded because of obsolescence. 5. To yield an ordinary interest return on the capital legiti- mately invested (to be estimated at current normal prices or from records of actual recent investment, undiminished by depreciation). 6. To cover ordinary hazards of the business. 7. To cover a fair allowance for management. 31; 318 VALUATION, DEPRECIATION AND THE RATE-BASE 8. To cover a fair allowance of profit — thus giving the owner participation in the general prosperity, which his utility helps to create. Items 2, 3 and 4 by definition are of a temporary character. Ttems 6 and 7 are not to be capitalized when value is estimated from present and prospective earnings. These two items and item 8 can ordinarily be brought into a fair relation with the volume of business. There is no accepted method of evaluating intangibles. Capitalization of the increment of earnings for which they are responsible is apparently the best method of approach. CHAPTER XVII SUPPLEMENT he] VALUATION, DEPRECIATION AND THE RATE-BASE TABLES Nos. 19 to 33 (Note: In these Tables which are supplementary to “ Valuation, Depreciation and the Rate-Base ”” both paging and table numbering have for convenience been made continuous. The tables in the preceding 318 pages are illustrative of the text and not for reference as is the case with this series.) NEW YORK JOHN WILEY & SONS, Inc. Loxpon: CHAPMAN & HALL, LnoTep rt 1024 TABLES RELATING TO VALUATION, INTEREST, DISCOUNT, DEPRECIATION AND RELATED SUBJECTS FOR THE USE OF VALUATION EXPERTS, BANKERS AND ECONOMISTS C. E. GRUNSKY C. E. GRUNSKY, Jr. AUTHORS: VALUATION, DEPRECIATION AND THE RATE-BASE RV INDEX TO INTEREST, ANNUITY, VALUATION AND INVESTMENT TABLES TABLE PAGE 19. SIMPLE INTEREST TABLE — 360 DAY YEAR. .......00vevesansine. 320 Interest on one dollar for one day and for one month at interest rates from 1 per cent to 25 per cent per annum. Carried out to 12 decimal places. 20. THE Numer oF EacH Day oF THE YEAR..................... 328 The number of each day of the year is indicated for both ordinary and leap years. 21. SIMPLE INTEREST TABLE — 365 AND 366 DAY YEARS............ 329 Interest on one dollar for one day at rates of 1 per cent to 25 per cent per annum. Carried out to 12 decimal places. 2». AMOUNT OF ONE DoLLAR AT COMPOUND INTEREST.............. 332 The amount is given for all years to 1oo years at interest rates of 1 per cent to 1o per cent per annum, together with an abbreviated table for interest rates of 12, 15, 20 and 25 per cent. Carried out to 11 decimal places. 23. AMOUNT oF ONE Dorrar AT ComPOUND INTEREST COMPOUNDED EVERY Six MONTHS......... Feiss ut 348 Interest rates 1 to 1o per cent. Carried out to 9 decimal places. 24. AMOUNT OF ONE DorrAr AT CoMPOUND INTEREST COMPOUNDED QUARTERLY..." . eves : ori ewes Interest rates 2.5 to 6 per cent. Carried out to g decimal places. 25. PRESENT VALUE oF ONE DoLLAR DUE AT A FUTURE DATE........ 351 Values are noted for every year to 100 years. Interest rates 1 to 10 per cent per annum. Carried out to 8 decimal places. 2 AMOUNT OF AN ANNUITY OF ONE DOLLAR...................... 304 The amount is given for every year to 100 years. Interest rates, 1 to 10 per cent per annum. Carried out to 8 decimal places. Annuity WHICH WiLL AMOUNT TO ONE DOLLAR IN A GIVEN TIME.. 377 The annuities are noted for periods of years up to 100 years. In- terest rates, 1 to 1o per cent per annum. Carried out to 8 decimal places. 22 PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR............... 300 The present values are given for periods of any number of years up to 100. Interest rates 1 to 1o per cent per annum. Carried out to 8 decimal places. 323 324 VALUATION, DEPRECIATION AND THE RATE-BASE 29. ANNurrYy WHICH ONE DOLLAR WILL PURCHASE ................. 463 These annuities are given for periods of years up to 100 years. Interest rates 1 to 10 per cent per annum. Carried out to 8 decimal places. 30. THE PrOBABLE USEFUL LIFE OF MACHINERY STRUCTURES AND ABP EAN CE rato e ee er To ee La te lr le Tok reife ala Uo AL 5 The probable useful life is noted in this table for a large variety of items, together with authority for same. 31. EXPECTANCY AND REMAINING VALUE ON THE ASSUMPTION THAT No ArticLE WILL SURVIVE TWICE ITs ORIGINAL EXPECTANCY. 432 A discussion of the method of estimating the expectancy or re- maining life and the remaining value of an article which is no longer new, precedes the table. 32. Expectancy oF Human Lape. ........000 00000 0 lL LLL 446 This table is based on the experience of life insurance companies. 33. AMORTIZATION AND DEPRECIATION.................coooveniennn.. 452 The usual information covering interest rates from 4 to 7 per cent per annum and useful life terms of 2 to 75 years is given in these tables. In addition by use of sub-headings the table also gives the present value of articles whose remaining useful life is known. The table is preceded by an explanatory statement. , INTRODUCTORY STATEMENT There have been prepared by the authors and are here pre- sented a number of tables which are intended to meet the ordi- nary requirements of the valuation engineer and the economist. Where values are not noted in the tables for every year from I to 100 years, as is the case in some of the tables, methods are indicated whereby values can be combined, or other tables can be called to aid. It is believed that all values have been noted with sufficient accuracy, that is with a sufficient number of decimal places to meet every ordinary demand. Particular reference should perhaps be made to a novel feature incorporated in Table 33, entitled “ Amortization or Deprecia- tion and Remaining Value.” It will be noted that sub-headings have been given to some of the columns in this table. By use of these sub-headings, whenever the remaining life or expectancy of any article new or old is known it is made possible to take out of the table in the appropriate column its remaining or present value. Because this set of tables is a supplement to and a part of “ Valuation, Depreciation and the Rate-Base” the paging and table numbering have been preserved. The set covers pages 319 to 475 and Tables 19 to 33. Where in this Supplement other pages or other tables are referred to, they will be found in main portion of ‘“ Valuation, Depreciation and the Rate-Base.” 228 326 VALUATION, DEPRECIATION AND THE RATE-BASE EXPLANATION OF TABLE 19 SiMpPLE INTEREST ON ONE DOLLAR FOR ONE DAY AND FOR ONE MONTH — 360 DAY YEAR This table has been calculated on the basis of a 360 day year with twelve months of thirty days each. The calculations have been carried to 12 decimal places. To obtain the interest on one dollar for any number of days or months, the figure for one day or one month at the interest rate required should be taken from the table and multiplied by the number of months or number of days involved. A com- bination of months and days can be obtained by two such simple multiplications and the addition of the multiplicands. Example. — (a) What is the simple interest at 53 per cent on $1 for 8 months and 23 days? Take from the “ Day ” column the figure for interest at 53 per cent and multiply by 23. Take from the ¢“ Month ”’ column the figure for interest at 53 per cent and multiply by 8. Add the results together. $o.000152777778 X 23 = $0.003513888889 0.004583333333 X 8 = 0.036666666667 $o.040180555556 Answer = $o.0402. (b) What is the simple interest at 33 per cent on $1462.15 for 3 months and ro days? Take from the “ Day” column the figure for interest on $1 at 31 per cent, multiply it by 10 and then by $1462.15. Take from the “ Month ” column the figure for interest on $1 at 31 per cent, multiply it by 3 and then by $1462.15 Add the two results. $1462.15 X 0.000090277778 X 10 = $ 1.3200 $1462.15 X 0.002708333333 X 3 = 11.8800 $13.2000 Answer = $13.2000. TABLES TABLE 19. SIMPLE INTEREST ON ONE DOLLAR FOR ONE DAY AND FOR ONE MONTH, AT RATES RANGING FROM 1 TO 25 PER CENT On basis of 360 day vear and 30 day month interes we One day. One month. I $.000 027 777 778 $.000 833 333 333 : .000 041 666 667 .00I 250 000 000 .000 055 555 556 .oo1 666 666 667 af .000 069 444 444 .002 083 333 333 .000 083 333 333 .002 500 000 000 .000 090 277 778 .002 708 333 333 .000 097 222 222 .002 916 666 667 .000 104 166 667 .003 125 000 O00 .000 ITI IIT III .003 333 333 333 .000 118 055 556 .003 541 666 667 .000 125 O00 000 .003 750 000 000 .000 131 944 444 .003 958 333 333 .000 138 888 889 .004 166 666 667 .000 145 833 333 .004 375 000 000 .000 152 777 778 .004 583 333 333 .000 159 722 222 .004 791 666 667 .000 166 666 667 .003 000 000 000 ,000 173 6IT III .005 208 333 333 .000 180 555 556 .005 416 666 667 : .000 187 500 000 .005 625 000 000 .000 104 444 444 .005 833 333 333 .000 208 333 333 .006 250 000 000 .000 222 222 222 .006 666 666 667 se .000 236 IIT III .007 083 333 333 .000 250 000 000 .007 500 000 000 ( .00o 263 888 889 .007 916 666 667 Io .000 277 777 778 .008 333 333 333 1+ .000 333 333 333 .OIO 000 000 000 3 .000 416 666 667 .0I2 500 OOO OOO z .000 555 555 556 .016 666 666 667 37 .000 694 444 444 .020 833 333 333 327 328 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 20. THE NUMBER OF EACH DAY OF THE YEAR Dest) Jan. | Feb. | Mar. Sill May. | June. | July. | Aug. | Sept. Oct. Nov. | Dec. Eee fee ee fee Ue 32 boii or iizeT | 152 1821 213 | 244 tian ll 305 [11335 33 | 61 | 92 1221353 183 214 | 245 | 275 | 306 | 336 3 34| 62| 93 123 154 + 184 1 215 | 246 | 276 | 307 337 4 35| 63| 04 124155 | 185 216 | 247 | 277 ' 308 | 338 5 36 | 64 | 95 125 | 156 | 186 217 248 | 278 309 | 339 6 37 | 65 | 96 126 | 157 | 187 218 | 249 | 279 310, 340 7 38! 66] 97 127 158 188 219 | 250 | 280 3II | 34I 8 39 67 98 128! 159 139 220 23I } 312 , 342 , 9 40 68! 99 129 160.190 22I 252 282 313 343 19 10 AT 69 100 130 161 . II 222 5s | 283 314 344 11 | 11 42 70 71or 131 162 | 192 223 254 | 284 315 345 ik 12 43 wg 102 132 163 | 193 224 255 285 316 346 : 13 44 72 103 133 164 | 194 225 255 | 286 317 347 ; 14 45 73 104 134 1651 195 226 257 | 287 318 348 ro | 15 46 74 105 135 166 196 227 1 258 | 288 319 349 19 16 47 7s 106 136 167 197 228 2501 289 320 35¢C 17 1 48 76 107 137 168 198 229 260 200 321 35I 18 13 hag 77 108 138 169 199 230 261 | 291 322, 352 19 19 so 78 109 139 170] 200 23I « 262 . 202 323 353 20 20 5% 79 110 140 1I7I 201 232, 263 293 324 354 21 21 52 8 111 141 172 202 2331 264 294 325. 355 22 22 53 81 112 142 173 203 234 265 205 326 356 21 + 23| sa 82 113 143 174 204 235 266 206 327 | 357 24 24 55 83 114 144 173 205 236: 267 297 3281 358 25 | 25 6 84 115 1451 176 206 237 | 268 298 329 359 26 26 57 8s 116 | 146 | 177 + 207 | 238 | 269 299 330 360 27 27 58 86 117 iE 178 208 BE I 270 300 | 331 361 28 28 sg | 87 118 | 148 179 209 | 240 271 301 332 362 29 ZO 88 119 | 149 180 2101 241 272 302 333 363 30 ZO kl 89 120 150 181 2II JE 273 303 334, 364 3I 210 ago. ToT A. Bak 2 AL 243 I. .. BN SOLE. +i: 365 Note: For leap years the number of February 29th is 60, and the num- bers of the following days will all be increased by one. TATRLES EXPLANATION OF TABLE 21 SIMPLE INTEREST ON ONE DOLLAR FOR ONE DAY oN Basis oF 365 Dav YEAR AND 366 DAy YEAR This table has been calculated both for the normal 3635 day years and for leap years, the interest on $1 for one day being given in the appropriate column. By using the table of “ The Number of Each Day of the Year ” given on the preceding page the interest on $1 which has accrued between any two days of the year can be calculated by multi- plying the interest for one day by the number of days involved. Example. — (a) What is the interest on $1 from Jan. 1 to Aug. 23, at the rate of 7 per cent (not a leap year)? $0.000191780822 X 234 = $0.044877 Answer = $0.0435. (b) What is the interest on $2,125,602.10 from Feb. 1 to Nov. 3, at the rate of 5 per cent (leap year)? $2,125,602.10 X 0.000136612022 X 276 = $80,145.653 Answer = $80,145.65. ‘BL 320 330 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 2:1. SIMPLE INTEREST ON ONE DOLLAR FOR ONE DAY AT RATES RANGING FROM 1 TO 25 PER CENT On basis of 365 day year and 366 day year Lnterolh vais: per 365 day year. 366 day year. : $.000 027 397 260 $.000 027 322 404 ri .000 041 095 890 .000 040 983 607 2 .000 054 794 521 .000 054 644 809 23 .000 068 493 I5I .000 068 306 OIL .000 082 191 781 .000 081 067 213 .000 089 041 096 .000 088 797 814 : .000 095 890 4II .000 095 628 415 : .000 102 739 726 .000 102 459 OI6 .000 109 589 041 .000 109 289 617 2 .000 116 438 356 .000 116 120 219 . .000 123 287 671 .000 122 950 820 a .000 130 136 986 .000 129 781 42I .000 136 986 301 .000 136 612 022 .000 143 835 616 .000 143 442 623 .000 150 684 932 .000 150 273 224 z .000 157 534 247 .000 157 103 325 .000 164 383 562 .000 163 934 426 .000 171 232 877 .000 170 765 027 q .000 178 082 192 .000 177 595 628 ( .000 184 931 507 .000 184 426 230 , ,000 I9I 780 322 .000 191 256 831 ’ .000 205 479 452 .000 204 9I8 033 « .000 219 178 082 .000 218 579 235 & .000 232 876 712 .000 232 240 437 ( .000 246 575 342 .000 245 90I 639 ot .000 260 273 973 .000 259 562 842 id .000 273 972 603 .000 273 224 044 .000 328 767 123 ooo 327 868 852 . .000 410 958 904 000 409 836 066 : ,000 547 945 205-1 000 546 448 087 25 .000 684 931 507 .000 683 060 109 TARLES EXPLANATION OF TABLE 22 CoMPOUND INTEREST Amount of one dollar at interest compounded annually In Table 22 the amount is given of $1 at interest rates from I to 10 per cent, interest being compounded annually for any number of years up to roo. The formula on which this table is based is the following: Let A’ represent the amount at the end of nth year of $1 plus interest compounded annually. Let n represent the number of years. Let 7 represent the interest rate expressed decimally as 0.03 for 5 per cent. Then 4’ = (a + I)" (19) Example. — What is the amount in 7 years of $400 at 6 per cent interest compounded annually? From Table 22 the amount of $1 at 6 per cent interest in 7 years is found to be $1.503630 and the amount of $400, therefore $400 X $1.503630 = $601.45. The section of Table 22 covering interest rates in excess of 10 per cent will be found serviceable for certain special purposes such as the determination of the present value of mining proper- ties. This section of the table has been abbreviated by the omission of certain individual years but it can nevertheless be made to serve in finding the amount of $1 at compound interest for any year by going into the table with any two years whose sum is equal to the number of years for which the amount is to be determined and obtaining the product of values found in the table for these two years. This product will be the required amount. Example. — What is the amount of $1 at 15 per cent com- pound interest in 46 years? The amount of $1 for 16 years at 15 per cent is found to be $9.357621. 331 332 VALUATION, DEPRECIATION AND THE RATE-BASE The amount of $1 for 30 years at 15 per cent is found to be $66.211772. Then 9.357621 X 66.211772 = $619.58, which is the amount of $1 at 15 per cent in 46 years. While occasion may rarely arise when it is necessary to know the amount of $1 at these high rates of interest for a long term of years this section of the table is valuable for other purposes. It can be used to determine the present value of $1 due at a future date; the amount of an annuity of $1, and also the present value of an annuity of $1. The method of use for these purposes is explained in connection with the respective tables which follow. To Illustrate. — What is the present value of a mine yielding $10,000 net per annum whose estimated life is ro years and which, owing to the hazards of the enterprise, should yield a net return of 20 per cent per annum? From Table 22 it is found that $1 at 20 per cent compound interest will amount to $6.191736 in 10 years. According to formula (23) in the explanation of Table 26 the amount of an annuity of $1 for ro years will be 61917301 oe = $25.95868. And by formula (25) in the explanation of Table 27 the present value of an annuity of $1 for 10 years 25.05868 ant = $4.192149. Consequently the value of the mine equipped to produce the net annual amount of $10,000: 10,000 X 4.192149 = $41,921.49. TAI: ES 333 TABLE 22. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY End of I per cent. I; per cent. 2 per cent 1.01 1.015 1.02 1.0201 1.030 225 1.040 4 1.030 301 1.045 678 375 1.061 208 1.040 604 oI 1.061 363 550 63 1.082 432 16 1.051 OIO O50 I 1.077 284 003 88 1.104 080 803 2 1.061 520 150 60 1.093 443 263 94 1.126 162 419 26 1.072135.352 1 1.109 844 912 QO 1.148 685 667 65 1.082 856 7035 63 1.126 492 586 60 1.171 659 381 00 1.093 685 272 68 1.143 389 975 39 1.195 092 568 62 . 1.104 622 125 41 1.160 540 825 03 1.218 994 419 99 1.115 668 346 67 1.177 948 937 40 1.243 374 308 39 1.126 825 030 13 1.195 618 171 46 1.268 241 794 56 1.138 093 280 43 1.213 552 444 03 1.293 606 630 45 : 1.149 474 213 24 1.231 755 730 69 1.319 478 763 06 ; 1.160 968 955 37 1.250 232 066 65 1.345 868 338 32 1.172 578 644 92 1.268 985 547 65 1.372 785 705 09 1.184 304 431 37 1.288 020 330 87 I.400 24I 419 IQ 1 1.196 147 475 69 1.307 340 635 83 1.428 246 247 58 ic 1.208 108 950 44 1.326 950 745 37 1.456 811 172 53 23 I.220 190 039 95 1.346 855 006 55 1.485 947 395 98 v I.232 39I 940 35 1.367 o57 831 63 1.515 666 343 90 ¢ 1.244 715 859 75 1.387 563 699 12 1.545 979 670 78 ‘ 1.257 163 018 35 1.408 377 154 61 1.576 899 264 19 : 1.269 734 648 53 1.429 502 811 93 1.608 437 249 48 . 1.282 431 995 02 1.450 945 354 II 1.640 605 994 46 ? 1.295 256 314 97 1.472 709 534 42 1.673 418 114 35 1.308 208 878 12 1.494 800 177 44 1.706 886 476 64 z 1.321 290 966 go 1.517 222 180 10 1.741 024 206 17 29 1.334 503 876 57 1.539 980 512 80 1.775 844 690 30 1.347 848 915 33 1.563 080 220 49 1.811 361 584 10 1.361 327 404 49 1.586 526 423 8o 1.847 588 815 79 I.374 940 678 53 1.610 324 320 16 1.884 540 592 10 1.388 690 0835 32 1.634 479 184 96 1.922 231 403 94 1.402 576 986 17 1.658 996 372 73 1.960 676 032 02 1.416 602 756 03 1.683 881 318 32 1.999 889 552 66 1.430 768 783 59 1.709 139 538 10 2.039 387 343 72 1.445 076 471 43 1.734 776 631 17 2.080 635 090 59 1.459 527 236 14 1.760 798 280 64 2.122 298 792 40 1 1.474 122 508 50 1.787 210 254 85 2.164 744 768 25 ¢ 1.488 863 733 59 1.814 018 408 67 2.208 039 663 61 q 1.503 752 370 92 1.841 228 684 80 2.252 200 456 89 1.518 789 894 63 1.868 847 115 07 2.2097 244 466 o2 ‘ 1.533 977 793 58 1.896 879 821 8o 2.343 189 355 35 ! 1.549 317 571 52 1.925 333 019 12 2.390 053 142 45 4 1.564 810 747 23 1.954 213 OI4 41 2.437 854 205 30 4 - 1.580 458 854 70 1.983 526 209 63 2.486 611 289 41 4 1.596 263 443 25 2.013 279 102 77 2.536 343 515 20 4. 1.612 226 077 68 2.043 478 289 31 2.587 070 385 50 49 1.628 348 338 46 2.074 130 463 65 2.638 811 793 21 co 1.644 631 821 84 2.105 242 420 61 2.691 588 029 07 RL" 334 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 22. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY (Continued) Bat 1 per cent. 1} per cent. 2 per cent. 5I 1.661 078 140 06 2.136 821 056 92 2.745 419 789 66 52 1.677 688 921 46 2.168 373 372 77 2.800 328 185 45 ne 1.694 465 810 68 2.201 406 473 36 2.856 334 749 16 : 1.711 410 468 78 2.234 427 570 46 2.913 461 444 14 1.728 524 573 47 2.267 943 984 02 2.971 730 673 02 5 1.745 809 819 21 2.301 963 143 78 3.031 165 286 48 1.763 267 917 40 2.336 492 590 94 3.091 788 592 21 1.780 900 596 57 2.371 539 979 80 3.153 624 364 06 1.798 709 602 54 2.407 113 O79 50 3.216 696 851 34 1.816 696 698 56 2.443 219 775 69 3.281 030 788 37 t 1.834 863 665 55 2.479 868 072 33 3.346 651 404 13 { 1.853212/302 21 2.517 066 0093 41 3.413 584 432 22 ( 1.871 744 425 23 2.554 822 084 81 3.481 856 120 86 1.890 461 869 48 2 593 144 416 08 5.551 493 243/28 1.909 366 488 17 2.632 041 582 32 2.622 523 108 14 - 1.928 460 153 06 2.671 522 206 06 3.604 973 570 31 1.947 744 754 59 2.711 595 039 15 3.768 873 041 71 1.967 222 202 13 2.752 268 964 74 3.844 250 502 55 . 1.986 894 424 15 2.793 552 999 2I 317921 135 512/60 2.006 763 368 40 2.835 456 294 20 3.999 558 222 85 2.026 831 002 08 2.877 988 138 61 4.079 549 387 31 2.047 099 312 IO 2.921 157 960 69 4.161 140 375 OF 2.067 570 305 22 2.964 975 330 IO 4.244 363 182 55 2.088 246 008 27 3.009 449 960 05 4.329 250 446 20 2.109 128 468 36 3.054 591 709 45 4.415 835 455 13 J 2.130 219 753 04 3.100 410 585 09 4.504 152 164 23 2.151 521 950 57 3.146 916 743 87 4.594 235 207 51 2.173 037170 03 3.104 120 495 03 4.686 119 911 67 2.194 767 541 78 0-242 032 302 45 4.779 842 309 90 2.216 715 217 19 3.290 662 786 99 4.875 439 156 10 2.238 832 369 37 1.340 022 728 79 4.972 947 939 22 2.261 271 193 06 4.390 123 069 73 5.072 406 898 oc 2.283 883 904 99 +440 974 915 77 5.173 855 035 96 2.306 722 744 04 3-492 589 539 51 5.277 332 136 68 2.329 789 971 48 3-544 978 382 60 5.382 878 779 42 ¢ 2.353 087 871 20 3-598 153 058 34 5.490 536 355 00 ‘ 2.376 618 749 91 2.652 125 354 22 5.600 347 082 10 : 2.400 384 937 41 2.706 907 234 53 5.712 354 023 75 & 2.424 388 786 78 z 762 510 843 05 5.826 601 104 22 « 2.448 632 674 635 3.818 948 505 69 5.943 133 126 31 ( 2.473 IIQ OOI 40 3.876 23273323 6.061 995 788 83 f 2.497 850 I9I 41 3.934 376 224 28 6.183 235 704 61 ¢ 2.522 828 603 32 3.993 391 867 64 6.306 9oo 418 70 ( 2.548 056 980 26 4.053 292 745 66 6.433 038 427 o7 C 2.573 537 550 06 4.114 092 136 84 6.561 699 195 62 6. 2.599 272 925 56 4.175 803 518 89 6.692 933 179 53 q: 2.625 265 654 82 4.238 440 571 68 6.826 791 843 12 98 2.651 518 311 36 4.302 o17 180 25 6.963 327 679 98 99 2.678 033 494 48 4.366 547 437 96 7.102 594 233 58 100 2.704 813 829 42 4.432 045 649 53 7.244 646 118 25 TABLES ; TABLE 22. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY (Continued) Pug 2} per cent. 3 per cent. 3% per cent. f 1.025 1.030 000 00 1.035 1.050 625 1.060 goo co 1.071 22§ 1.076 890 6253 1.092 727 00 1.108 717 875 1.103 812 890 63 1.125 508 81 1.147 523 000 63 1.131 408 212 89 1.159 274 074 30 1.187 686 305 65 1.159 693 418 21 1.194 052 296 53 1.229 255 326 34 1.188 685 753 67 1.229 873 863 42 1.272 279 262 77 1.218 402 897 51 1.266 770 081 39 1.316 809 036 96 1.248 862 969 953 1.304 773 183 83 1.362 897 353 26 ‘oe 1.280 084 544 20 1.343 916 379 34 1.410 598 760 62 pi 1.312 086 657 80 1.384 233 870 72 1.459 969 717 24 1.344 888 824 253 1.425 760 886 83 1.511 068 657 35 1 1.378 511 044 85 1.468 533 713 45 1.563 956 obo 35 3 1.412 973 82097 1.512 589 724 86 1.618 694 522 47 ; 1.448 298 166 50 1.557 967 416 60 1.675 348 830 75 1) 1.484 505 620 66 1.604 706 439 10 1.733 986 039 83 1 1.521 618 261 18 1.652 847 632 27 1.794 675 551 22 T= 1.559 658 717 71 1.702 433 061 24 1.857 489 195 52 1 1.598 650 185 63 1.753 506 053 08 1.922 501 317 36 47 1.638 616 440 29 1.806 111 234 67 1.989 788 863 47 2 1.679 581 851 30 1.860 204 571 71 2.059 431 473 69 : I.72I 571 397 58 1.916 103 408 86 2.131 511 575 29 : 1.764 610 682 52 1.973 586 511 13 2.206 114 480 40 2 1.808 725 949 58 2.032 794 106 46 2.283 328 487 21 2 1.853 944 098 32 2.093 777 929 65 2.363 244 984 27 2° 1.900 292 700 78 2.156 591 267 54 2.445 958 558 72 alts 1.947 800 018 30 2.221 289 005 57 2.531 567 108 27 % 1.996 495 018 76 2.287 927 675 74 2.620 171 957 06 ? 2.046 407 394 23 2.356 565 506 or 2.711 877 975 56 ; 2.097 567 579 o8 2.427 262 471 19 2.806 793 704 70 2.150 0ob 768 56 2.500 080 345 33 2.905 031 484 37 2.203 756 937 77 2.575 082 755 69 3.006 707 586 32 2.258 850 861 22 2.652 335 238 36 }.III 942 351 84 2.315 32213275 2.731 QO5 295 51 }.220 860 334 16 2.373 205 186 07 2.813 862 454 37 §.333 590 445 85 2.432 535 315 72 2.898 278 328 oo :.450 266 111 46 2.493 348 698 61 2.985 226 677 84 1.571 025 425 36 2.555 682 416 08 3.074 783 478 18 ;.696 or1 315 24 a 2.619 574 476 48 3.167 026 982 52 ;.825 371 711 28 i 2.685 063 838 39 3.262 037 792 co 3.959 259 721 17 4 2.752 190 434 35 3-359 898 925 76 4.097 833 811 41 ‘ 2.820 995 195 21 3.460 695 893 53 4.241 257 994 81 ‘ 2.891 520 075 09 3.564 516 770 34 4.389 702 024 63 ‘ 2.963 808 076 97 1.671 452 273 45 4.543 341 595 49 5 3.037 903 278 89 3-781 595 841 65 4.702 358 551 34 é 3.113 850 860 86 3.895 043 716 go 4.866 941 100 63 4 3.191 697 132 38 4.011 895 028 41 5.037 284 039 16 4+ 3.271 489 560 69 4.132 251 879 26 5.213 588 980 53 43 3.353 276 799 71 4.256 219 435 64 5.396 064 594 84 gO 2.42% 108 719 70 4.383 gob 018 71 5.584 926 855 66 335 336 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 22. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY (Continued) Pata 2} per cent. 3 per cent. 33 per cent. 51 3.523 036 437 70 4.515 423 199 27 5.780 399 295 61 22 3.611 112 348 64 4.650 885 895 25 5.982 713 270 96 a 3.701 390 I57 35 4.790 412 472 10 6.192 108 235 44 . 3.793 924 9II 29 4.934 124 846 27 6.408 832 023 68 3.888 773 034 oF 5.082 148 591 65 6.633 141 144 5I : 3.985 992 359 92 5.234 613 049 40 6.865 301 084 57 4.085 642 168 92 3-391 651 440 89 7.105 586 622 53 4.187 783 223 14 3.553 400 984 II 7.354 282 154 32 ad 4.292 477 803 72 5 720 003 013 64 7.611 682 029 72 th 4.399 789 748 82 -.891 603 104 O35 7.878 ogo goo 76 4.509 784 492 54 0.068 351 197 17 8.153 824 082 28 4.622 529 104 85 6.250 401 733 08 8.439 207 925 16 4.738 092 332 47 6.437 913 785 07 8.734 580 202 55 4.856 544 640 78 6.631 051 198 63 9.040 290 509 63 ; 4.977 958 256 8o 6.829 932 734 59 9.356 700 677 47 20 5.102 407 213 22 7.034 882 216 62 9.684 185 201 18 : 5.229 967 393 55 7.245 928 683 12 10.023 131 683 22 {res 5.360 716 578 39 7.463 306 543 62 10.373 941 292 14 69 5.494 734 492 85 7.687 205 739 92 10.737 029 237 36 73 5.632 102 855 17 7.917 821 912 12 11.112 825 260 67 ‘ 5.772 905 426 55 8.155 356 569 49 11.501 774 144 79 5.917 228 062 21 8.400 017 266 57 11.904 336 239 86 6.065 158 763 77 8.652 017 784 57 12.320 988 008 26 6.216 787 732 86 8.911 578 318 10 12.752 222 588 55 ; 6.372 207 426 19 9.178 925 667 65 13.198 550 379 14 y 6.531 512 611 84 9.454 293 437 68 13.660 499 642 41 ; 6.694 800 427 14 9.737 922 240 81 14.138 617 129 90 J 6.862 170 437 82 10.030 059 908 03 14.633 468 729 45 : 7.033 724 698 76 10.330 961 705 27 15.145 640 134 98 « 7.209 567 816 23 10.640 890 556 43 15.675 737 539 70 : 7.389 807 o11 64 10.960 117 273 12 16.224 388 353 59 ‘ 7.574 552 186 93 11.288 920 791 32 16.792 241 045 97 . 7.763 915 991 60 11.627 588 415 06 17.379 970 414 OF 7.958 013 891 39 11.976 416 067 5I 17.988 269 378 57 ¢ 8.156 964 238 67 12.335 708 549 53 18.617 858 806 82 &. 8.360 888 344 64 12.705 779 806 02 19.269 483 865 06 ¢ 8.569 910 553 26 13.086 953 200 20 19.943 915 800 33 on 8.784 158 317 09 13.479 561 796 21 20.641 952 853 34 8. 9.003 762 275 02 13.883 948 650 09 21.364 421 203 21 Co. 9.228 856 331 89 14.300 467 109 59 22.112 I75 O45 32 ¢ 9.459 577 740 I9 14.729 481 122 88 22.886 102 103 41 oF 9.696 067 183 69 15.171 365 556 57 23.687 115 677 03 9; 9.938 468 863 29 15.626 506 523 27 24.516 164 725 73 94 10.186 930 584 87 16.095 301 718 96 25.374 230 491 I3 95 10.441 603 849 49 16.578 160 770 53 26.262 328 558 32 96 10.702 643 945 73 17.075 505 593 65 27.181 510 057 86 97 10.970 210 044 37 17.587 770 761 46 28.132 862 gog 88 98 11.244 465 295 48 18.115 403 884 30 20.117 513 111 73 99 11.525 576 927 87 18.658 866 ooo 83 30.136 626 o70 64 100 11.813 716 351 06 19.218 631 980 86 31.191 407 983 II TABLES TABLE 22. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY (Continued) fad of 4 per cent. 43 per cent. 5 per cent. I.040 1.045 1.05 1.081 6 1.092 025 1.102 5 1.124 864 I.I41 166 123 1.157625 1.169 858 56 1.192 518 600 63 1.215 506 25 1.216 652 902 4 1.246 181 937 65 1.276 281 562 5 1.265 319 018 50 1.302 260 124 85 1.340 095 640 63 1.315 931 779 24 1.360 861 830 47 1.407 100 422 66 1.368 569 050 41 1.422 100 612 84 1.477 455 443 79 1.423 311 812 42 1.486 095 140 41 1.551 328 21598 1.480 244 284 92 1.552 969 421 73 1.628 894 626 78 4 1.539 454 056 32 1.622 853 045 71 1.710 339 358 12 1.601 032 218 57 1.695 881 432 77 1.795 856 326 02 : 1.665 073 507 31 1.772 196 097 24 1.885 649 142 32 1.731 676 447 60 1.851 944 921 62 1.979 931 599 44 1.800 943 505 51 1.935 282 443 09 2.078 928 179 41 Tr) 1.872 981 245 73 2.022 370 153 03 2.182 874 588 38 : 1.947 900 495 56 2.113 376 809 92 2.292 018 317 80 =P, 2.025 816 515 38 2.208 478 766 36 2.406 619 233 69 : 2.106 849 175 99 2.307 860 310 83 2.526 950 195 38 : 2.I9T 123 I43 O3 2.411 714 024 84 2.653 297 705 14 : 2.278 768 068 75 2.520 241 155 96 2.785 962 590 40 2.369 918 791 50 2.633 652 007 97 2.925 260 719 92 2.464 715 543 17 2.752 166 348 33 3.071 523 755 92 : 2.563 304 164 89 2.876 o13 834 or 3.225 009 943 71 2.665 836 331 49 3.005 434 456 54 3.386 354 940 90 5 2.772 469 784 75 3.140 679 coy 08 3.555 672 687 94 : 2.883 368 576 14 3.282 009 562 40 3.733 456 322 34 : 2.998 703 319 18 3.429 699 992 71 3.920 129 138 46 ‘ 3.118 651 451 95 3.584 036 492 38 4.116 135 595 38 : 3.243 397 51003 3.745 318 134 54 4.321 942 375 15 3-373 133 410 43 3.913 857 450 59 4.538 039 493 91 3.508 058 746 85 4.089 981 035 87 4.764 941 468 60 3.648 381 096 72 4.274 030 182 48 5.003 188 542 03 3.794 316 340 59 4.466 361 540 69 5.253 347 969 14 3.946 088 994 21 4.667 347 810 02 5.516 o15 367 59 4.103 932 553 98 4.877 378 461 48 5.791 816 135 97 4.268 089 856 14 5.006 860 492 24 5.081 406 942 77 4.438 813 450 39 5.326 219 214 39 6.385 477 289 91 : 4.616 365 988 40 5.565 899 079 04 6.704 751 154 40 5 4.801 020 627 94 5.816 364 537 60 7.039 988 712 12 LC 4.993 061 453 05 6.078 100 941 79 7.391 988 147 73 5.192 783 911 18 6.351 615 484 17 7.761 587 555 12 5.400 495 267 62 6.637 438 180 96 8.149 666 932 87 5.616 515 078 33 6.936 122 899 10 8.557 150 279 52 5.841 175 681 46 7.248 248 429 56 8.985 007 793 49 . 6.074 822 708 72 7.574 419 608 89 9.434 258 183 17 6.317 815 617 07 7.915 268 491 29 9.905 971 092 33 : 6.570 528 241 75 8.271 455 573 40 10.401 269 646 94 4 6.833 349 371 42 8.643 671 074 20 10.02T 333 129 29 <0 7.106 683 346 28 9.032 636 272 54 11.467 399 785 75 337 3 38 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 22. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY (Continued) id 4 per cent. 43 per cent. 5 per cent. 51 7.390 950 630 13 9.439 104 904 80 12.040 769 775 04 to 7.686 588 707 33 9.863 864 625 52 12.642 808 263 79 11 7.994 052 255 63 10.307 738 533 67 13.274 948 676 98 8.313 814 345 35 10.771 586 767 68 13.938 696 110 83 8.646 366 919 69 11.256 30% 172 23 14.635 630 916 37 8.992 221 596 47 11.762 842 039 98 15.367 412 462 19 9.351 910 460 33 12.292 169 931 78 16.135 783 085 30 9.725 936 878 75 12.845 317 578 71 16.942 572 239 57 10.115 026 353 90 13.423 356 869 75 17.789 700 851 55 ; 10.519 627 408 05 14.027 407 928 89 18.679 185 894 12 10.0940 412 504 37 14.658 641 285 69 19.613 145 188 83 11.378 029 004 55 15.318 280 143 55 20.503 802 448 27 11.833 150 164 73 16.007 602 750 OI 21.623 492 570 68 12.306 476 171 32 16.727 944 873 76 22.704 667 199 22 12.798 735 218 17 17.480 702 393 08 23.839 900 559 18 13.310 684 626 90 18.267 334 000 76 25.031 895 587 14 13.843 112 O11 98 19.089 364 030 80 26.283 490 366 50 . 14.396 836 492 46 19.948 385 412 18 27.597 664 884 82 6 14.972 709 952 I5 20.846 062 755 73 28.977 548 129 06 i 15.571 618 350 24 21.784 135 579 74 30.426 425 535 51I ; 16.194 483 084 25 22.764 421 680 33 31.047 746 812 29 3 16.842 262 407 62 23.788 820 656 47 33.545 I34 152 90 17.515 952 903 93 24.859 317 586 or 35.222 390 860 55 18.216 591 020 08 25.977 986 877 38 36.983 510 403 58 18.945 254 660 89 27.146 996 286 86 38.832 685 923 76 : 19.703 064 847 32 28.368 611 119 77 40.774 320 2I9 94 20.491 187 441 21 29.645 198 620 16 42.813 036 230 94 ) 21.310 834 938 86 30.979 232 558 07 44.953 688 042 49 22.163 268 336 42 32.373 298 023 18 47.201 372 444 61 ‘ 23.049 799 069 87 33.830 006 434 22 49.561 441 066 84 23.971 791 032 67 35.352 450 773 76 52.039 513 120 18 24.930 662 673 97 36.943 311 058 58 54.641 488 776 19 : 25.927 889 180 93 38.605 760 056 22 57.373 563 215 00 : 26.965 004 748 17 40.343 019 258 75 60.242 241 375 75 28.043 604 938 10 42.158 455 125 39 63.254 353 444 54 : 29.165 349 135 62 44.055 585 606 03 66.417 071 116 77 ‘ 30.331 963 IOI OF 46.038 086 958 30 69.737 924 672 61 < 31.545 241 625 09 48.109 800 871 43 73.224 820 906 24 &9 32.807 051 200 09 50.274 741 910 64 76.886 061 951 55 00 34.119 333 341 70 52.537 105 296 62 80.730 365 049 13 ox 35.484 106 675 36 54.901 275 034 97 84.766 883 301 58 C2 36.903 470 942 38 57.371 832 411 54 89.005 227 466 66 ¢ 38.379 609 780 07 59.953 564 870 06 93.455 488 840 00 ( 39.914 794 171 28 62.651 475 289 21 98.128 263 281 99 ch 41.511 385 938 13 65.470 791 677 23 103.034 676 446 09 ab 43.171 841 375 65 68.416 977 302 70 108.186 410 268 40 97 44.898 715 030 68 71.495 741 281 33 113.595 730 731 82 98 46.694 663 631 91 74.713 049 638 99 119.275 517 320 9I 99 48.562 450 177 18 78.075 136 872 74 125.239 293 186 96 100 50.504 948 184 27 81.588 518 032 oI 131.501 257 846 30 T.. ..ES . TABLE 22. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY (Continued) Bad of 53 per cent. 6 per cent. 63 per cent. 1.055 1.06 1.065 Y.113 025 ¥.1236 1.134 225 1.174 241 375 1.191 016 1.207 949 625 1.238 824 650 63 1.262 476 96 1.286 466 350 63 1.306 960 006 41 1.338 225 577 6 1.370 086 663 42 1.378 842 806 76 1.418 519 112 26 1.459 142 296 54 1.454 679 161 13 1.503 630 258 99 1.553 986 545 81 1.534 686 515 00 1.593 848 074 53 1.654 995 671 29 1.619 094 273 32 1.689 478 959 co 1.762 570 389 92 1.708 144 458 35 1.790 847 696 54 1.877 137 465 27 II 1.802 092 403 56 1.898 298 558 34 1.999 ISI 400 5I '2 1.901 207 485 76 2.012 196 471 84 2.129 096 241 55 3 2.005 773 897 48 2.132 928 260 15 2.267 487 497 25 : 2.116 091 461 84 2.260 903 955 75 2.414 874 184 57 ; 2.232 476 492 24 2.396 558 193 10 2.571 841 006 56 10 2.355 262 699 31 2.540 351 684 69 2.739 oro 672 oo 7 2.484 802 147 77 2.692 772 785 77 2.917 046 365 67 1s 2.621 466 265 go 2.854 339 152 91 3.106 654 379 44 1) 2.765 646 910 53 3.025 599 502 09 3.308 586 914 10 zo 2.917 757 490 60 3.207 135 472 21 3.523 645 063 52 1 3.078 234 152 59 3.399 563 600 55 3.752 681 992 65 2 3.247 537 030 98 3.603 537 416 58 3.996 606 322 17 3.426 151 567 68 3.819 749 661 57 4.256 385 733 11 | 3.614 589 903 91 4.048 934 641 27 4.533 050 805 76 x 3.813 392 348 62 4.291 870 719 74 4.827 699 108 14 20 4.023 128 927 80 4.549 382 962 93 5.I4I 499 550 16 ‘2 4.244 401 018 82 4.822 345 940 70 5.475 697 020 93 od 4.477 843 074 86 5.111 686 697 15 5.831 617 327 29 z 4.724 124 443 98 5.418 387 898 97 6.210 672 453 56 4.983 951 288 40 5.743 491 172 91 6.614 366 163 og 5.258 068 609 26 6.088 100 643 29 7.044 299 963 64 5.547 262 382 77 6.453 386 681 89 7.502 179 461 28 5.852 361 813 82 6.840 589 882 80 7.989 821 126 26 6.174 241 713 58 7.251 025 275 77 8.509 159 499 46 . 6.513 825 007 82 7.686 086 792 31 9.062 254 866 93 Go 6.872 085 383 26 8.147 251 999 85 9.651 301 433 28 7.250 050 079 33 8.636 087 119 84 10.278 636 026 44 ! 7.648 802 833 70 9.154 252 347 03 10.946 747 368 16 : 8.069 486 989 55 9.703 507 487 85 11.658 285 947 09 « 8.513 308 773 98 10.285 717 937 13 12.416 074 533 65 4 8.981 540 756 54 10.902 861 013 35 13.223 119 378 34 ¢ 9.475 525 498 15 11.557 032 674 15 14.082 622 137 93 4. 9.996 679 400 55 12.250 454 634 60 14.997 992 576 90 é 10.546 496 767 58 12.985 481 912 68 15.972 862 094 40 4 11.126 554 089 8o 13.764 610 827 44 17.011 098 130 53 4; 11.738 514 564 74 14.590 487 477 09 18.116 819 509 02 4! 12.384 132 8635 80 15.465 916 725 71 19.204 412 777 10 43 13.065 260 173 42 16.393 871 729 26 20.548 549 607 62 4) 13.783 849 482 96 17.377 504 033 OI 21.884 205 332 11 50 14.541 961 204 52 18.420 154 274 99 23.2306 678 678 70 ARI 220 340 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 22. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY (Continued) Pa 5% per cent. 6 per cent. 63 per cent. 5¥ 15.341 769 o70 77 19.525 363 531 49 24.821 612 792 81 52 16.185 566 369 66 20.696 885 343 38 26.435 o17 624 35 : 17.075 772 519 99 21.938 698 463 98 28.153 293 769 93 18.014 940 008 59 23.255 020/371 32 29.983 257 864 97 19.005 761 709 07 24.650 321 504 I3 31.932 169 626 20 20.051 078 603 06 26.129 340 889 78 34.007 760 651 go 21.153 887 926 23 27.697 10I 343 17 36.218 265 004 27 22.317 351 762 18 29.358 927 423 76 38.572 452 325 40 23.544 806 109 09 31.120 463 069 18 41.079 661 726 55 : 24.839 770 445 09 32.987 690 853 33 43.749 839 738 78 26.205 957 819 58 34.966 952 304 53 46.593 579 321 80 27.647 285 499 65 37.064 969 442 80 49.622 161 977 72 29.167 886 202 13 39.288 867 609 37 52.847 602 506 27 30.772 119 943 25 41.646 199 665 93 56.282 696 669 18 32.464 586 540 13 44.144 971 645 89 59.941 O71 952 67 : 34.250 138 799 84 46.793 669 944 64 63.837 241 629 60 36.133 896 433 83 49.601 290 I4I 32 67.986 662 335 52 . 38.121 260 737 69 52.577 367 549 80 72.405 795 387 33 tb 40.217 930 078 26 55.732 009 602 79 7.112 172 087/51 : 42.429 916 232 56 59.075 930 178 96 82.124 463 273 19 44.763 561 625 36 62.620 485 989 70 87.462 553 385 95 47.225 557 514 75 66.377 715 149 08 93.147 619 356 04 49.822 963 178 06 70.360 378 058 02 99.202 214 614 18 52.563 226 152 85 74.582 000 74I 50 105.650 358 564 10 55.454 203 591 26 79.056 920 785 99 112.517 631 870 77 ; 58.504 184 783 78 83.800 336 033 15 119.831 277 942 37 / 61.721 914 952 16 88.828 356 195 14 127.620 311 008 62 . 65.116 620 274 53 94.158 057 566 35 135.915 631 224 18 ; 68.698 034 389 63 99.807 541 020 86 144.750 147 253 76 ; 72.476 426 281 06 105.795 993 482 II 154.158 gob 825 25 76.462 629 726 52 112.143 753 09I 04 164.179 235 768 89 80.668 074 361 48 118.872 378 276 50 174.850 886 093 87 ] 85.104 818 451 36 126.004 720 973 09 186.216 193 689 97 : 89.785 583 466 18 133.565 004 231 48 198.320 246 279 82 § 94.723 790 556 82 141.578 904 485 37 211.211 062 288 or ¢ 99.933 599 037 45 150.073 638 754 49 224.939 781 336 73 ¢ 105.429 946 984 51 159.078 057 079 76 239.560 867 123 61 ¢ 111.228 504 068 66 168.622 740 504 54 255.132 323 436 65 & 117.346 166 742 43 178.740 104 934 82 271.715 924 513 28 ¢ 123.800 205 913 27 189.464 511 230 OI 289.377 459 606 64 G 130.609 217 238 50 200.832 381 904 76 308.186 994 481 08 GC. 137.792 724 186 62 212.882 324 319 05 328.219 149 122 35 ¢ 145.371 324 016 88 225.655 264 308 19 349.553 393 815 30 C 153.366 746 837 81 239.194 580 166 68 372.274 364 413 29 g. 161.801 917 913 89 253.546 254 976 68 396.472 198 100 16 99 170.701 023 399 I5 268.759 030 275 28 422.242 890 976 67 97 180.089 579 686 10 284.884 572 091 80 449.688 678 890 13 98 189.994 506 568 84 301.977 646 417 31 478.918 443 018 or 99 200.444 204 430 13 320.096 305 202 34 510.048 141 814 18 100 211.468 635 673 78 339.302 083 514 49 543.201 271 032 IO i. Ss [ TABLE 22. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY (Continued) Had ot 7 per cent. 8 per cent. 9 per cent. 1.07 1.08 1.09 1.144 9 1.166 4 1.188 1 1.225043 1.259 712 1.295 029 1.310 796 oI 1.360 488 96 1.411 581 61 1.402 55I 730 70 1.469 328 076 8 1.538 623 954 9 1.500 730 35I 85 1.586 874 322 94 1.677 100 110 84 1.605 781 476 48 1.713 824 268 78 1.828 039 120 82 1.718 186 179 83 1.850 930 210 28 1.992 562 641 69 1.838 459 212 42 1.999 004 627 10 2.171 893 279 44 Io 1.967 151 357 29 2.158 924 997 27 2.367 363 674 59 2.104 851 952 30 2.331 638 997 05 2.580 426 405 31 19 2.252 191 588 96 2.518 170 116 82 2.812 664 781 78 2.409 845 000 19 2.719 623 726 16 3.0635 804 612 14 L 2.578 534 150 20 2.937 193 624 26 3.341 727 027 24 2.759 031 540 72 3.172 169 114 20 3.642 482 459 69 2.952 163 748 57 3.425 942 643 33 3-970 305 881 06 3.158 815 210 96 3.700 018 054 80 4.327 633 410 35 ! 3.379 932 275 73 3.996 o19 499 18 4.717 120417 29 1y 3.616 527 535 03 4.315 70I 059 I2 5.141 661 254 84 20 3.869 684 462 49 4.660 957 143 85 5.604 410 767 78 zy 4.140 562 374 86 5.033 833 715 36 6.108 807 736 88 22 4.430 401 741 10 5.436 540 412 59 6.658 600 433 20 * 4.740 529 862 98 5.871 463 645 59 7-257 874 472 20 25 5.072 366 953 39 6.341 180 737 24 7.911 083 174 68 on 5.427 432 640 12 6.848 475 196 22 8.623 o8o 660 40 26 5.807 352 924 93 7-396 353 211 92 9.399 157 919 84 a 6.213 867 629 68 7.988 ob1 468 87 10.245 082 132 63 % 6.648 838 363 75 8.627 106 386 38 11.167 139 524 56 29 7.114 257 049 22 9.317 274 897 29 12.172 182 081 77 20 7.612 255 042 66 10.062 656 889 07 13.267 678 469 13 2 8.145 112 895 65 10.867 669 440 20 14.461 769 531 35 ; 8.715 270 798 34 11.737 082 995 42 15.763 328 789 17 9.325 339 754 23 12.676 049 635 05 17.182 028 380 20 9.978 113 537 02 13.690 133 605 85 18.728 410 934 42 10.676 581 484 62 14.785 344 294 32 20.413 967 918 52 : 11.423 942 188 54 15.968 171 837 87 22.251 225'031:18 12.223 618 141 74 17.245 625 584 go 24.253 835 283 99 13.079 271 411 66 18.625 275 631 69 26.436 680 459 55 J 13.994 820 410 47 20.115 297 682 22 28.815 981 700 91 ‘ 14.974 457 839 21 21.724 521 496 80 31.409 420 053 99 al 16.022 669 887 95 23.462 483 216 54 34.236 267 858 85 ‘1 17.144 256 780 11 25.339 431 873 87 37.317 531 966 14 2h 18.344 354 754 72 27.366 640 423 78 40.676 109 843 10 41 19.628 459 587 55 29.555 971 657 68 44.336 959 728 98 4. 21.002 45I 758 67 31.920 449 390 29 48.327 286 104 58 46 22.472 623 381 78 34.474 085 341 52 52.676 741 854 oo 47 24.045 707 018 31 37.232 012 168 84 57.417 648 620 86 4> 25.728 gob 509 8o 40.210 573 142 34 62.585 236 996 73 49 27.529 929 965 49 43.427 418 993 73 68.217 908 326 44 Ne) 29.457 025 063 07 46.901 612 513 23 74.3587 520 07% 82 TABLES 34! 342 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 22. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY (Continued) Bala 7 per cent. 8 per cent. 9 per cent. 51 31.519 016 817 49 50.653 741 514 29 81.049 696 882 64 Lt 33.725 347 994 71 54.706 040 835 43 88.344 169 602 08 C3 36.086 122 354 34 59.082 524 102 27 96.295 144 866 27 38.612 150 919 14 63.809 126 030 45 104.961 707 904 23 41.315 00I 483 43 68.913 856 112 88 114.408 261 615 61 44.207 051 587 33 74.426 964 601 92 124.705 005 I61 02 47.301 545 1938 44 80.381 121 770 OF 135.928 455 625 51 50.612 653 362 33 86.811 611 5II 67 148.162 016 631 81 54.155 539 097 69 93.756 540 432 61 161.496 598 128 67 ) 57.946 426 834 53 101.257 063 667 22 176.031 291 960 25 62.002 676 712 95 109.357 628 760 59 191.874 108 236 67 66.342 8364 082 86 118.106 239 06I 44 209.142 777 977 97 70.986 864 568 66 127.554 738 186 36 227.965 627 995 99 75.955 945 088 46 137.759 117 241 27 248.482 534 515 63 81.272 861 244 66 148.779 846 620 57 270.845 962 622 03 Vs 86.961 961 531 78 160.682 234 350 21 295.222 099 258 02 93.049 298 839 o1 173.536 813 098 23 321.792 088 191 24 Co 99.562 749 757 74 187.419 758 146 09 350.753 376 128 45 t 106.532 142 240 78 202.413 338 797 77 382.321 179 980 OI / 113.989 392 197 63 218.606 405 9o1 60 416.730 086 178 21 ¥ 121.968 649 651 47 236.004 918 373 72 454.235 793 934 25 ; 130.506 455 127 OF 254.982 511 843 62 495.117 o15 388 33 139.641 906 985 96 275.381 112 791 1I 539.677 546 773 28 : 149.416 840 474 98 297.411 601 814 40 588.248 525 982 83 159.876 019 308 23 321.204 529 959 55 641.190 893 321 34 z 171.067 340 659 81 346.900 892 356 32 698.898 073 720 26 : 183.042 054 505 99 374.652 963 744 82 761.798 900 355 08 ’ 195.854 998 32T 4I 404.625 200 844 41 830.360 8o1 387 04 209.564 848 203 91 436.995 216 911 96 905.093 273 SII 87 « 224.234 387 578 19 471.954 834 264 92 986.551 668 127 94 : 239.930 794 708 66 500.711 221 006 11 ~~ 1075.341 318 259 46 256.725 950 338 27 550.488 118 686 60 1172.122 036 9o2 81 274.696 766 861 94 504.527 168 181 53 1277.613 020 224 ob 203.925 540 542 28 642.089 341 636 05 1392.598 192 044 23 . 314.500 328 380 24 693.456 488 966 94 1517.932 029 328 21 ¢ 336.515 351 366 86 748.933 008 084 29 1654.545 911 967 75 “- 360.071 425 962 54 808.847 648 731 03 1803.455 044 044 84 1 385.276 425 779 91 873.555 460 629 52 1965.765 998 008 83 5 412.245 775 584 5T 943.430 897 479 88 2142.684 937 829 68 00 441.102 979 875 42 1018.915 089 278 27 2335.526 582 234 35 471.980 188 466 70 1100.428 296 420 53 2545.723 974 635 44 505.018 8o1 659 37 1188 .462 560 134 17 2774.839 132 352 63 240.370 T17 775 53 1283.539 564 044 9T 3024.574 654 264 37 578.106 026 019 82 1386.222 730 140 50 3206.786 373 143 16 LL 618.669 747 841 20 1497.120 548 551 74 3593-497 146 731 50 9 661.976 630 190 09 1616.890 192 435 88 3916.911 889 037 33 u7 708.314 904 303 39 1746.24I 407 830 75 4269.433 960 031 69 98 757.807 043 004 63 1885.040 720 457 21 4653.683 016 434 54 99 810.040 836 977 96 2036.815 978 003 78 5072.514 487 913 65 100 867.716 325 566 41 2199.761 256 341 20 5529.040 791 825 88 TABLES ; TABLE 22. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY (Continued) Bagot 10 per cent. Fad of 10 per cent. - X.1 51 129.129 938 167 66 1.21 52 142.042 931 984 43 1.331 ol 156.247 225 182 87 1.464 1 © 171.871 947 701 16 1.610 51 . 189.059 142 471 28 1.771 561 207.965 056 718 41 1.948 717 1 228.761 562 390 25 2.143 588 81 ; 251.637 718 629 27 2.357 947 691 276.801 490 492 20 3 2.593 742 460 1 , 304.481 639 541 42 Ii 2.853 116 706 11 ly 334.929 803 495 56 Te 3.138 428 376 72 (2 368.422 783 845 12 1; 3.452.271 21430 Cg 405.265 062 229 63 Ty 3.797 498 335 83 445.791 568 452 59 4.177 248 169 42 . 490.370 725 297 85 10 4.594 972 986 36 £5 539.407 797 827 63 5.054 470 284 99 on 593.348 577 610 40 i} 1-559 917 313 49 £3 652.683 435 371 44 ij 3.115 909 044 84 ©) 717.951 778 908 58 ?> 0.727 499 949 33 = 789.746 956 799 44 oh 7.400 249 944 26 868.721 652 479 38 8.140 274 938 68 955.593 817 727 32 8.954 302 432 55 IO5I.I53 199 500 03 “ 9.849 732 675 81 1156.268 519 450 06 10.834 705 943 39 1271.895 371 395 06 2" 11.918 176 537 73 1399.084 908 534 57 13.109 994 I9I 50 1538.993 399 388 03 . 14.420 993 610 65 1692.892 739 326 83 15.863 092 971 71 1862.182 013 259 3I . 17.449 402 268 89g 2048 .400 214 585 47 19.194 342 495 78 2253 .240 236 044 oI 21.113 776 745 35 2478 .564 250 648 41 23.225 154 419 89 2726 .420 685 613 26 25.547 669 861 88 2999.062 754 174 58 28.102 436 848 06 3298.969 029 592 04 30.912 680 532 87 : 3628.865 932 551 24 34.003 948 586 16 3991.752 525 806 37 37-404 343 444 77 . 4390.927 778 387 00 . 41.144 777 789 25 ¥) 4830.020 556 225 70 : 45.259 255 568 18 in 5313.022 611 848 27 - 49.785 181 124 99 t 5844.324 873 033 10 ‘ 54.763 699 237 49 2 6428.757 360 336 41 ‘ 60.240 069 161 24 i 7071.633 096 370 05 : 66.264 076 077 37 : 7778 .796 406 007 06 72.890 483 685 10 8556.676 046 607 76 ( 80.179 532 053 61 ud 9412.343 651 268 54 ‘ 88.197 485 258 97 7 10353.578 016 395 39 3 97.017 233 784 87 4 11388.935 818 034 93 4) 106.718 957 163 36 99 12527.829 399 838 43 50 117.390 852 879 70 100 13780.612 339 822 27 343 344 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 2:1. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED ANNUALLY (Concluded) (Amounts are noted for the end of each year) Years. | 12 per cent. 15 per cent. 20 per cent. 25 per cent. I $1.12 $1.15 $1.20 $1.25 2 1.2544 1.3225 1.440 1.5625 3 1.404928 1.520875 1.7280 1.953125 1 1.573519 1.749006 2.07360 2.441406 J 1.762342 2.011357] 2.488320 3.051758 S 1.973823 | 2.313061 2.985984 3.814697 y 2.210681 2.660020 3.583181 4.768372 ¢ 2.475963 3.059023 4.299817 5.960464 o 2.773079 3.517876! 5.159780 7.450581 10 3.105848 4.045558 6.191736 9.313226 Ti 3.478550 4.652301 7.430084 11.641532 12 3.895976 5.350250 8.916100 14.55I915 3 4.363493 6.152788 10.699321 18.189894 4.887112 7.075706 12.839185 22.737368 Lo 5.473566 8.137062! 15.407022 28.421709 10 6.130394 9.357621! 18.488426 35.527137 17 6.866041 10.761264 22.186111 44 .408021 18 7.689966 12.375454 26.623333 §5.51TI5T £0) 8.612762 14.231772 31.948000 69.388939 20 9.646293 16.366537 38.337600 86.736174 21 10.803848 18.821518 46 .005120 108 .420217 22 12.1003I0 21 .644746] 55.200144 135.525271 23 13.552347 24.891458 66.247373 169 .406589 24 15.178629 28.625176 79.496847 211.758236 2b 17 .000064 32.918953] 95.396217 264.697796 30 29.959922 66.211772] 237.376314 807.793567 36 | 52.799620 133.175523! 590.668229 2,465.190326 40 93 .050970 267 .863546 1,469.771568 7,523.163845 46° 163.987604 538.769269 3,657.261983 22,958.874039 60 | 289.002190 1,083 .657442 9,100.438150 70,064 .923216 60 ' 897.596933 4,383.998746! 56,347.514353 652,530.446800 | 70 | 2,787.709828 17,735.720039 348,888.956032 6,077,163.357286 80 8,658.483100 71,750.879401 2,160,228.462010 56,597,994 . 242667 90 26,891.934223 290,272 .325206'13,375,565 . 248934 527,109,897 .161526 100 83,522.265727 1,174,313.450700i82,817,974.522015 4,909,093,465 .297726 T/ZZES EXPLANATION OF TABLE 23 AMOUNT OF ONE DoLLAR AT INTEREST CoMPOUNDED EVERY Six MONTHS Table 23 gives the amount of $1 at interest rates from 1 per cent to 10 per cent compounded every six months. These amounts are given for every year up to and including 10 years and for ro-year periods from 10 years to so years. The use of this table for periods of years not specifically given in the table is illustrated by the examples. Example. — (a) What is the amount of $1 at 33 per cent interest for 37 years? The figures for thirty years and for seven years are taken from the 3} per cent column and multiplied together. $1 X 2.107181347 X 1.189954749 = $2.507450453. (b) What is the amount of $1 at 6 per cent interest for 70 years? The figures for 20 years and for 50 years are taken from the 6 per cent column and multiplied together. $1 X 10.218631981 X 3.262037792 = $62.691903701. (¢c) What is the amount of $1,623,425.25 at 4 per cent interest for 14 years? The figures for 10 years and for 4 years are taken from the 4 per cent column, multiplied together and the result multiplied by $1,623,425.25. $1.485947396 X 1.171659381 X 1,623,425.25 = $2,826,422.65. BL 345 346 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 23. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED EVERY SIX MONTHS Patt I per cent. 11 per cent. 2 per cent. 23 per cent. 1.005 000 000 ~~ 1.007 500 000 I.0IO O00 000 1.012 500 000 1.010 025 000 I.0I5 056 250 1.020 I00 000 1.025 156 250 1.020 150 50I 1.030 339 IOI 1.040 604 010 1.050 945 337 1.030 377 509 1.045 852 235+ 1.061 520 I3I 1.077 383 181 1.040 707 044 1.061 598 848 1.082 856 706 1.104 486 101 1.051 I40 132 1.077 582 545+ 1.104 622 125+ 1.132 270 830 1.061 677 812 1.093 806 898 1.126 825 030 1.160 754 518 1.072321 132 1.110 275 528 1.149 474 213 1.189 954 749 1.083 O7I I5I 1.126 992 114 1.172 578 645— 1.219 889 548 1.003 928 940 1.143 960 389 1.196 147 476 1.250 577 394 o 1.104 895 577 1.161 184 142 1.220 IQO 040 1.282 037 232 205 1.220 794 236 1.348 348 612 1.488 863 734 1.643 619 463 ie 1.348 850 153 1.565 681 027 1.816 696 699 2.107 181 347 49 1.490 338 568 1.818 043 980 2.216 715 217 2.701 484 941 50 1.646 668 492 2.111 083 840 2.704 813 829 3.463 404 275— nl 3 per cent. 3% per cent. 4 per cent. 43 per cent. 1.0I5 000 000 I.0I7 500 000 1.020 000 000 1.022 500 000 1.030 225 000 1.035 306 250 1.040 400 000 1.045 506 250 1.061 363 551 1.071 859 031 1.082 432 160 1.093 083 319 1.093 443 264 1.109 702 354 1.126 162 419 1.142 825 442 1.126 492 587 1.148 881 783 1.171 659 381 1.194 831 142 1.160 540 825+ 1.189 444 490 1.218 004 420 1.249 203 426 1.195 618 171 1.231 439 315— 1.268 241 795— 1.306 049 990 1.231 755 731 1.274 916 819 1.319 478 763 1.365 483 427 1.268 985 548 1.319 929 351 1.372 785 705+ 1.427 621 457 1.307 340 636 1.366 531 107 1.428 246 248 1.492 587 156 I< 1.346 855 007 1.414 778 196 1.485 947 396 1.560 509 201 206 1.814 018 409 2.001 597 343 2.208 039 664 2.435 188 965+ 30 2.443 219 776 2.831 816 278 3.281 030 788 3.800 134 786 40 3.200 662 787 4.006 301 924 4.875 439 156 5.930 145 297 50 4.432 045 650— 5.668 155 938 7.244 646 118 0.254 046 298 TATIES TABLE 23. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED EVERY SIX MONTHS (Concluded) Fado 5 per cent. 53 per cent. 6 per cent. 63 per cent. 1.025 000 000 1.027 500 000 1.030 000 000 1.032 500 000 1.050 625 ooo 1.055 756 250 1.060 goo 000 1.066 056 250 1.103 812 891 1.114 621 259 1.125 508 810 1.136 475 928 1.159 693 418 1.176 768 361 1.194 O52 297 1.211 547 266 1.218 402 898 1.242 380 552 1.266 770 081 1.291 577 535-F 1.280 084 544 1.311 651 033 1.343 916 379 1.376 894 304 1.344 888 824 1.384 783 775% 1.425 760 887 1.467 846 778 1.412 973 821 1.461 994 126 1.512 589 725— 1.564 807 232 1.484 505 621 1.543 509 436 1.604 706 439 1.668 172 530 1.559 658 718 1.629 569 734 1.702 433 061 1.778 365 751 } 1.638 616 440 1.720 428 431 1.806 111 235- 1.895 837 924 7 2.685 063 838 2.959 873 987 3.262 037 792 3.594 20I 434 4.399 789 749 5.092 251 361 5.891 603 104 6.814 023 385-4 4s 7.209 567 816 8.760 854 020 [10.640 890 556 12.918 283 949 50 11.813 716 351 15.072 422 338 119.218 631 081 24.490 972 624 Bad of 7 per cent. 8 per cent. 9 per cent. 10 per cent. 1.035 000 000 1.040 000 000 1.045 000 000 1.050 000 000 1.071 225 000 1.081 600 000 1.092 025 000 1.102 500 000 1.147 523 OOI 1.169 858 560 1.192 518 601 1.215 506 250 1.229 255 326 1.265 319 018 1.302 260 125 1.340 095 641 1.316 809 037 1.368 569 050+ 1.422 100 613 1.477 455 444 1.410 598 761 1.480 244 285— 1.552 969 422 1.628 894 627 1.511 068 657 1.601 032 219 1.695 881 433 1.795 856 326 1.618 694 522 1.731 676 448 1.851 944 922 1.979 93I 599 1.733 986 040 1.872 081 246 2.022 370 153 2.182 874 588 1.857 489 196 2.025 816 515+ 2.208 478 766 2.406 619 234 ; 1.989 788 863 2.191 123 143 2.411 714 O25 2.653 297 705+ 4 3.959 259 72I 4.801 020 628 5.816 364 538 7.039 988 712 7.878 090 gor 10.519 627 408 14.027 407 929 18.679 185 894 a+ [15.675 737 540 23.049 799 070 183-830 096 434 49.561 441 067 50 [21.101 407 082 0.504 048 184 81.588 18 022 121.501 257 846 Bit 347 348 VALUATION, DEPRECIATION AND THE RATE-BASE EXPLANATION OF TABLE 24 AMOUNT OF ONE DOLLAR AT INTEREST COMPOUNDED QUARTERLY Table 24 gives the amount of $1 at interest rates from 23 per cent to 6 per cent for each year up to ro years and then for every 10 years from 10 to 50 years. The amount for other years can be obtained by multiplying together the figures given in the table as in the examples given below. Examples. — (a) What is the amount of $1 in 27 years at 3% per cent interest compounded quarterly? From the 31 per cent column take the figures given for 20 years and for 7 years and multiply them together. $1 X 1.910516438 X 1.254303900 = $2.306368219. (b) What is the amount of $24,360.50 in 11 years at 4 per cent interest compounded quarterly? From the 4 per cent column take the figures given for 10 years and for 1 year and multiply them together, then multiply the result by $24.360.50. $1.488863734 X 1.040604010 X 24,360.50 = $37,742.15. (¢c) What will be the amount of $13,240,762.10 in 33 years at 3 per cent compounded quarterly? From the 3 per cent column take the figures for 3 years and for one-half year, multiply them together and then multiply the result by $13,240,762.10. $1.093806808 X 1.015056250X $13,240,762.10 = $14,700,804.16. TT) 5 TABLE 24. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED QUARTERLY ad of 2} per cent. 3 per cent. 3% per cent. 1.006 250 000 1.007 500 000 1.008 125 000 1.012 539 063 1.015 056 250 1.016 316 016 1.018 867 432 1.022 669 172 1.024 573 533 ¥.025 235 353 1.030 339 IQI 1.032 898 244 1.051 107 529 1.061 598 848 1.066 878 782 1.077 632 599 1.093 806 898 I.IO0I 977 220 1.104 827 038 1.126 992 114 1.138 230 335 1.132.707 738 1.161 184 142 1.175 676 114 1.161 292 018 1.196 413 529 1.214 353 793 1.190 597 632 1.232 711 7438 1.254 303 QO0O 1.220 642 784 1.270 III 224 1.295 568 295 - | 1.251 446 135 1.308 645 371 1.338 190 216 IJ 1.283 026 821 1.348 348 612 1.382 214 324 29 1.646 157 822 1.818 043 980 1.910 516 438 30 2.112 064 637 2.451 357 078 2.640 743 187 av 2.709 835 576 3.305 283 915— 3.650 073 059 50 3.476 791 723 4.456 674 980 5.045 183 266 End of 31 per cent. 31 per cent. 4 per cent. 1.008 750 000 1.009 375 000 1.0I0 000 000 1.017 576 563 1.018 837 891 1.020 100 000 1.026 480 357 1.028 389 496 1.030 301 000 1.035 462 ob1 1.038 030 647 1.040 604 010 1.072 181 679 1.077 507 625— 1.082 856 706 I.1I0 203 450 1.118 485 937 1.126 825 030 1.149 573 552 1.161 022 682 1.172 578 645 1.190 339 799 1.205 177 126 1.220 190 040 1.232 551.701 1.251 OIO 792 1.269 734 649 1.276 260 524 1.298 587 542 1.321 290 967 I.32I 519 352 1.347 973 663 1.374 940 679 1.368 383 152 1.399 237 974 1.430 768 784 Lr 1.416 9o8 838 1.452 451 905 - 1.488 863 734 2) 2.007 630 655-1 2.109 616 536 2.216 715 217 4 2.844 629 618 3.064 116 556 3.300 386 891 42 4.030 580 847 4.450 481 927 4.913 826 349 50 ¢.710 965 624 6.464 110 953 2.216 o17 844 ABLL.: 349 350 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 24. AMOUNT OF ONE DOLLAR AT INTEREST COM- POUNDED QUARTERLY (Concluded) add 4% per cent. 43 per cent. 43 per cent. 1.010 625 000 I.0II 250 O00 1.011 875 000 1.021 362 891 1.022 626 563 1.023 891 016 1.032 214 871 1-034 131 TTT 1.036 049 721 1.043 182 154 1.045 765 086 1.048 352 812 1.088 229 00% 1.003 624 616 1.099 043 618 1.135 221 080 1.143 674 441 1.152 135 467 1.184 242 372 1.196 014 800 1.207 896 875— 1.235 380 509 1.250 730 52I 1.266 302 085— 1.288 726 gor 1.307 991 226 1.327 531.352 1.344 376 904 1.367 851 558 1.391 721 225+ 1.402 429 996 1.430 451 402 1.459 o14 860 1.462 989 944 1.495 916 134 1.529 562 331 1 1.526 165 002 1.564 376 865+ 1.603 520 970 z 2.329 179 613 2.447 274 977 2.571 279 503 < 3.554 712 407 3.828 460 357 4.123 100 603 4 5.425 077 667 5.989 154 813 6.611 478 281 50 8.279 563 667 9.369 295 233 10.601 644 069 Pa 5 per cent. 5% per cent. 6 per cent. 1.012 500 000 1.013 750 000 1.0I5 O00 000 1.025 156 250 1.027 689 063 1.030 225 000 1.037 970 703 1.041 819 787 1.045 678 375k 1.050 945 337 1.056 144 809 1.061 363 551 1.104 486 101 1.115 441 858 1.126 492 587 1.160 754 518 1.178 068 128 1.195 618 171 1.219 889 548 1.244 210 538 1.268 985 548 1.282/037:232 1.314 066 502 1.346 855 007 1.347 35I 050 1.357 344 515~- 1.429 502 812 1.415 992 304 1.465 764 780 1.517 222 180 1.488 130 509 1.548 059 864 1.610 324 320 1.563 943 819 1.634 975 390 1.709 139 538 is 1.643 619 463 1.726 770 77% 1.814 018 409 20) 2.701 484 941 2.981 737 296 3.200 662 787 oo 4.440 213 229 5.148 776 809 5.969 322 854 40 7.298 020 885 8.890 757 301 10.828 461 545— 50 11.995 169 172 15.352 299 840 19.643 028 580 T+ "ES EXPLANATION OF TABLE 25 THE PRESENT VALUE OF ONE DorrAarR DUE AT A FUTURE DATE The present value of $1 due at some future time is the sum which placed at compound interest will amount to $1 at that time. The formula on which Table 25 is based is as follows: Let P represent the present value of $1 due at the end of n years. Let n represent any number of years. Let 7 represent the interest rate expressed decimally as 0.05 for 5 per cent. I Then P = (x +3)" (20) Table 235 has been prepared for only a few selected years because the present value of $1 due at a future time is also readily obtain- able from Table 22. According to equation (19), A’ may be substituted for (1 + ¢)”, equation (20) may then be written: I P= VL (21) That is to say, the present value of $1 due at any future time is the reciprocal of $1 at compound interest for the same time. Example. — What is the present value of $600 due in 8 years at 4 per cent interest? From Table 22 the amount of $1 at 4 per cent compound interest in 8 years is $1.368569, consequently the present value of $1 due in 8 years will be I + 1.368560 = 0.730690 and the present value of $600 due in 8 years at 4 per cent will be 0.730690 X 600 = $438.41. Note. — To find the present value of $1 due at the end of any number of years # not noted in this table, select two or . ABIL. 351 352 VALUATION, DEPRECIATION AND THE RATE-BASE more lines from the table the sum of whose years is equal to » and multiply the values found in the interest column on these lines. Example. — What is the present value of $1 at 5 per cent due in 36 years? Present value of $1 due in 30 years at 5 per cent = 0.231377. Present value of $1 due in 6 years at 5 per cent = 0.746215. 0.231377 X 0.746215 = $0.172657, the required present value. TABLES 3 TABLE 25. PRESENT VALUE OF ONE DOLLAR DUE AT A FUTURE DATE Mad oy I per cent. 1} per cent. 2 per cent. .990 09g oI .985 221 67 .980 392 16 .980 296 o5— .970 661 75— .961 168 78 1970 590 15— -956 316 99 .942 322 33 960 980 34 .942 184 23 -923 845 43 951 463 69 .928 260 33 .905 730 81 .942 045 24 .914 542 19 .887 971 38 .932 718 05+ gor 026 79 .870 560 18 923 483 22 887 711 12 .853 490 37 914 339 82 874 592 24 836 755 27 : gos 286 95+ .861 667 23 .820 348 30 1 .896 323 72 .848 933 23 .804 263 04 .887 449 23 .836 387 42 .788 493 18 878 662 60 .824 027 02 .773 032 53 .869 962 97 .811 849 28 757 875 oz 861 349 47 799 851 50+ .743 014 73 ly .852 821 26 788 031 04 .728 445 81 ; 844 377 49 776 385 26 714 162 56 836 017 31 .764 911 59 .700 159 37 : 827 739 92 1753 607 47 686 430 76 819 544 47 .742 470 42 672 971 33 : 811 430 17 .731 497 95- 659 775 82 803 396 21 .720 687 63 .646 839 og 1795 441 79 710 037 08 634 155 92 = .787 566 13 699 543 92 621 721 49 779 768 44 689 205 83 609 530 87 gk 772 047 96 679 020 52 .597 579 28 .764 403 92 .668 985 74 .585 862 og 756 835 57 659 099 25- 574 374 55+ ‘ 749 342 15— .649 358 87 563 112 31 741 922 92 639 762 43 552 070 89 734 577 15- 630 307 81 541 245 97 727 304 11 .620 992 g2 .530 633 30 .720 103 OF 611 815 68 520 228 73 .712 973 34 .602 774 o7 510 028 17 .705 914 20 .593 866 08 .500 027 61 698 924 95— .585 089 74 -490 223 15+ 692 oo4 go .576 443 09 .480 610 93 685 153 37 .567 924 23 .471 187 19 678 369 67 .559 531 26 .461 948 22 x 671 653 14 .551 262 32 .452 890 42 01 665 003 11 .543 115 59 .444 O10 21 658 418 92 1535 089 25 - .435 304 13 651 899 92 527 181 53 -426 768 75+ : 645 445 46 519 390 67 .418 400 74 ‘ 639 054 92 511 714 94 .410 196 80 £) 632 727 64 .504 152 65+ .402 153 73 47 626 463 or .496 702 12 .394 268 36 43 .620 260 41 .489 361 70 .386 537 61 ) 614 119 21 .482 129 75— .378 958 44 50 .608 038 82 .475 oo4 68 .271 27 88 25- 354 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 25. PRESENT VALUE OF ONE DOLLAR DUE AT A FUTURE DATE (Continued) Gl 1 per cent. 1; per cent. 2 per cent. 5I .602 018 64 .467 984 91 364 243 02 57 .596 058 06 .461 068 87 .357 IOI 00 i .590 156 49 .454 255 05— .350 099 02 5 .584 313 36 -447 541 92 -343 234 33 7 .578 528 08 .440 928 oo .336 504 25- i .572 800 08 .434 411 82 .329 906 13 .567 128 79 -427 991 94 .323 437 38 .561 513 65+ .421 666 94 .317 095 47 : .555 954 11 .415 435 41 .310 877 91 or 550 449 62 .409 295 97 .304 782 27 ( 544 999 62 .403 247 26 .298 806 14 .539 603 58 .397 287 94 .292 947 20 .534 260 97 .391 416 69 .287 203 14 | .528 971 26 .385 632 21 23157170 .523 733 92 .379 933 2I .276 050 69 .518 548 44 1374 318 43 .270 637 93 513 414 30 368 786 63 .265 331 30 508 330 99 .363 336 58 .260 128 73 ue 503 298 oI .357 967 o8 .255 028 17 79 .498 314 86 .352 676 92 .250 027 61 y 1493 381 05— 347 464 95— .245 125 II : .488 496 09 .342 330 00 .240 318 74 .483 659 49 .337 270 93 .235 606 61 .478 870 78 332 286 63 .230 986 87 -474 129 49 .327 375 99 .226 457 7% .469 435 14 .322 537 93 .222/017.37 .464 787 26 317177336 .217 664 08 , .460 185 41 1313107523 .213 396 16 ; .455 629 12 308 448 50— .209 2II 92 ¢ 451 117 94 303 890 15— .205 109 73 .446 651 42 .299 399 16 .201 087 97 ‘ 442 229 13 -294 974 54 -197 145 o7 ¢ .437 850 63 .2090 615 31 .193 279 48 ‘ .433 515 47 .286 320 50+ .189 489 68 : .429 223 24 .282 089 17 .185 774 20 : .424 973 50+ .277 920 36 .182 131 57 : .420 765 85— .2731872 16 .178 560 36 en .416 509 85— .269 766 66 .175 059 I8 e .412 475 10 .265 779 96 .171 626 65— G3 .408 391 19 .261 852 18 .168 261 42 ¢ .404 347 71 .257 982 45-— .164 962 17 G .400 344 27 .254 169 90 .161 727 62 ¢ 1396 380 46 .250 413 69 158 556 49 ¢ 392 455 90 .246 713 00 .155 447 54 G .388 570 20 .243 066 99 .152 399 55— Gs 384 722 97 .239 474 87 .149 411 32 97 .380 013 83 .235 935 83 .146 481 69 98 .377 142 41 .232 449 09 .143 609 50— 99 .373 408 32 .229 013 89 140 793 63 100 .300i 71121 .225 629 45 .138 032 97 T. 3 5 TABLE 25. PRESENT VALUE OF ONE DOLLAR DUE AT A FUTURE DATE (Continued) End of | Year, I 2} per cent. 3 per cent. 3} per cent. .975 609 76 .970 873 79 .966 183 57 .951 814 40 -942 595 91 1933 510 70 .928 599 41 915 141 66 .QOI 942 70 905 950 64 .888 487 o5— 871 442 23 .883 854 29 862 608 78 .841 973 17 .862 296 87 .837 484 26 .813 500 64 841 265 24 .813 091 51 .785 990 96 820 746 57 .789 409 23 .759 411 56 .800 728 36 .766 416 73 .733 730 97 I .781 198 40 .744 093 91 708 918 81 762 144 78 .722 421 28 684 9435 71 743 555 89 701 379 83 661 783 30 .725 420 38 .680 951 34 .639 404 15+ .707 727 20 661 117 81 .617 781 79 .690 465 56 .641 861 95— .596 890 62 673 624 93 623 166 94 .576 705 91 .657 195 06 .605 016 45— .557 203 78 .641 165 91 .587 394 61 .538 361 14 : 1,625 527 72 .570 286 03 .520 155 69 2 .610 270 94 .553 675 75+ .502 565 88 : .595 386 29 .537 549 28 .485 570 90 ‘ .580 864 67 521 892 50+ .469 150 63 ; .566 697 24 .506 691 75— .453 285 63 2 .552 875 35+ -491 933 74 437 957 13 : :539 390 59 .477 605 57 .423 146 99 2 .526 234 72 .463 694 73 -408 837 67 « 513 399 73 -450 189 06 .395 012 24 ‘ .500 877 78 -437 076 75+ .381 654 34 2 .488 661 25+ .424 346 36 .368 748 15+ 1 .476 742 69 .411 986 76 .356 278 41 .465 114 81 -399 987 15— .344 230 35 - -453 770 55+ 388 337 03 .332 589 71 .442 702 98 .377 026 25-— .321 342 71 : -431 905 34 .366 044 90 .310 476 05} -421 371 07 .355 383 40 .299 976 86 411 093 72 .345 032 43 .289 832 72 .401 067 o5- .334 982 94 .280 031 61 .391 284 92 .325 226 15+ .270 561 94 : .381 741 39 .315 753 55— .261 412 30 4 .372 430 62 1306 556 84 .252 572 47 ¢ .363 346 95— .297 628 oo .244 O31 37 .354 484 83 .288 959 22 .235 779 10 - .345 838 86 .280 542 94 .227 805 go ' .337 403 76 292 37158 .220 102 31 g .329 174 40 .264 438 62 .212 659 24 4: .321 145 76 .256 736 53 .205 467 87 4 .313 312 04 .249 258 77 .198 519 68 : .305 671 16 .241 998 80 .191 806 45-+ § 1 .298 215 76 .234 950 29 .185 320 24 50 .200 042 21 .228 107 08 .179 053 37 ‘ABLES 35: 3 56 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 25. PRESENT VALUE OF ONE DOLLAR DUE AT A FUTURE DATE (Continued) Pe 23 per cent. 3 per cent. 33 per cent. 5I .283 846 06 .221 463 18 .172 998 43 52 .276 922 98 .215 o12 80 .167 148 24 53 .270 168 76 .208 750 29 .161 495 89 54 .263 579 28 .202 670 19 .156 034 67 .257 150 52 .196 767 17 1501758 14 : .250 878 55 .191 036 09 .145 660 04 : .244 759 56 .185 471 93 .140 734 33 0 .238 789 82 .180 069 84 .135 975 20 : .232 965 63 .174 825 08 131 377 0% C. .227 283 59 .169 733 09 .126 934 31 6 .221 740 09 .164 789 41 .122 641 84 6 .216 331 79 .159 989 72 .118 494 53 { .2I1 055 4I .1551320:82 .114 487 47 € .205 QO7 71 .150 805 65 .1I0 615 9I € .200 885 57 .146 413 25+ .106 875 28 € .195 985 93 .142 148 79 .103 261 14 ( 101 705173 .138 008 53 .099 769 22 ¢ .186 542 23 .133 988 87 .096 395 38 € .181 992 41 .130 086 28 .093 135 63 : 377155353 .126 297 36 .089 986 12 : .173 223 00 .122 618 80 .086 943 II ’ .168 998 o5— .119 047 37 .084 003 oo 164 376/15— .115 579 98 .081 162 32 .160 854 78 112 213157 .078 417 70 .156 931 49 .108 045 21 .075 765 go .153 103 89 1051772 05+ .073 203 76 ; .149 369 65+ .102 691 3I .070 728 27 .145 726 49 .09Q 700 30 .068 336 50— , “14237218 .096 796 41 .066 025 60 ‘ .138 704 57 .093 977 10 .063 792 85+ ‘ .135 32I 53 .09I 239 90 .061 635 61 oo .132 021 OI .088 582 43 .059 55I 3I .128 800 98 .086 002 36 057 1537 50— .125 659 49 .083 497 43 .055 591 78 .I122 594 63 .081 065 47 053 711137 & .119 604 52 .078 704 34 .051 895 53 . .116 687 33 .076 411 98 .050 140 60 L113 84I 30 .074 186 39 .048 445 03 a .I111 064 68 .072 025 62 .046 806 79 GJ .108 355 79 .069 927 79 .045 223 95+ OI .105 712 96 067 891 05+ .043 694 64 nz .103 134 60 .065 913 64 .042 217 O4 Cs .100 619 I2 .063 993 83 .040 789 41 0g .098 165 0co— .062 129 93 .039 410 06 95 .095 770 73 .060 320 32 .038 077 35+ 96 .093 434 36 .058 563 42 .036 789 71 97 .091 155 96 .056 857 69 .035 545 62 98 .088 932 64 .055 201 64 .034 343 59 99 .086 763 55+ .033 593 83 .033 182 21 100 .084 647 37 .052 032 84 .032 060 II TAL. ES ] TABLE 25. PRESENT VALUE OF ONE DOLLAR DUE AT A FUTURE DATE (Continued) Pa 4 per cent. 4} per cent. § per cent. .961 538 46 .956 937 80 .952 380 95+ .924 556 21 915 729 95+ .907 029 48 .888 996 36 .876 296 60 .863 837 60 854 804 19 838 561 34 .822 702 47 .821 927 11 .802 451 05— .783 526 16 .790 314 53 .767 895 74 .746 215 46 .759 917 81 .734 828 46 .710 681 33 .730 690 20 703 185 13 .676 839 36 702 586 74 672 904 43 .644 608 92 Lo 675 564 17 643 927 68 613 913 25+ : .649 58093 616 198 74 584 679 29 2 .624 597 o5— 589 663 86 556 837 42 .600 574 09 564 271 64 530 321 35+ .577 475 08 .539 972 86 505 067 95+ .555 264 50+ .516 720 44 .481 017 10 .533 908 18 .494 469 32 458 111 52 .513 373 25— 473 176 39 -436 296 69 .493 628 12 .452 800 37 .415 520 65-- 1 474 642 42 433 301 79 -395 733 96 20 .456 386 95- 414 642 86 .376 889 48 2: -438 833 60 396 787 43 .358 942 36 7! 421 955 39 379 700 89 .341 849 87 405 726 33 .363 350 13 -325 571 31 -390 121 47 1347 703 47 .310 067 91 .375 116 80 332 730 60 .2095 302 77 , .360 689 23 318 402 48 .281 240 73 .346 816 57 304 691 37 .267 848 32 : -333 477 47 .291 570 69 .255 093 64 24 .320 651 41 .279 O15 02 .242 946 32 Ct .308 318 67 .267 ooo 02 .231 377 45 - .296 460 26 .255 502 41 .220 359 47 .285 057 94 .244 499 91 .209 866 17 -274 094 17 .233 971 21 .199 872 54 .263 552 09 .223 8935 89 .190 354 80 .253 415 47 .214 254 44 .181 290 29 Ge .243 668 72 .205 028 17 .172 657 41 .234 296 85- .196 199 21 .164 435 63 or .225 283 43 .187 750 44 .156 603 36 39 .216 620 61 .179 665 49 .149 147 97 40 .208 289 og .171 928 70 .142 045 68 4x .200 277 92 .164 525 07 .135 281 60 42 .192 574 93 .157 440 26 .128 839 62 4; .185 168 20 .150 660 54 .122 704 40 4, .178 046 35 - .144 172 76 .116 861 33 4 .I71 198 41 .137 964 37 LITT 206 51 4 .164 613 86 .132 023 32 .105 996 68 47 .158 282 56 .126 338 10 .100 949 21 4) .152 194 76 .120 897 71 .096 142 11 49 .146 341 12 .115 691 58 .091 563 91 50 .140 712 62 .110 709 65— .087 203 73 ABLES 35~ 353 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 25. PRESENT VALUE OF ONE DOLLAR DUE AT A FUTURE DATE (Continued) os 4 per cent. 43 per cent. 5 per cent. 5I .135 300 59 10504225 — .083 O51 17 G6 .130 096 72 .101 380 14 .079 096 35+ ; .125 093 00 .097 OI4 49 .075 329 86 .120 281 73 .092 836 83 .O7I 742 72 .115 655 5I .088 839 o7 .068 326 40 L111l207 22 .085 013 47 .065 072 76 .106 930 02 .081 352 60 .061 974 06 .102 817 33 .077 849 38 .059 022 9I ] .098 862 82 .074 497 oI .056 212 30 .095 060 40 .071 289 or .053 535 52 .00I 404 23 ,068 219 I15— .050 986 21 ro .087 888 68 .065 281 48 .048 558 30 : .084 508 35-+ .062 470 32 .046 246 oo .081 258 03 .059 780 21 .044 043 81 L075 13272 .057 205 94 .041 946 48 .075 127 60 .054 742 53 .039 949 03 .072 238 09 .052 385 19 .038 046 70 .069 459 70 .050 129 37 .036 234 95— Ce .066 788 18 .047 970 69 .034 509 48 .064 219 40 .045 904 97 .032 866 17 .061 749 42 .043 928 20 {0311301 (TY .059 374 45— .042 036 55+ .029 810 58 .057 090 81 .040 226 37 .028 391 03 .054 895 or .038 494 13 .027 039 08 .052 783 67 .036 836 49 .025 751 50+ A .050 753 53 .035 250 23 .024 525 24 .048 801 47 .033 732 28 .023 357 37 ; .046 924 49 .032 279 69 .022 245 I2 : .045 IIQ 70 .030 889 66 .021 185 82 « .043 384 33 .029 559 48 .020 176 98 . .04T 715 70 .028 286 58 .019 216 17 040 111 25— .027 068 50— .018 30I II : .038 568 51 .025 9o2 87 .017 429 63 : .037 085 10 .024 787 44 .016 599 65— ¢ .035 658 75+ .023 720 03 .o15 809 19 ¢ .034 287 26 .022 698 60 .015 056 37 { .032 968 52 lo2T iy 2115— .0I4 339 40 { .031 700 50+ .020 785 79 .o13 656 57 & .030 481 25+ .019 890 70 .o13 006 26 C. .029 308 go .0IQ 034 17 .012 386 91 C .028 181 63 .018 214 51 .0II 797 0b « .027 097 72 .0I7 430 16 .0II 235 30 ¢ .026 055 50+ .016 679 58 .0I0 700 28 ¢ .025 053 37 .015 961 32 .0I0 190 74 S, .024 089 78 .015 273 99 .009 705 47 96 L025 163 25— .o14 616 26 .009 243 31 97 .022 272 35+ .013 986 85— .008 803 15— 98 .021 415 72 .013 384 54 .008 333 95+ 99 .020 592 04 .012 808 17 .007 984 71 100 .019 800 04 .o12 256 63 .007 604 49 : : / TABLE 25. PRESENT VALUE OF ONE DOLLAR DUE AT A FUTURE DATE (Continued) ig 5} per cent. 6 per cent. 63 per cent. : 1947 867 30 -943 396 23 -938 967 14 .898 452 42 .889 996 44 .881 659 28 851 613 66 .839 619 28 .827 849 og .807 216 74 .792 093 66 “777 323 09 765 134 35+ 747 258 17 -729 880 84 725 245 83 704 960 54 685 334 12 687 436 81 665 057 11 .643 506 21 .651 598 87 627 412 37 .604 231 19 .617 629 26 .591 898 46 .567 353 23 .585 430 58 558 394 78 532 726 o4 .554 910 50+ .526 787 53 500 212 24 .525 981 52 .496 969 36 .469 682 85+ .498 560 68 .468 839 02 .441 016 76 : -472 569 37 -442 300 96 +414 100 25— 447 933 05 - .417 265 06 388 826 52 -424 581 og -393 646 28 365 095 33 .402 446 53 .371 364 42 .342 812 51 .381 465 90 -350 343 79 321 889 68 1 .361 579 06 .330 513 OI 302 243 84 : .342 728 96 .311 804 73 .283 797 03 2 .324 861 58 .204 155 40 .266 476 o8 2 .307 925 67 .277 505 10 .250 212 28 .291 872 67 .261 797 26 .234 941 11 2 .276 656 56 .246 978 55- .220 bor g8 2 .262 233 70 .232 998 63 .207 138 or 26 .248 562 75+ .219 810 03 -194 495 79 2° .235 604 50+ .207 367 95+ .182 625 15+ z3 .223 321 81 .195 630 14 .171 479 02 21 211 679 44 .184 556 74 .161 013 16 : .200 644 02 .174 110 13 .151 186 07 .190 183 go .164 254 84 .141 958 75— .180 269 10 .154 957 40 .133 204 60 .170 871 19 .146 186 22 .125 159 25— .161 963 21 137 9I1'53 .1I7 520 42 .153 519 63 .130 105 22 .110 347 81 145 516 24 .122 740 77 .103 612 97 .I137 930 08 .I15 793 18 .097 289 17 .130 739 41 -109 238 85+ ‘091 351 34 .123 923 62 .103 055 52 .085 775 90 ¢ .II7 463 14 .097 222 19 .080 540 75+ L III 339 47 .091 719 OF - .075 625 12 yc .105 535 04 .086 527 40 .071 009 50+ os .100 033 22 .081 629 62 .066 675 59 le .004 818 22 .077 009 08 .062 606 19 4 .089 875 og .072 650 07 .058 785 15+ 40 .085 189 65-4 .068 537 81 .055 197 33 41 .080 748 49 .064 658 31 .051 828 47 43 .076 538 85+ .060 998 40 .048 665 24 49 .072 548 67 .057 545 66 .045 695 06 50 .068 766 52 .054 288 36 .042 ob 16 TABLES 350 360 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 25. PRESENT VALUE OF ONE DOLLAR DUE AT A FUTURE DATE (Continued) ni ok 5% per cent. 6 per cent. 6% per cent. 51 .065 181 53 .05I 215 44 .040 287 47 52 .061 783 44 .048 316 45— .037 828 61 53 .058 562 50-+ .045 531 56 .035 519 82 £ .055 509 48 .043 0OT 47 .033 351 95— .052 615 62 .040 567 42 .031 316 38 : .049 872 63 .038 271 15+ .020 405 05+ .047 272 63 .036 104 86 .027 610 38 i .044 808 18 .034 061 19 .025 925 24 .042 472 2I 032/133 20 .024 342 95- : .040 258 02 .030 314 34 .022857 23 : .038 159 26 .028 598 43 .021 462 18 . .036 169 92 .026 979 65+ .020 152 29 { .034 284 28 .025 452 50+ .018 922 33 .032 496 95- .024 OIT 79 .017 767 45+ : .030 802 79 .022 652 64 .016 683 o5- .029 196 96 .021 370 41 .o15 664 84 .027 674 85— .020 160 77 .014 708 77 .026 232 08 .0IQ 0IQ 59 L013 373 o5— ‘ .024 864 53 .OI7 943 OI .012 968 12 .023 568 28 016192737 .012 176 64 .022 339 60 .015 969 21 .OIT 433 46 .021 174 98 .015 065 30 .0IO 735 65— .020 O71 QF .0I4 212 54 .010 080 42 ,01Q 024 7I .013 408 06 .009 465 18 .018 032 gO .012 649 11 .008 887 50— ! .017 092 79 .OII 033 13 .008 345 07 Co .016 201 70 .011!25767 .007 835 74 oo .015 357 06 .010 620 44 007 357 51 7 .014 556 46 .010 019 28 .006 908 46 ) .013 797 59 .009 452 15+ .006 486 81 .013 078 28 .008 917 13 .006 09o go .012 396 48 .008 412 38 .005 719 16 .OI1 750 22 .007 936 21 .005 370 IO O11 137 65- .007 486 99 .005 042 35- : .0IO 557 OI .007 063 20 .004 734 60 HI .010 006 64 .006 663 40 .004 445 63 ‘ .009 484 97 .006 286 22 .004 174 30 £ .008 990 49 .005 930 40 .003 919 53 : .008 521 80 .005 594 72 .003 680 31 < .008 077 53 .005 278 03 .003 455 69 ] .007 656 43 .004 979 28 .003 244 78 v .007 257 28 .004 697 43 .003 046 74 ¢ .006 878 04 .004 431 54 .002 860 79 ( .006 520 32 .004 180 70 .002 686 19 ¢ .006 180 40 .003 944 05-1 .002 522 24 GJ .005 858 20 .003 720 81 .002 368 31 G7 .005 552 79 .003 5I0 I9 .002 223 76 a8 .005 263 31 .003 311 50+ .002 088 04 99 .004 988 92 .003 124 06 .0o1 960 60 100 .004 728 83 .002 047 23 .001 840 04 T... £3 TABLE 25. PRESENT VALUE OF ONE DOLLAR DUE AT A FUTURE DATE (Continued) Bod of 7 per cent. 8 per cent. 9 per cent. 1934 579 44 +925 925 93 917 431 19 -873 438 73 -857 338 82 -841 679 99 .816 297 88 .793 832 24 772 183 48 .762 895 21 735 029 85+ 708 425 21 .712 986 18 680 583 20 .649 931 39 666 342 22 630 169 63 .596 267 33 622 749 74 583 490 40 .547 034 24 582 00g 10 540 268 88 .501 866 28 543 933 74 500 248 97 -460 427 78 i .508 349 29 463 193 49 -422 410 81 Ir 475 092 80 .428 882 86 .387 532 85+ Te 444 o11 96 -397 113 76 -355 534 73 i: 414 964 45- 367 697 92 -326 178 65— "y 387 817 24 .340 461 04 -299 246 47 i. .362 446 o2 315 241 71 .274 538 04 5 .338 734 60 .291 890 47 .251 869 76 so .316 574 39 .270 268 95+ .231 073 18 -295 863 92 -250 249 03 -2IT 993 74 1) .276 508 33 .231 712 06 .194 489 67 20 .258 419 oo .214 548 21 .178 430 89 21 .241 513 OQ .198 655 75— .163 698 0b 22 22503 .183 940 51 .150 181 ¥1 .210 946 88 .170 315 28 .137 781 39 21 .197 146 62 .157 699 34 .126 404 04 > .184 249 18 .146 o17 go .115 967 84 20 172 195 49 .135 201 76 .106 392 51 57 .160 930 37 .125 186 82 .097 607 81 ’ .150 402 21 .115 913 72 .089 548 45- 21 .140 562 82 .107 327 52 .082 154 54 131 367 12 -099 377 33 .075 371 14 . .122(773 o1 .092 016 o5— .069 147 83 ' 114 741 13 .085 200 05— .063 438 38 .107 234 70 .078 888 93 .058 200 35 - -100 219 34 .073 045 31 .053 394 81 ; .093 662 94 .067 634 54 .048 986 o7 Co .087 535 46 .062 624 58 .044 941 35 .081 808 84 .057 983 72 .04I 230 59 ; .076 456 86 .053 690 48 .037 826 23 : .071 455 OI .049 713 41 .034 702 96 ‘ .066 780 38 .046 030 93 .031 837 58 ¢ .062 411 57 .042 621 23 .029 208 79 a .058 328 57 .039 464 11 .026 797 ob . .054 512 68 .036 540 84 .024 584 46 2 .050 946 43 .033 834 11 .022 554 55 - . .047 613 49 .031 327 88 .020 692 24 40 .044 498 59 .029 007 30 .018 983 71 47 .041 587 47 .026 858 61 .017 416 25- 43 .038 866 79 .024 869 08 .015 978 21 4) .036 324 10 .023 026 93 .014 658 91 50 .033 947 76 .021 321 23 .0I3 448 54 ABLT: 261 362 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 25. PRESENT VALUE OF ONE DOLLAR DUE AT A FUTURE DATE (Continued) Pe : 7 per cent. 8 per cent. 9 per cent. 5I .031 726 88 o19 741 88 .012 338 1X 52 .029 651 29 .018 279 52 .OII 319 37 53 .027 711 48 .016 925 48 .010 384 74 i .025 898 58 .015 671 74 .009 527 28 . .024 204 28 .014 510 87 .008 740 63 nh .022 620 83 .013 435 99 .008 018 92 , ,021 140 96 .0I2 440 73 .007 356 81 . .0I9 757 OI ,OII 5IQ 20 .006 749 37 .018 465 33 .010 6635 92 .006 192 08 6. O17 257.32 .009 875 85+ .005 680 81 61 .016 128 34 ,009 I44 31 .005 211 75+ Gros .0I5 073 2I .008 466 95+ .004 781 42 . .014 087 11 .007 839 77 .004 386 63 « .013 165 53 .007 259 05 — .004 024 43 : .0I2 304 23 .006 721 34 .003 692 14 ( .OIT 499 28 .006 223 46 .003 387 28 [ .010 746 99 .005 762 47 .003 107 60 ¢ .OIO 043 92 .005 335 62 ,002 85I OI ¢ .009 386 84 .004 940 39 .002 615 60 : .008 772 75— .004 574 43 .002 399 63 j .008 198 83 .004 235 58 .002 20I 50— .007 662 46 .003 921 84 .002 OIQ 72 .007 I6I 17 .003 631 33 .oo1 852 96 .006 692 69 .003 362 34 .0o1 699 96 .006 254 85— .003 113 28 .001 559 60 ; .005 845 65+ .002 882 67 .00I 430 82 .005 463 23 .002 669 14 .0o1 312 68 .005 105 82 .00Z 471 42 .00I 204 30 : .004 771 79 .002 288 35+ 001 104 86 ‘3 .004 459 62 .002 118 85— .001 013 63 .004 167 87 .0o01 961 go .000 929 94 .003 895 20 .oo1 816 57 .000 853 15% .003 640 38 .0o1 682 or ,000 782 71 .003 402 22 .00I 557 42 .000 718 08 .003 179 65- .00I 442 05+ .000 658 79 a .002 971 63 .00I 335 23 .000 604 40 < L002! 777.23 .001 236 33 .000 554 49 &s .002 595 54 .00I 144 75— .000 508 71 89 .002 425 74 .00I 059 95+ .000 466 70 ao .002 267 04 .000 981 44 .000 428 17 Gu .002 118 73 .000 908 74 ,000 392 82 92 .00I 980 12 .000 841 42 .000 360 38 G .oo1 850 58 .000 779 10 .000 330 63 ¢ .00I 729 52 .000 721 38 .000 303 33 C .001 616 37 .000 667 95— .000 278 28 9b .00I 510 63 .000 618 47 .000 255 30 97 .00I 411 80 ,000 572 66 000 234 22 98 .00I 319 44 .000 530 24 .000 214 83 99 .00I 233 I2 .000 490 96 .000 197 I4 100 LOOT I52 45+ .000 454 59 .000 180 86 T,.™ ES TABLE 25. PRESENT VALUE OF ONE DOLLAR DUE AT A FUTURE DATE (Concluded) Engs I0 per cent. Et 10 per cent. -909 090 91 ST -007 744 14 .826 446 28 v2 .007 040 13 .751 314 80 53 .006 400 11 .683 o13 46 : .0035 818 29 .620 921 32 .0035 289 35+ .564 473 93 ' .004 808 50+ .513 158 12 .004 371 36 .466 507 38 .003 973 97 .424 097 62 J .003 612 70 IO .385 543 29 to .003 284 27 TI .350 493 90 dq .002 985 70 7 .318 630 82 2 .002 714 27 2h .289 664 38 3 .002 467 52 .263 331 25+ i .002 243 20 -239 392 05 — Cy -002 039 27 19 .217 629 14 b) .oor 853 88 po .197 844 67 ’ .0o1 683 35— il .179 858 79 : .00I 532 14 1) .163 507 99 bg .oor 392 85+ 2) .148 643 63 hy .001 266 23 27 .135 130 57 .00I ISI I2 z .122 845 97 .001 046 47 y .111 678 16 .000 951 34 z .I0I 525 60 .000 864 85+ : .092 296 co .000 786 23 2h .083 905 45+ .000 714 75% Z 076 277 68 .000 649 78 2: .069 343 35— .000 590 70 2 .063 039 41 .000 537 00 : .057 308 55+ .000 488 19 : .052 098 68 .000 443 81 .047 362 44 .000 403 46 .043 056 76 .000 366 78 :039 142 51 1000 333 44 . .035 584 10 \ .000 303 13 4 .032 349 18 EH .000 275 57 ) .029 408 35- a= .000 250 52 oo .026 734 86 $s 000 227 74 "1 .024 304 42 89 000 207 04 4 3 .022 0094 93 on .000 188 22 é ,020 086 30 C1 000 I7I II i .018 260 27 02 000 155 55 r .016 600 23 ‘ 000 I41 41 ‘ ,OI5 OQI I3 G .000 128 53 . .,OI3 719 2I ¢ .000 116 87 I) .0I2 472 OI 04 .000 106 24 4! ,0IT 338 19 o7 .000 096 58 43 .0I0 307 45— 98 .000 087 8o 49 .009 370 41 99 ,000 079 82 50 .008 518 55-4 100 .000 072 57 ABL- 2032 304 VALUATION, DEPRECIATION AND THE RATE-BASE EXPLANATION OF TABLE 26 Tae AMOUNT OF AN ANNUITY OF ONE DOLLAR An annuity is a sum uniform in amount due annually. The amount of an annuity in any term or number of years is the sum of the several annual installments with interest thereon during the term compounded annually. Table 26 shows the amount of an annuity of one dollar paid at the end of each year with the earned interest increments of each year added at the end of the year. To find the amount of an annuity of $1 paid at the beginning of each year subtract $1 from the figures noted in the table and the result will then apply at the beginning of each year, or, which is the same, at the end of the preceding year. Thus for 6 per cent interest at the beginning of the year 1, the amount is zero; at the end of year 11, or beginning of the year 12, it is $16.37 — 1.00 = $15.37. The values given in Table 26 are calculated by the following formula: Let A” represent the amount of an annuity of $1 paid at the end of each year. Let i represent the interest rate expressed in percentage, as o.os for 5 per cent. Let # represent the number of years. Then A (rhiiy — 3 (2+) 7 and it follows from equation (19) that: ! Al = 4 (22a) The amount of an annuity of $1 paid at the end of each year can be found, in other words, from any table giving the amount of $1 at compound interest by subtracting $1 from the amount found in the compound interest table and dividing the remainder by the rate of interest expressed decimally. re Lo Ti 7S ; Example. — What is the amount of an annuity of $35 at the end of 17 years at 5 per cent interest? From Table 26 the amount of an annuity of $1 for 17 years at 5 per cent is found to be $25.84037, consequently the amount of an annuity of $35 will be 35 X 25.84037 = $904.41. Or from Table 22 the amount of $1 at 5 per cent compound interest for 17 years is found to be 2.292018, therefore, according to equation (22a), vo 2.202018 — 1 A" = Oe 25.84036 and the amount of the annuity of $35 will be 35 X 25.84036 = $904.41. When the annuity is applied at the beginning instead of at the end of the year and the amount thereof is designated by A’, then: ABLL 365 (25 366 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 26. AMOUNT OF AN ANNUITY OF ONE DOLLAR For annuity applied at end of each year A 1 per cent. 1} per cent. 2 per cent. 1.000 000 O00 1.000 000 000 1.000 O00 000 2.0I0 000 O00 2.015 O00 000 2.020 000 000 3.030 100 000 3.045 225 000 3.060 400 000 4.060 401 000 4.090 903 375 4.121 608 000 5.IO0I 005 OIO 5.152 266 926 5.204 040 160 6.152 015 obo 6.229 550 930 6.308 120 963 7-213 535 211 7-322 994 193 7-434 283 382 8.285 670 563 8.432 839 106 8.582 969 050 9.368 527 268 9.559 331 693 9.754 628 431 10.462 212 541 10.702 721 668 10.949 72I 000 1 11.566 834 667 11.863 262 493 12.168 715 420 1 12.682 503 013 13.041 2II 431 13.412 089 728 3 13.809 328 043 14.236 829 602 14.680 331 523 14.947 421 324 15.450 382 046 15.973 938 153 J 16.096 895 537 16.682 137 777 17.293 416 916 1 17.257 864 492 17.932 369 844 18.639 285 255 ! 18.430 443 137 19.201 355 39T 20.012 070 960 1 19.614 747 569 20.489 375 722 21.412 312 379 1, 20.810 895 044 21.796 716 358 22.840 558 626 2h 22,019 003 995 23.123 667.103 24.297 369 799 Zi 23.239 194 035 24.470 522 110 25.783 317 195 2 24.471 585 975 25.837 579 942 27.298 983 539 : 25.716 301 835 27.225 143 641 28.844 963 210 : 26.973 464 853 28.633 520 795 30.421 862 474 : 28.243 199 502 30.063 023 607 32.030 299 723 : 29.525 631 497 31.513 968 961 33.670 gos 718 2 30.820 887 812 32.986 678 496 35.344 323 332 32.129 096 690 34.481 478 673 37.051 210 309 “x 33.450 387 657 35.998 700 853 38.792 234 515 7d 34.784 891 533 37.538 681 366 40.568 079 205 36.132 740 449 39.101 761 587 42.379 440 789 37.494 067 853 40.688 288 o10 44.227 029 605 38.869 008 532 42.298 612 331 46.111 570 197 40.257 698 617 43.933 09I 515 48.033 8o1 601 41.660 275 603 45.592 087 888 49.994 477 633 43.076 878 359 47.275 969 207 51.994 367 186 44.507 647 143 48.985 108 745 54.034 254 530 45.952 723 614 50.719 835 376 56.114 939 620 47.412 250 850 52.480 683 656 58.237 238 412 = 48.886 373 359 54.267 893 911 60 401 983 181 50.375 237.002 56.081 912 320 62.610 022 844 51.878 989 463 57.923 I4I 005 64.862 223 301 53-397 779 358 59.791 988 120 67.159 467 767 : 54.931 757 152 61.688 867 942 69.502 657 123 ‘ 56.481 074 723 63.614 200 961 71.892 710 265% 4 58.045 885 470 65.568 413 975 74.330 564 470 4 59.626 344 325 67.551 940 185 76.817 175 760 4 61.222 607 768 69.565 219 288 70.353 519275 4) 62.834 833 846 71.608 697 577 81.940 589 660 50 64.463 182 184 73.682 828 041 84.579 401 454 TABLES | TABLE 26. AMOUNT OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity applied at end of each year Fad of I per cent. 1} per cent. 2 per cent. 5I 66.107 814 006 75.788 070 461 87.270 989 483 uz 67.768 892 146 77.924 891 518 90.016 409 272 (i 69.446 581 068 80.093 764 891 92.816 737 458 a 71.141 046 878 82.295 171 364 95.673 072 207 72.852 457 347 84.529 598 935 98.586 533 651 74.580 981 921 86.797 542 919 101.558 264 324 76.326 791 740 89.099 506 062 104.589 429 611 : 78.090 059 657 91.435 998 653 107.681 218 203 Pe 79.870 960 254 93.807 538 633 110.834 842 567 ) 81.669 669 856 96.214 651 713 114.051 539 418 83.486 366 555 98.657 871 488 117.332 570 207 35.321 230 221 IOI.I37 739 561 120.679 221 611 87.174 442 523 103.654 805 654 124.092 806 043 89.046 186 948 106.209 627 739 127.574 662 164 | 90.936 648 817 108.802 772 153 131.126 155 407 * 92.846 o15 306 111.434 813 737 134.748 678 515 94.774 475 459 114.106 335 943 138.443 652 086 ) 96.722 220 213 116.817 930 983 142.212 525 127 t, 98.689 442 415 119.570 199 947 146.056 775 630 ; 100.676 336 840 122.363 752 946 149.977 9II 142 102.683 100 208 125.199 209 241 153.977 469 365 104.709 931 210 128.077 197 379 158.057 018 753 106.757 030 522 130.998 355 340 162.218 159 128 108.824 600 827 133.963 330 670 166.462 522 310 110.912 846 836 136.972 780 630 170.791 772 756 113.02I 975 304 140.027 372 340 175.207 608 212 115.152 195 O57 143.127 732.023 179.711 760 376 117.303 717 008 146.274 699 669 184.305 995 583 119.476 754 178 149.468 820 164 188.992 115 495 121.671 321.719 152.710 852 466 193.771 957 803 123.888 236 937 156.001 515 253 198.647 396 961 126.127 119 306 159.341 537 982 203.620 344 goo 128.388 390 499 162.731 661 052 208.692 751 798 130.672 274 404 166.172 635 967 213.866 606 834 132.978 997 148 169.665 225 507 219.143 938 971 135.308 787 120 173.210 203 889 224.526 817 7350 137.661 874 991 176.808 356 948 230.017 354 IO ¢ 140.038 493 741 180.460 482 302 235.617 701 187% & 142.438 878 678 184.167 389 536 241.330 035 211 € 144.863 267 465 187.929 goo 380 247.156 656 315 2 147.311 QOO I40 191.748 848 883 253.099 789 442 149.785 019 141 195.625 081 618 259.161 785 230 152.282 869 332 199.559 457 843 265.345 020 935 : 154.805 698 026 203.552 849 710 271.651 921 354 . 157.353 755 006 207.606 142 456 278.084 959 781 96 159.927 292 556 211.720 234 593 284.646 658 976 a7 162.526 565 482 215.896 038 112 291.339 592 156 98 165.151 831 136 220.134 478 683 298.166 383 999 99 167.803 349 448 224.436 495 864 305.129 711 679 100 170.481 382 042 228.803 043 302 312.232 305 O13 mE 26% 368 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 26. AMOUNT OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity applied at end of each year Pr 21 per cent. 3 per cent. 33 per cent. I 1.000 O00 O00 1.000 000 000 1.000 000 000 - 2.025 000 000 2.030 000 000 2.035 000 000 3.075 625 000 3.000 OO 000 3.106 225 000 4.152 515 625 4.183 627 000 4.214 942 875 5.256 328 516 5.309 135 810 5.362 465 876 6.387 736 729 6.468 409 884 6.550 152 181 7-547 430 147 7.662 462 181 7.779 407 508 8.736 115 goo 8.892 336 046 9.051 686 770 9.954 518 798 10.159 106 128 10.368 495 807 1 11.203 381 768 11.463 879 311 IY 17311303 161 12.483 466 312 12.807 795 691 13.I4I 99I 921 13.795 552 970 14.192 029 562 14.601 961 638 15.140 441 794 15.617 790 448 16.113 030 296 16.518 952 839 17.086 324 162 17.676 986 356 : 17.931 926 660 18.598 913 887 19.295 680 879 ae 19.380 224 826 20.156 881 303 20.971 029 709 20.864 730 447 21.761 587 742 22.705 OI5 749 : 22.386 348 708 23.414 435 375 24.499 691 300 19 23.946 007 426 25.116 868 436 26.357 180 496 20 25.544 657 612 26.870 374 489 28.279 681 813 ok 27.183 274 052 28.676 485 724 30.269 470 677 22 28.862 855 903 30.536 780 295 32.328 9o2 150 74 30.584 427 30I 32.452 883 704 34.460 413 726 24 32.349 037 983 34.426 470 215 36.666 528 206 2. 34.157 763 933 36.459 264 322 38.949 856 693 2% 36.011 708 031 38.553 042 251 41.313 10I 678 2 37.912 000 732 40.709 633 519 43.759 obo 236 2% 39.859 800 750 42.030 922 525 46.290 627 345 29 41.856 295 769 45.218 850 200 48.910 799 302 30 43.902 703 163 47.575 415 706 51.622 677 277 . 46.000 270 742 50.002 678 178 54.429 470 982 48.150 277 51I 52.502 758 523 57.334 502 466 . 50.354 034 449 55.077 841 279 60.341 210 053 . 52.612 885 310 57.930. 176/517 63.453 152 404 . 54.928 207 443 60.462 081 812 66.674 o12 739 a 57.301 412 629 63.275 944 267 70.007 603 184 59.733 947 944 66.174 222 595 73.457 869 296 62.227 296 643 69.159 449 273 77.028 894 721 5 64.782 979 059 72.234 232 751 80.724 906 037 43 67.402 553 536 75-40T 259 733 84.550 277 748 -. 70.087 617 374 78.663 297 525 88.509 537 469 o 72.839 807 808 82.023 196 451 92.607 371 280 Z 75.660 803 004 85.483 892 345 96.848 629 275 4 78.552 323 079 89.048 409 115 101.238 331 300 4. 81.516 131 156 92.719 861 388 105.781 672 895 4b 84.554 034 434 96.501 457 230 110.484 031 447 47 87.667 885 295 100.396 500 947 115.350 972 547 48 90.859 582 428 104.408 395 975 120.388 256 586 49 94.131 071 988 108.540 647 855 125.601 845 567 50 97.484 348 788 112.796 867 290 130.997 910 162 T i3 ; TABLE 26. AMOUNT OF AN ANNUITY OF ONE DOLLAR (Continued) For annuitv applied at end of each year End ot 2} per cent. 3 per cent. 3} per cent. 51 100.921 457 508 117.180 773 309 136.582 837 o17 52 104.444 493 946 121.696 196 508 142.363 236 313 5 108.055 606 294 126.347 082 403 148.345 949 584 : 111.756 996 452 131.137 494 876 154.538 o57 819 y 115.550 921 363 136.071 619 722 160.946 889 843 5 119.439 694 397 141.153 768 313 167.580 030 988 ) 123.425 686 757 146.388 381 363 174.445 332 072 127.511 328 926 151.780 032 804 181.550 918 695 131.699 112 149 157.333 433 788 188.905 200 849 Ua 135.991 589 953 163.053 436 802 196.516 882 879 : 140.391 379 701 168.945 039 906 204.394 973 780 144.901 164 194 175.013 39I 103 212.548 797 862 149.523 693 299 181.263 792 836 220.988 ooz 787 154.261 785 631 187.701 706 621 229.722 585 990 159.118 330 272 194.332 757 820 238.762 876 499 ¢ 164.096 288 529 201.162 740 554 248.119 577 177 169.198 695 742 208.197 622 771 257.803 762 378 174.428 663 136 215.443 551 454 267.826 894 obr vo 179.789 379 714 222.906 857 997 278.200 835 353 185.284 114 207 230.594 063 737 288.937 864 591 190.916 217 062 238.511 885 650 300.050 689 851 196.689 122 489 246.667 242 219 311.552 463 996 202.606 350 551 255.067 259 486 323.456 800 236 208.671 509 315 263.719 277 270 335.777 788 244 214.888 297 047 272.630 855 588 348.530 o10 833 221.260 504 474 281.809 781 256 361.728 561 212 227.792 o17 083 291.264 074 694 375.389 obo 854 234.486 817 513 301.001 996 934 389.527 677 984 241.348 987 950 311.032 056 842 404.161 146 714 : 248.382 712 649 321.363 018 548 419.306 786 849 255.592 280 465 332.003 909 104 434.982 524 383 262.982 087 477 342.964 026 377 451.206 912 742 270.556 639 664 354.252 947 169 467.999 154 6838 278.320 555 656 365.880 535 584 485.379 125 102 286.278 569 547 377.856 951 651 503.367 394 480 ‘ 294.435 533 786 390.192 660 201 521.985 253 287 302.796 422 130 402.898 440 007 541.254 737 152 , 311.366 332 684 415.985 393 207 561.198 652 953 C1 320.150 491 0OI 429.464 955 003 581.840 605 806 <3 329.154 253 276 443.348 903 653 603 . 205 027 009 : 338.383 109 608 457.649 370 763 625.317 202 955 ’ 347.842 687 348 472.378 851 886 648.203 305 058 357-538 754 531 487.550 217 442 671.890 420 735 . 367.477 223 395 503.176 723 965 696.406 585 461 377.664 153 980 519.272 025 684 721.780 815 952 Cy 388.105 757 829 535.850 186 455 748.043 144 510 tu 398.808 401 775 552.925 692 049 775.224 654 568 C3 409.778 611 819 570.513 462 810 803.357 517 478 99 421.023 O77 115 588.628 866 694 832.475 030 590 100 432.548 654 042 607.287 732 695 862.611 656 660 "ABLES 260 370. VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 26. AMOUNT OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity applied at end of each year Brit 4 per cent. 4% per cent. 5 per cent. 1.000 000 O00 I.000 000 000 1.000 000 000 2.040 000 000 2.045 000 000 2.050 000 000 3.121 600 000 3.137 025 000 3.152 500 000 4.246 464 ooo 4.278 191 125 4.3I0 125 000 5.416 322 560 5.470 709 726 5.525631 250 6.632 975 462 6.716 891 663 6.801 912 813 7.898 294 481 8.019 151 788 8.142 008 453 9.214 226 260 9.380 013 619 9.549 108 876 10.582 795 3II 10.802 114 231 11.026 564 320 IU 12.006 107 123 12.288 209 372 12.577 892 536 x 13.486 351 408 13.841 178 794 14.206 787 162 Ik 15.025 805 464 15.464 031 839 15.917 126 520 1 16.626 837 633 17.13910131272 17.712 982 846 i 18.291 QII 190 18.932 109 369 19.598 631 989 ; 20.023 587 638 20.784 054 291 21.578 563 588 I 21.824 531 143 22.719 336 734 23.657 491 768 1 23.697 512 389 24.741 706 887 25.840 366 356 a 25.645 412 884 26.855 083 697 28.132 384 674 1, 27.671 229 400 29.063 562 463 30.539 003 908 22 29.778 078 576 31.371 422 774 33.005 954 103 21 31.969 201 719 33.783 136 799 35.719 251 808 2e 34.247 969 788 36.303 377 955 38.505 214 398 7 36.617 888 579 38.937 029 963 41.430 475 118 Z 39.082 604 122 41.689 196 3II 44.501 998 874 z 41.645 908 287 44.565 210 145 47.727 098 818 26 44.311 744 619 47.570 644 602 51.113 453 759 27 47.084 214 403 50.711 323 609 54.669 126 447 28 49.967 582 980 53.993 333 171 58.402 582 769 29 52.966 286 299 57.423 033 164 62.322 711 908 oz 56.084 937 75T 61.007 069 656 66.438 847 503 a 59.328 335 261 64.752 387 791 70.760 789 878 a 62.701 468 671 68.666 245 242 75.298 829 372 66.209 527 418 va. 7561226 277 80.063 770 841 69.857 908 515 77.030 256 460 85.066 959 383 . 73.652 224 855 81.496 618 oor 90.320 307 352 77.598 313 850 86.163 965 811 95.836 322 719 81.702 246 403 OI .04I 344 272 101.628 138 855 85.970 336 260 06.138 204 764 107.709 545 798 Ce 00.409 149 710 101.464 423 979 114.095 023 088 4) 95.025 515 698 107.030 323 058 120.799 774 242 4 99.826 536 326 112.846 687 595 127.839 762 955 : 104.819 597 779 118.924 788 537 135.2311 751 102 ‘ 110.012 381 691 125.276 404 021 142.993 338 657 ‘ 115.412 876 958 131.913 842 202 151.143 005 590 4 121.029 392 037 138.849 965 10T 159.700 155 870 49 126.870 567 718 146.008 213 531 168.685 163 663 4 132.945 390 427 153.672 633 140 178.119 421 847 . 139.263 206 044 161.587 9oI 631 188.025 392 939 4; 145.833 734 286 169.859 357 204 198.426 662 586 50 152.667 083 657 178.503 028 279 209.347 995 715 TALES TABLE 26. AMOUNT OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity applied at end of each year Baa st 4 per cent. 4% per cent. 5 per cent. SI 159.773 767 003 187.535 664 551 220.815 395 501 52 167.164 717 683 196.974 769 456 232.856 165 276 52 174.851 306 391 206.838 634 082 245.498 973 540 « 182.845 358 646 217.146 372 615 258.773/922 217 : I9I.I59 172 992 227.917 959 383 272.712 618 327 4 199.805 539 912 239.174 267 555 287.348 249 244 208.797 761 508 250.937 109 595 302.715 661 706 218.149 671 969 263.229 279 527 318.851 444 791 : 227.875 658 847 276.074 597 106 335.794 017 031 t. 237.990 685 201 289.497 953 975 353.583 717 882 ‘ 248.510 312 609 303.525 361 9o4 372.262 903 777 259.450 725 114 318.184 003 190 391.876 048 965 [ 270.828 754 118 333.502 283 333 412.469 851 414 : 282.661 go4 283 349.3509 886 083 434.093 343 984 204.968 380 454 366.237 830 957 456.798 or1 184 €) 307.767 115 673 383.718 533 350 480.637 911 743 { 321.077 800 299 401.985 867 351 505.669 807 330 €; 334.920 912 3II 421.075 231 382 531.953 297 696 03 349.317 748 804 441.023 616 794 559.550 962 581 YB) 364.290 458 756 461.869 679 550 588.528 510 710 379.862 077 106 483.653 815 130 618.954 936 246 396.056 560 191 506.418 236 810 650.902 683 058 412.898 822 598 530.207 057 467 684.447 817 211 430.414 775 502 555.066 375 053 719.670 208 072 448.631 366 522 581.044 361 930 756.653 718 475 467.576 621 183 608.191 358 217 795.486 404 399 487.279 686 030 636.559 969 337 836.260 724 619 : 507.770 873 472 666.205 167 957 879.073 760 850 ; 529.081 708 410 697.184 400 515 924.027 448 892 551.244 976 747 729.557 698 538 971.228 821 337 574.294 775 817 763.387 794 972 1020.790 262 404 598.266 566 849 798.740 245 746 1072.829 775 524 623.197 229 523 835.683 556 8053 1127 .471 264 300 649.125 118 704 874.289 316 861 1184 .844 827 515 676.090 123 452 914.632 336 120 1245.087 068 891 Co 704.133 728 391 956.790 791 245 1308.341 422 335 733.299 077 526 1000.846 376 851 1374.758 493 452 i 763.631 040 627 1046 .884 463 810 1444 .496 418 125 Ea 795.176 282 252 1094 .994 264 681 1517 .721 230 O31 co 827.983 333 542 1145.269 006 592 1594 .607 300 983 Or 862.102 666 884 1197 .806 111 888 1675.337 666 032 C2 897.586 773 559 1252.707 386 923 1760.104 549 333 a 934.490 244 502 1310.079 219 335 1849 .109 776 800 972.869 854 282 1370.032 784 205 1942 .5635 2635 640 1012.784 648 453 1432.684 259 494 2040.693 528 922 ( 1054 .296 034 391 1498 .155 O51 I7I 2143 .728 205 368 (7 1097 .467 875 767 1566.572 028 474 2251.914 615 636 93 1142.366 590 798 1638.067 769 755 2365.510 346 418 99 1189.061 254 430 1712.780 819 304 2484 .785 863 739 100 1237.623 704 607 1790.855 956 267 2610.025 156 926 Bi. - 2377 372 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 26. AMOUNT OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity applied at end of each year Endof ! : year. 5% per cent. 6 per cent. 6% per cent. I 1.000 O00 000 1.000 000 000 1.000 000 000 2 2.055 O00 000 2.060 000 000 2.065 000 000 ? 3.168 025 000 3.183 600 000 3.199 225 000 4.342 266 375 4.374 616 000 4.407 174 625 5.581 091 026 5.637 092 960 5.693 640 976 : 6.888 o51 032 6.975 318 538 7.063 727 639 8.266 893 839 8.393 837 650 8.522 869 936 9.721 573 000 9.897 467 909 10.076 856 481 11.256 259 5I5 11.491 315 983 37.731 952 153 I. 12.875 353 788 13.180 794 942 13.494 422 543 i 14.583 498 247 14.971 642 639 15.371 560 008 1 16.385 590 650 16.869 941 197 17.370 711 408 18.286 798 136 18.882 137 669 19.499 807 650 20.292 572 033 21.015 065 929 21.767 295 147 7 22.408 663 495 23.275 969 335 24.182 169 332 16 24.641 139 987 25.672 528 078 26.754 o10 338 1- 26.996 402 687 28.212 879 763 29.493 021 OIO 13 29.481 204 335 30.905 652 549 32.410 067 376 19 32.102 671 100 33.759 991 70I 35.5161721 755 20 34.868 318 o11 36.785 591 204 38.825 308 670 2) 37.786 075 502 39.992 726 676 42.348 953 733 2 40.864 309 654 43.392 290 276 46.101 635 726 Z 44.111 846 635 46.995 827 693 50.098 242 048 2 47.537 998 253 50.815 577 354 54.354 627 781 2 51.152 588 157 54.864 511 996 58.887 678 587 29 54.965 980 505 59.156 382 715 63.715 377 695 27 58.989 109 433 63.705 765 678 68.856 877 245 28 63.233 510 452 68.528 111 619 74.332 574 266 29 67.711 353 527 73.639 798 316 80.164 191 593 2 72.435 477 971 79.058 186 215 86.374 864 047 77.419 429 259 84.801 677 383 92.989 230 210 : 82.677 497 868 90.889 778 031 100.033 530 173 88.224 760 251 97.343 164 713 107.535 709 635 94.077 122 065 104.183 754 596 115.525 530 761 3 100.251 363 779 111.434 779 872 124.034 690 260 ; 106.765 188 786 119.120 866 664 133.096 945 127 113.637 274 170 127.268 118 664 142.748 246 561 oO 120.887 324 249 135.904 205 784 153.026 882 587 : 128.536 127 083 145.058 458 131 163.973 629 955 49 136.605 614 072 154.761 965 619 175.631 915 902 41 145.118 922 846 165.047 683 556 188.047 990 436 40 154.100 463 603 175.950 544 569 201.271 109 814 4° 163.575 989 101 187.507 577 243 215.353 731 952 4 173.572 668 502 199.758 031 878 230.351 724 529 4, 184.119 165 269 212.743 513 791 246.324 586 624 46 195.245 719 359 226.508 124 618 263.335 684 754 47 206.984 233 924 241.098 612 095 281.452 504 263 44% 219.368 366 789 256.564 528 821 300.746 917 040 49 232.433 626 963 272.958 400 550 321.295 466 648 50 246.217 476 446 200.335 904 583 343.179 671 980 TABLES : TABLE 26. AMOUNT OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity applied at end of each year Fad of 53% per cent. 6 per cent. 63 per cent. 51 260.759 437 650 308.756 058 858 366.486 350 659 52 276.101 206 721 328.281 422 390 391.307 963 451 53 292.286 773 091 348.978 307 733 417.742 981 076 Li 309.362 545 611 370.917 006 197 445.896 274 846 5 327.377 485 619 394.172 026 569 475.879 532 711 ‘ 346.383 247 328 418.822 348 163 507.811 702 337% 366.434 325 931 444.951 689 053 541.819 462 989 : 387.588 213 858 472.648 790 396 578.037 728 083 : 409.9035 5635 620 502.007 717 820 616.610 180 409 { 433.450 371 729 533.128 180 889 657.689 842 135 458.290 142 174 566.115 871 742 701.439 681 874 484.496 099 994 601.082 824 047 748.033 261 196 512.143 385 493 638.147 793 490 797.655 423 173 541.311 271 695 677.436 661 09g 850.503 025 680 572.083 391 639 719.082 860 765 906.785 722 349 u 604.547 978 179 763.227 832 411 966.726 794 301 638.798 116 979 810.021 502 353 1030.564 035 931 674.932 013 412 859.622 792 497 1098.550 698 267 ( 713.053 274 150 912.200 160 047 1170.956 493 654 753.271 204 228 967.932 169 649 1248.068 665 741 795.701 120 461 1027 .008 099 828 1330.193 129 OI§ 840.464 682 086 1089.628 585 818 1417.655 682 401 887.690 239 6or1 1156.006 300 967 1510.803 301 757 937.513 202 779 1226.366 679 025 1610.005 516 371 990.076 428 932 1300.948 679 767 1715.655 874 935 1045.530 632 523 1380.005 600 553 1828.173 506 806 1104.034 817 312 1463 .805 936 586 1948.004 784 748 1165.756 732 264 1552.634 292 781 2075.625 095 757 1230.873 352 539 1646.792 350 348 2211.540 726 981 1299.571 386 928 1746.599 891 369 2356.290 874 235 1372.047 813 209 1852.395 884 851 2510.449 781 obo 1448.510 442 936 1964.539 637 942 2674.629 016 829 1529.178 517 297 2083 .412 016 218 2849.479 902 923 1614 .283 335 749 2209.416 737 191 3035.696 096 613 1704.068 919 215 2342.981 741 423 3234.016 342 892 1798.792 709 772 2484 .560 645 9o8 3445 .227 405 180 1898. 726 308 809 2634.634 284 663 3670.167 186 517 ; 2004.156 255 794 2793.712 341 742 3909.728 053 641 ta 2115.384 849 862 2062.335 082 247 4164 .860 377 127 : 2232.73 016 605 3I141.075 187 182 4436.576 301 641 2356.531 222 518 3330.539 698 413 4725.953 761 247 ' 2487.140 439 757 3531.372 080 317 5034.140 755 728 2624.933 163 943 3744.254 405 136 5362.359 904 851 2770.304 487 960 3969.909 669 445 5711.913 298 666 2923.671 234 798 4209.104 249 611 6084 .187 663 079 Gs 3085.473 152 712 4462 .650 504 588 6480.659 861 179 C 3256.174 176 111 4731.409 534 863 6902.902 752 156 Ci 3436.263 755 797 5016.294 106 955 7352.591 431 046 99 3626.258 262 366 5318.271 753 372 7831.509 874 064 100 3826.702 466 796 5638.368 058 575 8341.558 o15 878 372 374 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 26. AMOUNT OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity applied at end of each year | Ly 7 per cent. 8 per cent. 9 per cent. 1 1.000 000 000 1.000 000 000 I.000 O00 O00 2 2.070 000 000 2.080 000 000 2.090 000 000 ° 3.214 QOO 000 3.246 400 000 3.278 100 000 4.439 943 000 4.506 112 000 4.573 129 000 5.750 739 O10 5.866 600 960 5.984 710 610 ; 7-153 290 7471 7-335 929 037 7.523 334 565 8.654 021 093 8.922 803 360 9.200 434 676 10.259 802 569 10.636 627 629 11.028 473 797 11.977 988 749 12.487 557 839 13.021 036 438 I. 13.816 447 961 14.486 562 466 15.192 929 718 1d 15.783 599 319 16.645 487 463 17.560 293 392 12 17.888 451 271 18.977 126 460 20.140 719 798 : 20.140 642 860 21.495 296 577 22.953 384 579 Hy 22.550 487 860 24.214 920 303 26.019 189 192 13 25.129 022 OIO 27.152 113 927 29.360 916 219 16 27.888 053 551 30.324 283 042 33.003 398 678 17 30.840 217 300 33.750 225 685 36.973 704 559 18 33.999 032 510 37.450 243 740 41.301 337 970 19 37.378 964 786 41.446 263 239 46.018 458 387 20 40.995 492 321 45.761 964 298 51.160 119 642 21 44.865 176 784 50.422 921 442 56.764 530 410 22 49.005 739 159 55-456 755 157 62.873 338 147 27 53.436 140 900 60.893 295 570 69.531 938 580 24 58.176 670 763 66.764 759 215 76.789 813 052 2; 63.249 037 716 73.105 939 953 84.700 896 227 26 68.676 470 356 79.954 415 149 93.323 976 837 oi 74.483 823 281 87.350 768 361 102.723 134 807 2 80.697 690 911 95.338 829 830 112.968 216 940 2! 87.346 529 275 103.965 936 216 124.135 356 464 :- 94.460 786 324 113.233 271 113 136.307 538 546 : 102.073 041 366 123.345 868 002 149.575 217 OI5 110.218 154 262 134.213 537 443 164.036 986 546 ) 118.933 425 060 145.950 620 438 179.800 315 336 128.258 764 815 158.626 670 073 196.982 343 716 i 138.236 878 352 172.316 803 679 215.710 754 650 0 148.913 459 836 187.102 147 973 236.124 722 569 . 160.337 402 025 203.070 319 811 258.375 947 600 . 172.561 020 167 220.315 945 396 282.629 782 834 : 185.640 291 578 238.941 221 028 309.066 463 343 40 199.635 111 989 259.056 518 710 337.882 445 044 41 214.609 569 828 280.781 040 207 369.291 865 098 a2 230.632 239 716 304.243 523 423 403.528 132 957 ¢ 247.776 496 496 329.583 005 297 440.845 664 923 L 266.120 851 25I 356.949 645 721 481.521 774 766 4 285.749 310 838 386.505 617 379 525.858 734 495 46 306.751 762 597 418.426 066 769 574.186 020 600 47 329.224 385 979 432.900 I52 IIO 626.862 762 454 43 353.270 092 997 490.132 164 279 684.280 411 075 49 378.998 999 507 530.342 737 422 746.865 648 072 50 406.528 929 472 573.770 156 415 815.083 556 398 T. 3 375 TABLE 26. AMOUNT OF AN ANNUITY OF ONE DOLLAR (Continued) For annuitv applied at end of each year Pas 7 per cent. 8 per cent. 9 per cent. 51 435.985 954 536 620.671 768 929 889.441 076 474 52 467.504 971 353 671.325 510 443 970.490 773 356 53 501.230 319 348 726.031 551 278 1058.834 942 959 51 537.316 441 702 785.114 075 381 1155.130 087 825 575.928 592 621 848.923 201 411 1260.091 795 729 617.243 594 105 917.837 057 524 1374 .500 057 345 661.450 645 692 992.264 022 126 1499.205 062 506 : 708.752 190 890 1072.645 143 896 1635.133 518 131 759.364 844 253 1159.456 755 408 1783.295 534 763 813.520 383 350 1253.213 295 840 1944.792 132 892 871.466 810 185 1354.470 359 507 2120.823 424 852 - 933.469 486 898 1463 .827 988 268 2312.697 533 089 999.812 350 981 1581.934 227 329 2521.840 311 067 + 1070.799 215 549 1709.488 965 516 2749 .805 939 063 t, 1146.755 160 638 1847.248 082 757 2998.288 473 578 t3 1228.028 o21 883 1996.027 929 378 3269.134 436 200 I 1314.989 983 414 2156.710 163 728 3564.356 535 458 {, 1408.039 282 253 2330.246 976 826 3886.148 623 649 g 1507 .602 032 oII 2517.666 734 972 4236.901 999 778 Co 1614.134 174 252 2720.080 073 770 4619.223 179 758 ; 1728.123 566 450 2038.686 479 672 5035.953 265 936 1850.092 216 101 3174.781 398 045 5490.189 059 870 1980.598 671 228 3429.763 909 889 5985.306 075 259 2120.240 578 214 3705.145 022 680 6524.983 622 032 2269.657 418 689 4002.556 624 494 7113.232 148 015 2429.533 437 997 4323.761 154 454 7754 .423 041 336 2600.600 778 657 4670.662 046 810 8453.321 115 056 2783 .642 833 163 5045.315 OIO 555 92I5.120 OI5 412 : 2979.497 831 484 5449.940 211 400 10045 .480 816 799 v 3189.062 679 688 5886.935 428 311 10950.574 090 310 t 3413.297 067 267 6358.890 262 576 11937.125 758 438 : 3653.227 861 975 6868 .601 483 583 13012.467 076 698 3909.953 812 313 7419.089 602 269 14184.589 113 601 : 4184 .650 579 173 8013.616 770 451 15462.202 133 825 ‘ 4478 .576 119 718 8655.706 112 087 16854 .800 325 869 Fy 4793 .076 448 098 9349 .162 6or o54 18372.732 355 197 5I29.591 799 465 10098 .095 609 138 20027.278 267 1635 5489.663 225 427 10906 .943 257 869 21830.733 311 210 Xq 5874.939 651 207 11780.498 718 498 23796.499 309 219 £ 6287.185 426 792 12723.938 615 978 25939.184 247 048 vo 6728.288 406 667 13742.853 705 257 28274 .710 829 283 =3 7200.268 595 134 14843 .282 oor 677 30820.434 803 918 7705 .287 396 793 16031.744 561 811 33595.273 936 271 a4 8245.657 514 569 17315.284 126 756 36619.848 590 535 CL 8823.853 540 589 18701.506 856 897 39916.634 963 683 ab 9442.523 288 430 20198.627 405 448 43510.1I32 110 415 a” 10104 .499 918 620 21815.517 597 884 47427 .044 000 352 CS 10812.814 912 923 23561.759 005 715 51606.477 960 384 99 11570.711 956 828 25447.699 726 172 56350.160 976 818 100 12381.661 793 806 27484 .515 704 266 61422.675 464 732 ‘ABLES 47 37 6 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 26. AMOUNT OF AN ANNUITY OF ONE DOLLAR (Concluded) For annuity applied at end of each year Bad of 10 per cent. ad 10 per cent. y 1.000 000 000 51 1281.299 381 677 2.100 000 000 5 1410.429 319 844 3.310 000 000 ro 1552.472 251 829 4.641 000 000 ! 1708.719 477 O12 6.105 100 000 ; 1880.591 424 713 7.715 610 000 2069 650 567 184 9.487 171 000 ; 22%77.615 623 902 11.435 888 100 2506.377 186 293 13.579 476 910 : 2758.014 904 922 10 15.937 424 bor i 3034.816 395 414 : 18.531 167 061 ( 3339.298 034 956 3 21.384 283 767 ¢ 3674 227 838 451 24.522 712 144 ( 4042 .650 622 296 27.974 983 358 ( 4447.915 684 526 31.772 481 694 ( 4893.707 252 978 35.949 729 864 t 5384.077 978 276 40.544 702 850 \ 5923.485 776 104 45.599 173 135 &- 6516.834 353 714 IY 51.159 090 448 { 7169.517 789 086 20 57.274 999 493 ; 7887.469 567 994 2" 64.002 499 443 # 8677.216 524 794 22 71.402 749 387 : 9545.938 177 273 2 79.543 024 326 10501 .53I 995 OO z 88.497 326 758 : 11552.685 194 501 z 98.347 059 434 : 12708.953 713 951 2 109.181 765 377 , 13980.849 085 346 2 121.099 94I 915 ’ 15379.933 993 880 z 134.209 936 106 : 16918.927 393 268 2, 148.630 929 717 : 18611.820 132 595 i 164.494 022 639 ‘ 20474 .002 145 855 : 181.943 424 958 ¢ 22522.402 360 440 . 201.137 767 454 ‘ 24775 .642 596 484 . 222.251 544 199 . 27254.206 856 133 ; 245.476 698 619 29980.627 541 746 . 271.024 368 481 ¢ 32979 .690 295 920 2 209.126 805 329 #3 36278.659 325 512 2 330.039 485 362 Ei 39907 .525 258 064 : 364.043 434 448 Ls 43899.277 783 870 %. 401.447 777 893 &g 48290.205 562 257 4) 442.592 555 632 90 53120.226 118 483 41 487.851 811 250 1 58433 .248 730 331 ‘ 537.636 992 375 Ga 64277 .573 603 364 7 592.400 691 612 Cy 70706 .330 963 701 4 652.640 760 774 2 77777 .964 060 071 4 718.904 836 851 «, 85556.760 466 078 43 791.795 320 536 «5 94113.436 512 685 47 871.974 852 590 C7 103525. 780 163 954 48 960.172 337 849 Gs 113879.358 180 349 49 1057 .189 571 634 99 125268.293 998 384 50 1163.908 528 797 100 137796.123 398 223 TAI "ES EXPLANATION OF TABLE 2; Annuity WarcE WiLL AMOUNT To ONE DOLLAR IN A GIVEN TIME Table 27 shows the annual investment necessary to accumus- late $1 in a given number of years at interest rates ranging from I to 10 per cent per annum. The annuity is assumed to be applied at the end of each year. The table shows in each case the sum of the annual installments plus the interest earnings. This table is based on the following formula: Let a,’ represent the annual installment which at com- pound interest in # years will amount to $r. Let n represent the number of years required by the annu- ity to amount to $1. Let 7 represent the interest rate expressed in per cent, as 0.05 for 5 per cent. Then / L a, = CHT =a 4) and it follows from equation (22) that ; I OG =~. (24a) In other words the annuity which will amount to $1 in a given time can be found with the aid of a table showing the amount of an annuity of $1. It is the reciprocal of the latter. Example. — What annuity will amount at 5 per cent compound interest to $7500 in 31 years? From Table 27 the annuity which will amount to $1 in 31 years at 5 per cent is found to be 0.014132. The annuity which will amount to $7500 in 31 years is, therefore, 7500 X 0.014132 = $105.99. Or from Table 26 the amount of an annuity of $1 for 31 years at 5 per cent is found to be $70.76079, therefore, the annuity which will amount to $7500 in 31 years will be 7500 70.76079 $105.99. + BLL. 377 {ic 378 VALUATION, DEPRECIATION AND THE RATE-BASE When the annuity is applied at the beginning instead of at the end of the year and is called a,” then: a) = * =) i RE le or, by the aid of equation (23) iT: ay’ = Zr (250) These values are readily found with the aid of Table 26, it being remembered that A" is the value appearing in that table reduced by 1 (one). (25, TABLES . 9 TABLE 27. ANNUITY WHICH WILL AMOUNT TO ONE DOLLAR IN A GIVEN TIME For annuity applied at end of each vear End of I per cent. 1; per cent. 2 per cent. I.000 000 00 I.000 000 00 1.000 000 00 0.497 512 44 0.496 277 92 0.495 049 50+ 0.330 022 II 0.328 382 96 0.326 754 67 0.246 281 09 0.244 444 79 0.242 623 75+ 0.196 039 8o 0.194 089 32 0.192 158 39 0.162 548 37 0.160 525 21 0.158 525 81 0.138 628 28 0.136 556 16 0.134 511 96 0.120 690 29 0.118 584 02 0.116 509 80 0.106 740 36 0.104 609 82 0.I02 5I5 44 ID 0.095 582 08 0.093 434 18 0.091 326 53 I 0.086 454 o8 0.084 293 84 0.082 177 94 2 0.078 848 79 0.076 679 99 0.074 559 60 2 0.072 414 82 0.070 240 36 0.068 118 35+ 1] 0.066 gor 17 0.064 723 32 0.062 6o1 97 : 0.062 123 78 0.059 944 36 0.057 825 47 i 0.057 944 6o 0.055 765 08 0.053 650 13 0.054 258 06 0.052 079 66 0.049 969 84 T 0.050 982 05— 0.048 803 78 0.046 702 10 1, 0.048 o51 75+ 0.045 878 47 0.043 781 77 25 0.045 415 31 0.043 245 74 0.041 156 72 2 0.043 030 75+ 0.040 865 50— 0.038 784 77 : 0.040 863 72 0.038 703 32 0.036 631 40 : 0.038 885 84 0.036 730 75+ 0.034 668 10 : 0.037 073 47 0.034 924 10 0.032 871 10 : 0.035 406 75+ 0.033 263 45+ 0.031 220 44 2 0.033 868 88 0.031 731 96 0.029 699 23 i 0.032 445 53 0.030 3135 27 0.028 293 09 2 0.031 124 44 0.029 001 08 0.026 98g 67 2 0.029 8935 02 0.027 778 78 0.025 778 36 go 0.028 748 11 0.026 639 19 0.024 649 92 0.027 675 73 0.025 574 30 0.023 596 35 0.026 670 89 0.024 577 10 0.022 610 61 a 0.025 727 44 0.023 641 44 0.021 686 53 0.024 839 97 0.022 761 89 0.020 818 67 . 0.024 003 68 0.021 933 63 0.020 002 2I 0.023 214 3I 0.021 152 40 0.019 232 85 ¢ 0.022 468 o5— 0.020 414 37 0.018 506 78 * 0.021 761 50— 0.019 716 13 0.017 820 57 | 0.021 091 60 0.019 054 63 0.017 I7I 14 0.020 455 60 0.018 427 10 0.016 555 75 ‘ 0.019 851 02 0.017 831 06 0.015 971 88 0.019 275 63 0.017 264 26 0.015 417 29 0.018 727 37 0.016 724 65 ~ o.o14 889 93 0.018 204 41 0.016 210 38 0.014 387 94 0.017 705 O5— 0.015 719 76 0.013 909 62 0.017 227 75— 0.0I5 25I 25— 0.013 453 42 0.016 771 1I 0.014 803 42 0.013 O17 92 ‘ 0.016 333 84 0.014 375 00 — o.o12 6or 84 4 0.015 914 74 0.013 964 78 0.012 203 96 50 0.015 512 73 0.013 571 68 o.orr 823 21 3 380 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 27. ANNUITY WHICH WILL AMOUNT TO ONE DOLLAR IN A GIVEN TIME (Continued) For annuity applied at end of each year Tag af 1 per cent. 11 per cent. 2 per cent. ST o.o15 126 8o 0.013 194 69 0.011 458 56 52 0.014 756 03 0.012 832 87 0.0II I0Q 09 Gi 0.014 399 56 0.012 485 37 0.010 773 92 : 0.014 056 58 0.012 I5I 38 0.010 452 26 0.013 726 37 o.or1 830 18 0.010 143 37 0.013 408 24 0.011 521 0b 0.009 846 56 . 0.013 10I 56 0.0II 223 41 0.009 561 20 o.o12 805 73 0.010 936 61 0.009 286 67 0.0I2 520 20 0.010 660 12 0.009 022 43 i 0.012 244 45— 0.010 393 43 0.008 767 97 i 0.011 978 oo 0.010 136 04 0.008 522 78 0.0II 720 41 0.009 887 51 0.008 286 43 0.0II 471 25+ 0.009 647 41 0.008 058 48 0.0IT 230 I3 0.009 4I5 34 0.007 838 55— ; 0.010 996 67 0.009 190 94 0.007 626 24 : 0.0IO0 770 52 0.008 973 86 0.007 421 22 : 0.010 55I 36 0.008 763 76 0.007 223 16 | 0.010 338 89 0.008 560 33 0.007 031 73 \ 0.010 132 80 0.008 363 29 0.006 846 65-1 0.009 932 82 0.008(172/35~1 0.006 667 65— 0.009 738 70 0.007 987 27 0.006 494 46 0.009 550 I9 0.007 807 79 0.006 326 83 0.009 367 06 0.007 633 68 0.006 164 54 0.009 189 10 0.007 464 73 0.006 007 36 0.009 016 09 0.007 300 72 0.005 855 08 : 0.008 847 84 0.007 141 46 0.005 707 5I 0.008 684 16 0.006 986 76 0.005 564 47 ; 0.008 524 88 0.006 836 45+ 0.005 425 76 0.008 369 83 0.006 690 36 0.005 290I 23 0.008 218 85+ 0.006 548 32 0.005 160 71 0.008 071 79 0.006 410 19 0.005 034 05— 0.007 928 5I 0.006 275 83 0.004 9II IO 0.007 788 87 0.006 145 09 0.004 791 73 0.007 652 73 0.006 017 84 0.004 675 81 0.007 519 98 0.005 893 96 0.004 563 21 0.007 390 50+ 0.005%773133 0.004 453 81 0.007 264 18 0.005 655 84 0.004 347 50~ . 0.007 140 89 0.005 541 38 0.004 244 16 23) 0.007 020 56 0.005 429 84 0.004 143 70 00 0.006 903 06 0.005 321 13 0.004 046 02 ax 0.006 788 32 0.0035 215 16 0.003 95I OI C2 0.006 676 24 0.005 III 82 0.003 858 59 (1 0.006 566 73 0.005 OII O04 0.003 768 68 ¢ 0.006 459 71 0.004 912 73 0.003 681 18 93 0.006 355 II 0.004 816 81 0.003 596 02 96 0.006 252 84 0.004 723 21 0.003 513 13 97 0.006 152 84 0.004 631 86 0.003 432 42 98 0.006 055 03 0.004 542 68 0.003 353 83 99 0.005 959 36 0.004 455 60 0.003 277 29 100 0.005 865 74 0.004 370 57 0.003 202 74 TABLES 531 TABLE 27. ANNUITY WHICH WILL AMOUNT TO ONE DOLLAR IN A GIVEN TIME (Continued) For annuity applied at end of each vear Brae | 2} per cent. 3 per cent. 3% per cent. 1.000 000 00 1.000 000 00 1.000 000 00 0.493 827 16 0.492 610 84 0.491 400 49 0.325137 17 0.323 530 36 0.321 934 18 0.240 817 88 0.239 027 05— 0.237 251 14 0.190 246 86 0.188 354 57 0.186 481 37 0.156 549 97 0.154 597 50+ 0.152 668 21 0.132 495 43 0.130 506 35+ 0.128 544 49 0.114 467 35— 0.112 456 39 0.110 476 65— 0.100 456 89 0.098 433 86 0.096 446 or i 0.089 258 76 0.087 230 51 0.085 241 37 i 0.080 105 96 0.078 077 45— 0.076 091 97 12 0.072 487 13 0.070 462 og 0.068 483 95- 3 0.066 048 27 0.064 029 54 0.062 ob1 57 ; 0.060 536 52 0.058 526 34 0.056 570 73 0.055 766 46 0.053 766 58 0.051 825 07 14 0.051 598 99 0.049 610 85— 0.047 684 83 Lo 0.047 927 77 0.045 952 53 0.044 043 13 0.044 670 08 0.042 708 70 0.040 816 84 1 0.041 760 62 0.039 813 88 0.037 940 33 3.9 0.039 147 13 ©.037 215 7X 0.035 361 08 2 0.036 787 33 0.034 871 78 0.033 036 59 a 0.034 646 61 0.032 747 39 0.030 932 07 . 0.032 696 38 0.030 813 go 0.029 o18 8o 3 0.030 912 82 0.029 047 42 0.027 272 83 2 0.029 275 92 0.027 427 87 0.025 674 o4 % 0.027 768 75— 0.025 938 29 0.024 205 40 : 0.026 376 87 0.024 564 21 0.022 852 41 4 0.025 087 93 0.023 293 23 0.021 602 65 oF 0.023 891 27 0.022 114 67 0.020 445 38 : 0.022 777 64 0.021 019 26 0.019 37I 33 : 0.02I 739 OO 0.019 998 93 0.018 372 40 0.020 768 31 0.019 046 62 0.017 441 50+ 0.019 859 38 0.018 156 12 0.016 572 42 0.019 006 75+ 0.017 321 96 0.015 759 66 . 0.018 203 58 0.016 539 29 0.014 998 35— 4 0.017 451 58 o.o15 803 79 0.014 284 16 : 0.016 740 go 0.0135 IIT 62 0.013 613 25— ; 0.016 070 12 0.014 459 34 0.012 982 14 Po 0.015 436 15+ o.o13 843 85+ o.o12 387 75+ 4 0.014 836 23 0.013 262 38 o.o11 827 28 ‘ 0.014 267 86 0.012 712 41 0.011 298 22 0.013 728 76 0.012 191 67 o.o10 798 28 : o.o13 216 88 0.011 698 11 0.010 325 39 - 0.012 730 37 0.011 229 85— 0.009 877 68 ; 0.012 267 31 o.o10 785 18 0.009 453 43 . o.or1 826 76 o.o10 362 54 0.009 051 08 § 0.011 406 69 0.009 960 51 0.008 669 19 Ca 0.0II 005 99 0.009 §77 77 0.008 306 46 6 o.o10 623 48 0.009 213 14 0.007 961 67 50 o.o10 258 06 0.008 865 49 0.007 633 71 a <4 332 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 27. ANNUITY WHICH WILL AMOUNT TO ONE DOLLAR IN A GIVEN TIME (Continued) For annuity applied at end of each year Pd 21 per cent. 3 per cent. 3} per cent. 5I 0.009 908 70 0.008 533 32 0.007 321 56 52 0.009 574 46 0.008 217 18 0.007 024 29 hE: 0.009 254 49 0.007 914 71 0.006 741 00 5 0.008 947 99 0.007 625 58 0.006 470 go . 0.008 654 19 0.007 349 07 0.006 213 23 x 0.008 372 43 0.007 084 47 0.005 967 30 0.008 102 04 0.006 831 14 0.005 732 45+ 0.007 842 44 0.006 588 48 0.005 508 10 : 0.007 593 OF 0.006 355 93 0.005 293 66 . 0.007 353 40 0.006 132 96 0.005 088 62 : 0.007 I22 94 0.005 919 08 0.004 892 49 0.006 gor 26 0.005 713 S5= 0.004 704 80 0.006 687 90 0.005 516 82 0.004 525 I3 0.006 482 49 0.005 327 60 0.004 353 08 ; 0.006 284 63 0.005 145 81 0.004 188 26 ( 0.006 093 98 0.004 97I IO 0.004 030 3I t 0.005 9IO 2I 0.004 803 13 0.003 878 92 ; 0.005 733 00 0.004 641 59 0.003 733 75: t 0.005 562 06 0.004 486 18 0.003 594 53 , 0.005 397 12 0.004 336 63 0.003 460 95+ 0.005 237 90 0.004 192 66 0.003 332 77 0.005 084 17 0.004 054 04 0.003 209 73 0.004 935 68 0.003 920 53 0.003 09I 60 0.004 792 22 0.003 79I 9I 0.002 978 16 0.004 653 58 0.003 667 96 0.002 869 19 . 0.004 519 56 0.003 548 49 0.002 764 50+ Lo 0.004 389 97 0.003 433 31 0.002 663 go 0.004 264 63 0.003 322 24 0.002 567 21 0.004 143 38 0.003 2I35 IO 0.002 474 26 J 0.004 026 05— ©.003 TIT 75= 0.002 384 89 0.003 912 43 0.003 OI2 OI 0.002 298 94 0.003 802 54 0.002 915 76 0.002 216 28 0.003 696 08 0.002 822 84 0.002 136 76 0.003 592 98 0.002 733 13 0.002 060 25~ 0.003 493 IO 0.002 646 50+ 0.001 986 62 ca 0.003 396 33 0.002 562 84 0.001 915 76 0.003.302 55— 0.002 482 02 0.001 847 56 oS 0.003 211 65+ 0.002 403 93 0.001 781 90 a 0.003 123 53 0.002 328 48 o.oo1 718 68 (CH 0.003 038 09 0.002 255 56 o.oo1 657 81 : 0.002 955 23 0.002 185 08 0.00I 599 I9 : 0.002 874 86 0.002 116 94 0.00I 542 73 | 0.002 796 go 0.002 O51 07 0.001 488 34 0.002 721 26 0.001 987 37 0.00T 435 94 or 0.002 647 86 0.001 925 77 0.001 385 46 96 0.002 576 62 0.001 866 19 0.001 336 82 97 0.002 507 47 0.001 808 56 0.001 289 95— 98 0.002 440 34 0.001 752 81 0.001 244 78 99 0.002 375 17 o.oo1 698 86 0.001 20I 24 100 0.002 311 88 0.001 646 67 0.001 159 27 TABLES 3 TABLE 27. ANNUITY WHICH WILL AMOUNT TO ONE DOLLAR IN A GIVEN TIME (Continued) For annuity applied at end of each year ¥ad oy 4 per cent. 43 per cent. 5 per cent. I.000 000 00 1.000 000 00 I.000 000 00 0.490 196 08 0.488 997 55+ 0.487 804 88 0.320 348 54 0.318 773 36 0.317 208 56 0.235 490 05 — 0.233 743 65— 0.232 o11 83 0.184 627 11 0.182 791 64 0.180 974 80 0.150 761 go 0.148 878 39 0.147 O17 47 0.126 609 61 0.124 701 47 o.122 819 82 0.108 527 83 0.106 609 654 0.104 721 81 0.094 492 99 0.092 574 47 0.090 690 08 0.083 290 94 0.031 378 82 0.079 504 57 1 0.074 149 04 0.072 248 18 0.070 388 89 0.066 552 17 0.064 666 19 0.062 823 41 0.060 143 73 0.058 275 35+ 0.056 455 77 I 0.054 668 97 0.052 820 32 0.05I 023 97 0.049 941 10 0.048 113 81 0.046 342 29 11 0.045 820 00 0.044 O13 37 0.042 269 91 0.042 198 52 0.040 417 58 0.038 699 14 0.038 993 33 0.037 236 90 0.035 546 22 14 0.036 138 62 0.034 407 34 0.032 745 OI oh 0.033 581 75 | 0.031 876 14 0.030 242 59 2 0.031 280 II 0.029 600 57 0.027 996 11 2: 0.029 198 81 0.027 545 65— 0.025 970 5I 5 0.027 309 06 0.025 682 49 0.024 136 82 2 0.0235 586 83 0.023 987 03 0.022 470 QO Z 0.024 o11 96 0.022 439 03 0.020 952 46 2A 0.022 567 38 0.021 02I 37 0.019 564 32 2 0.021 238 54 0.019 719 46 0.018 291 86 2 0.020 012 98 0.018 520 81 0.017 122 53 20 0.018 879 93 0.017 414 61 0.016 045 51 s 0.017 830 10 0.016 391 54 0.0I5 O3I 44 0.016 855 35-4 0.015 443 45- 0.014 132 I2 0.015 948 359 0.014 563 20 0.013 280 42 ; 0.015 103 57 0.013 744 53 0.0I2 490 04 0.014 314 77 0.012 981 91 0.OII 755 45 ©.013 577 32 0.012 270 45— 0.0II O7I ¥I : o.or2 886 88 o.o11 6o5 78 0.010 434 46 0.012 239 57 0.010 984 02 0.009 839 79 : 0.011 631 92 0.010 401 69 0.009 284 23 a o.o11 obo 83 0.009 855 67 0.008 764 62 ¢ 0.0I0 523 49 0.009 343 15— 0.008 278 16 ¢ o.o10 017 38 0.008 861 58 0.007 822 29 ¢ 0.009 540 20 0.008 408 68 0.007 394 71 ‘ 0.009 089 89 0.007 982 35— 0.006 993 33 f 0.008 664 54 0.007 580 71 0.006 616 25 ! 4 0.008 262 46 0.007 202 02 0.006 261 73 dh 0.007 882 03 0.006 844 71 0.005 928 20 0.007 521 89 0.006 3507 34 0.0035 614 21 Lc 0.007 180 63 0.006 188 58 0.0035 318 43 19 0.006 857 12 0.003 887 22 0.0035 039 65- 0 0.006 550 20 0.005 602 15— 0.004 776 74 30 384 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 27. ANNUITY WHICH WILL AMOUNT TO ONE DOLLAR IN A GIVEN TIME (Continued) For annuity applied at end of each year Ea 4 per cent. 45 per cent. 5 per cent. 51 0.006 258 85— 0.005 332 32 0.004 528 67 52 0.005 982 12 0.005 076 79 0.004 294 50— 0 0.005 719 I5— 0.004 834 69 0.004 073 34 i 0.005 469 10 0.004 605 19 0.003 864 38 0.005 23I 24 0.004 387 54 0.003 666 86 i 0.005 004 87 0.004 181 o5-+ 0.003 480 10 0.004 789 32 0.003 985 06 0.003 303 43 0.004 584 OI 0.003 798 97 0.003 136 26 0.004 388 36 0.003 622 21 0.002 978 02 (a 0.004 201 85° 0.003 454 26 0.002 828 18 . 0.004 023 98 0.003 294 62 0.002 686 27 : 0.003 854 30 0.003 142 84 0.002 55I 83 0.003 692 37 0.002 998 48 0.002 424 42 : 0.003 537 80 0.002 861 15- 0.002 303 65+ | 0.003 390 I9 0.002 730 47 0.002 189 15+ 0.003 249 2I 0.002 606 08 0.002 080 57 0.003 114 5I 0.002 487 65— 0.001 977 58 0.002 985 78 0.002 374 87 0.001 879 86 “n 0.002 862 72 0.002 267 45+ | 0.001 787 15— 2 0.002 745 06 0.002 165 II 0.001 699 15+ 0.002 632 53 0.002 067 59 0.001 615 63 0.002 524 89 0.001 974 65-1 0.001 536 33 0.002 42I QO o.oo1 886 ob 0.001 461 03 0.002 323 34 o.oor1 801 59 0.001 389 53 0.002 2209 00 0.001 721 04 0.001 32I 61 0.002 138 69 0.001 644 22 0.00I 257 09 0.002 052 2I 0.00I 570 94 0.001 195 80 , 0.001 969 39 0.00I 50I 04 0.001 137 56 y 0.001 890 07 0.001 434 34 0.001 082 22 toa 0.001 814 08 0.001 370 69 0.001 029 62 ‘ 0.001 741 27 0.001 309 95+ 0.000 979 63 : 0.001 671 50— 0.00I 25I 97 0.000 932 II ¢ o.oor1 604 63 0.001 196 63 0.000 886 94 : 0.00I 540 54 0.001 I43 79 0.000 843 99 ‘ 0.00I 479 09 0.00I 0093 34 0.000 803 16 c 0.00T 420 18 0.001 045 16 0.000 764 33 ¢ 0.001 363 70 0.000 999 I5—+ 0.000 727 40 No 0.00I 309 53 0.000 955 22 0.000 692 28 Es 0.001 257 58 0.000 QI3 25— 0.000 658 88 « 0.001 207 75+ 0.000 873 16 0.000 627 II ( 0.001 159 95+ 0.000 834 86 0.000 596 89 ( 0.00I 114 IO 0.000 798 27 0.000 568 15— G 0.001 070 IO 0.000 763 31 0.000 540 80 0 0.001 027 89 0.000 729 OI 0.000 514 78 9. 0.000 987 38 0.000 697 99 0.000 490 03 99 0.000 948 50+ 0.000 667 49 0.000 466 48 97 0.000 9II IQ 0.000 638 34 0.000 444 07 98 0.000 875 38 0.000 610 48 0.000 422 74 99 0.000 841 CO 0.000 583 85— 0.000 402 45— 100 0.000 808 00 0.000 558 39 0.000 383 14 TABLES 5-5 TABLE 27. ANNUITY WHICH WILL AMOUNT TO ONE DOLLAR IN A GIVEN TIME (Continued) For annuity applied at end of each year End of 5} per cent. 6 per cent. 6% per cent. I.000 000 00 1.000 000 00 1.000 000 00 0.486 618 oo 0.485 436 89 0.484 261 50+ 0.315 654 07 0.314 109 81 0.312 575 70 0.230 204 49 0.228 591 49 0.226 goz 74 0.179 176 44 0.177 396 40 0.175 634 54 0.145 178 95— 0.143 362 63 0.141 568 31 0.120 964 42 0.IIQ I35 02 0.117 331.37 0.102 864 or 0.IOI 035 94 0.099 237 30 0.088 839 46 0.087 022 24 0.085 238 03 vy 0.077 667 77 0.075 867 96 0.074 104 69 od 0.068 570 65+ 0.066 792 94 0.065 055 21 v2 0.061 029 23 0.039 277 03 0.057 568 17 1 0.054 684 26 0.052 g6o 11 0.051 282 56 = 0.049 279 12 0.047 584 91 0.045 940 48 oo 0.044 6235 60 0.042 962 76 0.04I 352 78 ) 0.040 582 54 0.038 952 14 0.037 377 57 0.037 O41 97 0.035 444 8o 0.033 906 33 0.033 919 92 0.032 356 54 0.030 854 61 2) 0.03I 150 06 0.029 620 86 0.028 155 75+ 20 0.028 679 33 0.027 184 56 0.025 756 40 Zr 0.026 464 78 0.025 004 55— 0.023 613 33 22? 0.024 471 23 0.023 045 57 0.021 691 20 : 0.022 669 65— 0.021 278 48 0.019 g6o 78 1 0.021 035 80 0.019 679 oo 0.018 397 70 Z 0.019 549 35-+ 0.018 226 72 0.016 981 48 ‘ 0.018 193 07 0.016 9o4 35— 0.015 694 8o . 0.016 952 28 0.015 697 17 0.014 522 88 Z. 0.015 814 40 0.014 592 55+ 0.013 453 05+ 2) 0.014 768 57 0.013 579 61 0.012 474 40 2 0.013 8035 39 0.012 648 91 0.0II 577 44 0.012 916 654 0.0II 792 22 0.0IO0 753 93 0.0I2 095 I9 0.0II 002 34 0.009 996 65— 0.011 334 69 0.0I0 272 93 0.009 299 24 o.oro 629 58 0.009 598 43 0.008 656 10 0.009 974 93 0.008 973 86 0.008 062 26 3 0.009 366 35 0.008 394 83 0.007 513 32 0.008 799 93 0.007 857 43 0.007 005 34 0.008 272 17 0.007 358 12 0.006 534 80 Ps 0.007 779 9I 0.006 893 77 0.006 098 54 4 0.007 320 34 0.006 461 54 0.005 693 73 ‘ 0.006 8go go 0.006 058 86 0.005 317 79 or 0.006 489 27 0.005 683 42 0.004 968 42 ¢ 0.006 113 37 0.005 333 12 0.004 643 52 ‘ 0.005 761 28 0.005 006 06 0.004 341 19 5. 0.005 431 27 0.004 700 50— 0.004 059 68 a3 0.005 121 75+ 0.004 414 85+ 0.003 797 43 4 0.004 831 29 0.004 147 68 0.003 553 00 43 0.004 558 54 0.003 897 65+ 0.003 325 05 ! 4) 0.004 302 30 0.003 663 56 0.003 II2 40 50 0.004 061 45+ 0.003 444 29 0.002 913 93 2% 386 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 27. ANNUITY WHICH WILL AMOUNT TO ONE DOLLAR IN A GIVEN TIME (Continued) For annuity applied at end of each year Pw 5% per cent. 6 per cent. 63 per cent. 5I 0.003 834 95+ 0.003 238 80 0.002 728 61 ¢ 0.003 621 86 0.003 046 17 0.002 555 53 t 0.003 421 30 0.002 865 51 0.002 393 32 : 0.003 232 45+ 0.002 696 02 0.002 242 67 : 0.003 054 58 0.002 536 96 0.002 IOI 37 | 0.002 886 98 0.002 387 65— 0.001 969 23 0.002 729 00 0.002 247 44 0.001 845 63 0.002 580 06 0.002 II5 74 0.00T 729 99 0.002 439 59 0.00I 992 00 0.001 621 77 0.002 307 O7 0.001 875 72 0.00I 520 47 0.002 182 02 0.001 766 42 0.001 425 64 0.002 064 00 0.001 663 66 0.001 336 84 0.001 952 58 0.001 567 04 0.001 253 67 0.001 847 37 0.001 476 15+ 0.001 175 77 | 0.001 748 00 0.001 390 66 0.001 102 80 : 0.001 654 13 0.00I 3IO 22 0.001 034 42 0.001 565 44 0.001 234 54 0.000 970 34 0.001 481 63 0.001 163 30 0.000 910 29 t 0.00I 402 42 0.001 096 25+ 0.000 854 00 0.00I 327 54 0.001 033 I3 0.000 801 24 o.oo1 256 75+ 0.000 973 70 0.000 751 77 0.001 189 32 0.000 QI7 74 0.000 705 39 0.001 126 52 0.000 865 05— 0.000 661 go 0.001 066 65+ 0.000 815 42 0.000 621 12 0.00I OIO 02 0.000 768 67 0.000 582 87 0.000 956 45+ 0.000 724 63 0.000 546 99 0.000 905 77 0.000 683 15+ ©.000 513 35= ; 0.000 857 81 0.000 644 07 0.000 481 78 ’ 0.000 812 43 0.000 607 24 0.000 452 17 . 0.000 769 48 0.000 572 54 0.000 424 40 ¢ 0.000 728 84 0.000 539 84 0.000 398 33 0.000 690 36 0.000 509 03 0.000 373 88 0.000 653 95— 0.000 479 98 0.000 350 94 i 0.000 619 47 0.000 452 61 0.000 329 4I : 0.000 586 83 0.000 426 81 0.000 309 2I & 0.000 555 93 0.000 402 49 0.000 290 26 ¢ 0.000 526 67 0.000 379 56 0.000 272 47 < 0.000 498 96 0.000 357 95— 0.000 255 77 & 0.000 472 73 0.000 337 57 0.000 240 IO 9» 0.000 447 88 0.000 318 36 0.000 225 40 x 0.000 424 35+ 0.000 300 25+ 0.000 211 60 C2 0.000 402 OF 0.000 283 18 0.000 198 64 «> 0.000 380 96 0.000 267 08 0.000 186 49 oF. 0.000 360 97 0.000 251 89 0.000 175 OF Cy 0.000 342 04 0.000 237 58 0.000 164 36 cb 0.000 324 10 0.000 224 08 0.000 154 3I tn 0.000 307 II 0.000 211 35+ 0.000 144 87 Co 0.000 29I OI 0.000 199 35+ 0.000 136 OI 99 0.000 275 77 0.000 188 03 0.000 127 69 100 0.000 261 32 0.000 177 36 0.000 119 88 TABLES of TABLE 27. ANNUITY WHICH WILL AMOUNT TO ONE DOLLAR IN A GIVEN TIME (Continued) For annuity applied at end of each year Enda 7 per cent. 8 per cent. 9 per cent. I.000 000 00 I.000 000 00 I.000 000 00 0.483 091 79 0.480 769 23 0.478 468 go 0.311 051 67 0.308 033 51 0.305 054 76 ©.225.228 12 0.221 920 80 0.218 668 66 0.173 890 69 0.170 456 45+ 0.167 092 46 0.139 795 8o 0.136 315 39 0.132 919 78 0.115553 22 0.112 072 40 0.108 690 52 0.097 467 76 0.094 o14 76 0.090 674 38 0.083 486 47 0.080 079 71 0.076 798 &o i 0.072 377 50+ 0.069 029 49 0.065 820 og = 0.063 356 go 0.060 076 34 0.056 946 66 0.055 9oI 99 0.0352 695 02 0.049 6350 66 0.049 650 85— 0.046 521 81 0.043 566 56 3 0.044 344 94 0.041 296 85+ 0.038 433 17 i 0.039 794 62 0.036 829 54 0.034 058 88 1 0.035 857 65- 0.032 976 87 0.030 299 91 0.032 425 19 0.029 629 43 0.027 046 25— 1 0.029 412 60 0.026 702 10 0.024 212 29 1 0.026 753 or 0.024 127 63 0.02I 730 41 2 0.024 392 93 0.021 852 21 0.019 546 48 21 0.022 289 co o.o19 832 25+ o.o17 616 63 z 0.020 405 77 0.018 032 07 0.015 904 99 z 0.018 713 93 0.016 422 17 o.o14 381 88 2 0.017 189 02 0.014 977 96 0.013 022 56 z o.o15 810 52 o.o13 678 78 0.011 806 25-4 26h 0.014 561 03 0.012 507 13 0.010 715 36 27 0.0I3 425 73 0.0II 448 10 0.009 734 91 2d 0.0I2 39I 93 0.010 488 91 0.008 852 05— 2 0.011 448 65+ 0.009 618 54 0.008 055 72 : o.o10 586 40 0.008 827 43 0.007 336 35-4 ; 0.009 796 91 0.008 107 28 0.006 685 60 0.009 072 92 0.007 450 81 0.006 096 19 0.008 408 o7 0.006 851 63 0.003 561 73 0.007 796 74 0.006 304 IT 0.0035 076 60 0.007 233 96 0.005 803 26 0.004 635 84 : 0.006 715 31 0.005 344 67 0.004 235 O05 0.006 236 85— 0.004 924 40 0.003 870 33 0.005 795 05+ 0.004 538 94 0.003 538 20 0.005 386 76 0.004 185 13 0.003 235 55 Co 0.005 009 14 0.003 860 16 0.002 959 61 : 0.004 659 62 0.003 561 49 0.002 707 89 0.004 335 91 0.003 286 84 0.002 478 14 0.004 035 89 0.003 034 14 0.002 268 37 . 0.003 757 69 0.002 8or1 52 0.002 076 75— . 0.003 499 57 0.002 587 28 0.001 gor 65-4 ty 0.003 259 96 0.002 389 91 0.001 741 60 : 0.003 037 44 0.002 207 99 0.00I 595 25— ¢ 0.002 830 70 0.002 040 27 o.oor 461 39 44 0.002 638 53 o.oor1 885 57 0.001 338 93 50 0.002 459 85— 0.001 742 86 0.001 226 8% 33" 388 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 27. ANNUITY WHICH WILL AMOUNT TO ONE DOLLAR IN A GIVEN TIME (Continued) For annuity applied at end of each year ig 7 per cent. 8 per cent. 9 per cent. 5I 0.002 293 65+ o.oo1 611 16 0.001 124 30 r2 0.002 I39 OI 0.001 489 59 0.00I 030 4I 3 0.00I 995 09 0.001 377 35+ 0.000 944 43 e 0.001 861 10 0.00I 273 70 0.000 865 70 0.001 736 33 0.001 177 96 0.000 793 59 . 0.001 620 II 0.001 089 52 0.000 727 54 0.00I 5II 83 0.001 007 80 0.000 667 02 0.00I 4I0 93 0.000 932 27 0.000 611 57 o.oo1 316 89 0.000 862 47 0.000 560 76 a, 0.00I 229 23 0.000 797 95— 0.000 514 I9 0.00I I47 49 0.000 738 30 0.000 471 5I 0.00I O7I 27 0.000 683 14 0.000 432 40 0.00I 000 IQ 0.000 632 14 0.000 396 54 0.000 933 88 0.000 584 97 0.000 363 66 0.000 872 03 0.000 54I 35— 0.000 333 52 , 0.000 814 31 0.000 500 99 0.000 305 89 : 0.000 760 46 0.000 463 67 0.000 280 56 ) 0.000 7I0 2I 0.000 429 I4 0.000 257 32 (oo 0.000 663 31 0.000 397 19 0.000 236 02 , 0.000 619 53 0.000 367 64 0.000 216 49 0.000 578 66 0.000 340 29 0.000 198 57 0.000 540 5I 0.000 314 98 0.000 182 14 0.000 504 90 0.000 291 57 0.000 167 08 ; 0.000 471 64 0.000 269 89 0.000 153 26 ; 0.000 440 60 0.000 249 84 0.000 140 58 . 0.000 41I 60 0.000 231 28 0.000 128 96 . 0.000 384 53 0.000 214 I0 0.000 118 30 ; 0.000 359 24 0.000 198 20 0.000 108 52 0.000 335 63 0.000 183 49 0.000 099 55— <3 0.000 313 57 0.000 169 87 0.000 OQI 32 cr 0.000 292 97 0.000 157 26 0.000 083 77 0.000 273 73 0.000 145 59 0.000 076 85— 0.000 255 76 0.000 134 79 0.000 070 50— : 0.000 238 97 0.000 124 79 0.000 064 67 0.000 223 29 0.000 II5 53 0.000 059 33 i 0.000 208 63 0.000 106 96 0.000 054 43 t- 0.000 I94 95— 0.000 099 03 0.000 049 93 &3 0.000 182 16 0.000 091 68 0.000 045 81 &) 0.000 I70 21 0.000 084 89 0.000 042 02 eo 0.000 159 05+ 0.000 078 59 0.000 038 55+ if 0.000 148 63 0.000 072 77 0.000 035 37 on: 0.000 138 88 0.000 067 37 0.000 032 45— 0.000 129 78 0.000 062 38 0.000 029 77 . 0.000 121 28 0.000 057 75+ 0.000 027 31 Gy 0.000 I13 33 0.000 053 47 0.000 025 05+ oD 0.000 105 90 0.000 049 5I 0.000 022 98 C7 0.000 098 97 0.000 045 84 0.000 021 09 93 0.000 092 48 0.000 042 44 0.000 019 34 99 0.000 086 43 0.000 039 30 0.000 O17 75— 100 0.000 080 76 0.000 036 38 0.000 016 28 TABLES J TABLE 27. ANNUITY WHICH WILL AMOUNT TO ONE DOLLAR IN A GIVEN TIME (Concluded) For annuity applied at end of each year Fad of Io per cent. Bad of 10 per cent. r I.000 000 00 5I 0.000 780 46 0.476 190 48 iz 0.000 709 00 0.302 114 80 £3 0.000 644 13 0.215 470 80 ) 0.000 585 23 0.163 797 48 0.000 53I 75~ 0.129 607 38 : 0.000 483 17 0.1035 405 50— 0.000 439 06 0.087 444 02 : 0.000 398 98 0.073 640 54 0.000 362 58 1 0.062 745 39 J 0.000 329 5I L: 0.053 963 14 0.000 299 46 re 0.046 763 32 0.000 272 17 0.040 778 52 0.000 247 36 0.035 746 22 | 0.000 224 82 0.031 473 78 0.000 204 34 7 0.027 816 62 £3 0.000 183 73 0.024 664 13 0.000 168 82 0.02I 930 22 0.000 153 45— 0.019 546 87 | 0.000 139 48 2 0.017 459 62 | 0.000 126 78 0.015 624 39 0.000 II5 24 0.014 005 06 0.000 104 76 0.012 571 81 0.000 095 22 0.011 299 78 0.000 086 56 0.010 168 07 0.000 078 68 0.009 159 04 0.000 071 53 0.008 257 64 0.000 065 02 0.007 451 OI 0.000 059 II 0.006 728 07 0.000 053 73 0.006 079 25 ’ 0.000 048 84 0.003 496 21 0.000 044 40 0.004 971 72 0.000 040 36 0.004 499 41 0.000 036 69 0.004 073 71 0.000 033 35 ! 0.003 689 71 0.000 030 32 0.003 343 06 ) 0.000 027 56 0.003 029 94 0.000 025 06 0.002 746 92 0.000 022 78 0.002 490 98 : 0.000 020 71 : 0.002 259 41 ' 0.000 018 83 ‘ 0.002 049 80 0.000 O17 II o.oo1 859 99 0.000 015 56 ¢ o.oor1 688 o5— ¢ 0.000 014 14 : 0.00I 532 24 ¢ 0.000 012 86 . 0.00I 39I 00 qg, 0.000 o11 69 ¢ o.oo1 262 95+ 96 0.000 010 63 . 0.001 146 82 C7 0.000 009 66 ¢ 0.00I 041 48 98 0.000 008 78 4 0.000 945 90 99 0.000 007 98 50 0.000 859 17 100 0.000 007 26 38 300 VALUATION, DEPRECIATION AND THE RATE-BASE EXPLANATION OF TABLE 23 Tae PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR The present value of an annuity is the sum of the present values of the several annuity installments. The present value of an annuity of $1 receivable at the end of each year is presented for a few selected years in Table 28. This table is based on the following formula: Let P’ represent the present value of an annuity of $1 re- ceivable at the end of each year during # years. Let # represent any number of years, the term of the annuity. Let ¢ represent the rate of interest expressed decimally; thus for 5 per cent, ¢ = 0.05. Then: bs x a cn 1 ms Lil nf Bir mry S] (: G+ 5) GC This equation may be written: +9)" —1 I 1 mn ee eer _— reo l= eh (=) Or by reference to equations (19) and (22) AY P = ov iil =) In other words the present value of the annuity of $1 is the amount of an annuity of $1 in # years divided by the amount of $1 at compound interest in 7 years. The present value of an annuity of $1 receivable at the end of each year is therefore ascertainable for any number of years to 100 from Tables 22 and 26 by dividing the amount of an annuity of $1 found in Table 26 by the amount of $1 at com- pound interest found in Table 22. Example. — What is the present value of an annuity of $53 receivable at the end of each year for 20 years at 5 per cent interest? 6) i (H& TABLES I The amount of an annuity of $1 for 20 years at 5 per cent interest is found in Table 26 to be $33.06595. The amount of $1 at 5 per cent compound interest for 20 years is found in Table 21 to be $2.653208, consequently, the present value of an annuity of $1 at 5 per cent for 20 years: 33.00595 + 2.653208 = $12.46221. And the present value of the annuity of $53 for 20 years is 12.46221 X 53 = $660.50. 20: 3902 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 28. PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR For annuity receivable at end of each year Member or! 1 per cent. 1} per cent. 2 per cent. 0.990 099 OI 0.985 221 67 0.980 392 16 1.970 395 06 1.955 883 42 1.941 560 94 2.940 985 21 2.912 200 42 2.883 883 27 3.901 965 551 3.854 384 65— 3.807 728 70 4.853 431 24 4.782 644 97 4.713 459 51 5.795 476 47 5.697 187 17 5.601 430 89 6.728 194 53 6.598 213 96 6.471 99I OF 7.651 677 75+ 7.485 925 08 7.325 481 44 8.566 or7 58 8.360 517 32 8.162 236 71 . 9.471 304 53 9.222 184 55+ 8.982 585 or ye 10.367 628 25-— 10.071 II7 79 9.786 848 o5— ; II.255 O77 47 10.907 505 2I 10.575 341 22 ’ 12.133 740 OF 11.73% 532822 11.348373 75— . 13.003 703 04 12.543 381 50+ 12.106 248 77 13.865 052 52 13.343 233 OI 12.849 263 50+ i 14.717 873 78 14.131 264 05— 13.577 709 32 x T5.562/251 27 14.907 649 31 14.291 871 88 19 16.398 268 58 15.672 560 39 14.992 031 25+ 19 17.226 008 50— 16.426 168 37 15.678 462 or 29 18.045 552 97 17.168 638 79 16.351 433 35— 21 18.856 983 13 17.900 136 74 17.011 209 16 2 19.660 379 34 18.620 824 37 17.658 048 20 y 20.455 821 13 19.330 861 45— 18.292 204 12 % 21.243 387 26 20.030 405 37 18.913 925 60 2 22.023 155 70 20.719 611 20 19.523 456 47 24 22.795 203 66 21.398 631 72 20.121 035 76 2; 23.559 607 59 22.067 617 46 20.706 897 80 2° 24.316 443 16 22.726 716 71 21.281 272 36 20 25.065 785 30 23.376 075 58 21.844 384 66 3 25.807 708 22 24.015 838 o1 22.396 455 55+ : 26.542 285 37 24.646 145 82 22.937 70I 52 3 27.269 589 47 25.267 138 74 23.468 334 82 : 27.989 692 55— 25.878 954 42 23.988 563 55+ : 28.702 665 89 26.481 728 50— 24.498 59I 72 . 29.408 580 09 27.075 594 58 24.998 619 33 : 30.107 505 o4 27.660 684 31 25.488 842 48 30.799 509 94 28.237 127 40 25.969 453 42 31.484 663 31 28.805 051 63 26.440 640 60 35 32.163 032 98 29.364 582 83 26.902 588 83 43 32.834 686 11 29.915 845 20 27.355 479 24 41 33.499 689 22 30.458 960 79 27.799 489 45+ 47 34.158 108 14 30.994 050 04 28.234 793 58 4: 34.810 008 06 31.521 231157 28.661 562 33 4: 35.455 453 53 32.040 622 24 29.079 963 07 4. 36.004 508 44 32.552 337 18 29.490 159 88 46 36.727 236 08 33.056 489 83 29.892 313 60 4 37-353 699 09 33.553 191 95+ 30.286 581 97 4. 37-973 959 49 34.042 553 65— 30.673 119 57 45 38.588 078 71 34.524 683 39 31.052 078 OI 50 39.196 117 53 34.999 688 07 31.423 605 89 TAL. S oJ TABLE 28. PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity receivable at end of each year N Huber or I per cent. 1} per cent. 2 per cent. 51 39.798 136 17 35.467 672 98 31.787 848 92 52 40.394 194 23 35-928 741 85+ 32.144 949 92 51 40.984 350 72 36.382 996 go 32.495 048 94 a 41.568 664 08 36.830 538 82 32.838 283 27 : 42.147 192 16 37.271 146 68 33.174 787 52 so 42.719 992 24 37.705 878 63 33.504 693 65+ 43.287 121 03 38.133 870 58 33.828 131 03 43.848 634 68 38.555 537 51 34.145 226 50+ 44.404 588 79 38.970 972 92 34.456 104 41 44.955 038 41 39.380 268 89 34.760 886 68 45.500 038 03 39.783 516 14 35.059 692 82 46.039 641 61 40.180 804 08 35.352 640 02 46.573 902 59 40.572 220 77 35-639 843 16 47.102 873 85— 40.957 852 98 35.921 414 86 47.626 607 77 41.337 786 18 36.197 465 55-4 , 48.145 156 21 41.712 104 61 36.468 103 48 : 48.658 570 50+ 42.080 891 25— 36.733 434 79 = 49.166 gor 49 42.444 227 83 36.993 563 52 t 49.670 199 49 42.802 194 90 37.248 591 68 8 50.168 514 35— 43.154 871 83 37-498 619 29 50.661 895 39 43.502 336 78 37-743 744 41 SI.I50 391 48 43.844 666 77 37-984 063 14 51.634 050 97 44.181 937 71 38.219 669 75 52.112 921 75+ 44.514 224 34 38.450 656 62 52.587 o51 24 44.841 600 34 38.677 114 33 53.056 486 38 45.164 138 26 38.899 131 70 53-521 273 64 45.481 gog 62 39.116 795 78 53.981 459 05— 45-794 984 85— 39.330 191 94 54.437 083 17 46.103 433 35— 39-539 403 86 ‘ 54.888 206 11 46.407 323 49 39.744 513 59 55-334 857 53 46.706 722 66 39.945 6or1 56 55.777 086 66 47.001 697 20 40.142 746 63 56.214 937 29 47.292 312 51 40.336 026 11 56.648 452 76 47.578 633 or 40.525 515 79 57.077 676 oo 47.860 722 18 40.711 289 99 57.502 649 51 48.138 642 54 40.893 421 56 57-923 415 35+ 48.412 455 71 41.071 981 92 <r 58.340 o15 20 48.682 222 37 41.247 O41 10 ei 58.752 490 30 48.948 002 34 41.418 667 75— uo 59.160 881 49 49.209 854 52 41.586 929 16 oT 59.565 229 19 49.467 836 97 41.751 801 33 02 59.965 573 46 49.722 0ob 86 41.913 618 96 7 60.361 953 92 49.972 420 55+ 42.072 175 45— O; 60.754 409 82 50.219 133 55+ 42.227 622 gg 3 61.142 980 02 50.462 200 54 42.380 022 54 (3 61.527 702 99 50.701 675 41 42.529 433 86 C7 61.908 616 82 50.937 611 24 42.675 915 55— 98 62.285 759 23 51.170 obo 34 42.819 525 o5— 99 62.659 167 56 5I.399 074 22 42.960 318 67 100 63.028 878 77 51.624 703 67 43.0098 351 64 BLES 20> 394 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 28. PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity receivable at end of each year Rumber or 2% per cent. 3 per cent. 33 per cent. 0.975 609 76 0.970 873 79 0.966 183 57 1.927 424 15+ 1.913 469 70 1.899 694 28 2.856 023 56 2.828 611 35+ 2.801 636 98 3.761 974 21 3.717 098 40 3.673 079 21 4.645 828 50— 4.579 707 19 4.515 052 38 5.508 125 36 5.417 191 44 5.328 553 02 6.349 390 60 6.230 282 96 6.114 543 98 7.170 137 17 7.019 692 19 6.873 955 54 7.970 865 53 7.786 108 92 7.607 686 5I 8.752 063 93 8.530 202 84 8.316 605 32 oy 9.514 208 71 9.252 624 11 9.00I 55I 04 : 10.257 764 60 9.954 003 99 9.663 334 33 10.983 184 97 10.634 955 33 10.302 738 49 11.690 912 17 11.296 073 14 10.920 520 28 12-381 377 73 11.937 935 99 I1.5I7 410 90 1 13.055 002 66 12.561 102 O3 12.094 116 80 5 13.712 107 72 13.166 118 47 12.651 320 59 7 14.353 363 63 13.753 513 08 13.189 681 73 19 14.978 891 34 14.323 799 11 13.709 837 42 20 15.589 162 29 14.877 474 86 14.212 403 30 210 16.184 548 57 15.415 024 14 14.697 974 21 22 16.765 413 24 15.936 916 64 15.167 124 84 g 17.332 110 48 16.443 608 39 15.620 410 47 Z 17.884 985 83 16.935 542 I2 16.058 367 60 7 18.424 376 42 17.413 147 69 16.481 514 59 2 18.950 611 14 17.876 842 42 16.890 352 26 2 19.464 o10 87 18.327 031 48 17.285 364 5I 2 19.964 888 66 18.764 108 23 17.667 o18 85— 2 20.453 549 91 19.188 454 59 18.035 767 00 ; 20.0930 292 59 19.600 441 35— 18.392 045 41 ; 21.395 407 41 20.000 428 49 18.736 275 76 21.849 177 96 20.388 765 53 19.068 865 47 ) 22.291 830 94 20.765 791 78 19.390 208 18 22.723 786 28 21.131 836 63 19.700 684 23 . 23.145 157 34 21.487 220 OF 20.000 661 10 i 23.556 251 07 21.832 252 50— 20.290 493 31 23.957 318 II 22.167 235 44 20.570 525 42 . 24.348 603 04 22.492 461 59 20.841 087 36 : 24.730 344 43 22.808 215 13 21.102 499 87 42 25.102 775 05+ 23.114 771 97 21.355 072 34 41 25.466 122 00 23.412 399 98 21.599 I03 7I 42 25.820 606 33 23.701 359 20 21.834 882 81 44 26.166 445 69 23.981 902 14 22.062 688 71 Z; 26.503 849 45+ 24.254 273 92 22.282 791 02 4, 26.833 023 86 24.518 712 54 22.495 450 26 46 27.154 169 62 24.775 449 07 22.700 918 13 47 27.467 482 55+ 25.024 707 83 22.899 437 80 a% 27.773 153 71 25.266 706 64 23.091 244 25+ 4u 28.071 369 47 25.501 656 93 23.276 564 50— 50 28.362 311 68 25.729 764 o1 23.455 617 87 TABLES J TABLE 28. PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity receivable at end of each vear Nembes or 2} per cent. 3 per cent. 33 per cent. 51 28.646 157 74 25.951 227 19 23.628 616 30 Le 28.923 o8o 72 26.166 239 99 23.795 764 54 : 29.193 249 48 26.374 990 28 23.957 260 43 4 29.456 828 76 26.577 660 47 24.113 295 IO 29.713 979 28 26.774 427 64 24.264 053 23 ¢ 29.964 857 84 26.965 463 73 24.409 713 27 30.209 617 40 27.150 935 66 24.550 447 60 30.448 407 22 27.331 005 49 24.686 422 81 30.681 372 go 27.505 830 58 24.817 799 81 30.908 656 49 27.675 563 67 24.944 734 12 31.130 396 57 27.840 353 07 25.067 375 96 31.346 728 36 28.000 342 79 25.185 870 49 31.557 783 77 28.155 672 61 25.300 357 96 31.763 691 48 28.306 478 26 25.410 973 88 31.964 577 o5+ 28.452 891 52 25.517 849 16 3 32.160 562 98 28.595 040 31 25.621 110 30 32.351 768 76 28.733 048 84 25.720 879 51 32.538 310 99 28.867 037 71 25.817 274 89 32.720 303 40 28.997 123 99 25.910 4I0 53 32.897 856 98 209.123 421 35+ 26.000 396 64 33.071 079 98 29.246 040 15— 26.087 339 75+ 33.240 078 03 29.365 087 52 26.171 342 75-4 33.404 954 17 29.480 667 50— 26.252 505 08 33.565 808 g5— 29.592 881 06 26.330 922 78 33.722 740 44 29.701 826 28 26.406 688 68 33.875 844 33 29.807 598 33 26.479 892 44 34.025 213 98 29.910 289 64 26.550 620 72 34.170 940 47 30.009 989 94 26.618 957 21 34.313 112 65+ 30.106 786 35— 26.684 982 81 34.451 817 22 30.200 763 45— 26.748 775 67 34.587 138 75+ 30.292 003 35— 26.810 411 27 34.719 159 76 30.380 585 77 26.869 962 58 34.847 960 74 30.466 588 13 26.927 500 08 : 34.973 620 23 30.550 085 56 26.983 og1 86 ¢ 35.096 214 86 30.631 151 03 27.036 803 73 ¢ 35.215 819 38 30.709 855 37 27.088 699 26 35.332 506 71 30.786 267 35— 27.138 839 86 ¢ 35.446 348 o1 30.860 453 74 27.187 284 89 8 35.557 412 69 30.932 479 36 27.234 091 68 09 35.665 768 48 31.002 407 14 27.279 315 64 GI 35.771 481 45 31.070 298 20 27.323 o10 28 02 35.874 616 o4 31.136 211 84 27.365 227 32 0 35.975 235 16 31.200 205 67 27.406 016 73 C; 36.073 400 16 31.262 335 60 27.445 426 8o ¢ 36.169 170 89 31.322 655 92 27.483 504 15+ 96 36.262 605 75— 31.381 219 34 27.520 293 87 ih 36.353 761 70 31.438 077 03 27.555 839 48 95 36.442 694 35— 31.493 278 67 27.590 183 08 99 36.529 457 90 31.546 872 50— 27.623 365 29 100 36.614 105 27 31.598 905 34 27.655 425 40 20F 396 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 28. PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity receivable at end of each year Nore 4 per cent. 43 per cent. 5 per cent. 0.961 538 46 0.956 937 80 0.952 380 95+ 1.886 094 67 1.872 667 75+ 1.859 410 43 2.775 091 03 2.748 964 35+ 2.723 248 03 3.629 895 22 3.587 525 70 3.545 950 50+ 4.451 822 33 4.389 976 74 4.329 476 67 5.242 136 86 5.157 872 48 5.075 692 07 6.002 054 67 5.892 700 94 5.786 373 40 6.732 744 38 6.595 886 o7 6.463 212 76 7.435 331 61 7.268 790 49 7.107 821 63 i 8.110 895 78 7.912 718 18 7.721 734 93 8.760 476 71 8.528 916 92 8.306 414 22 : 9.385 073 76 9.118 580 78 8.863 251 64 9.985 647 85— 9.682 852 42 9.393 572 99 10.563 122 93 10.222 825 28 9.898 640 94 11.118 387 43 10.739 545 73 10.379 658 04 Co 11.652 295 61 11.234 OI5 O5— 10.837 769 56 12.165 668 85+ 11.707 191 43 11.274 066 25— 12.659 296 97 12.159 991 80 11.689 586 90 1, 13.133 939 40 12.593 293 59 12.085 320 86 22 13.590 326 34 13.007 936 45+ 12.462 210 34 x 14.029 159 95— 13.404 723 33 12.327152 71 22 14.451 II5 33 13.784 424 76 13.163 002 58 2 14.856 841 67 14.147 774 89 13.488 573 88 2 15.246 963 14 14.495 478 37 13.798 641 79 2 15.622 079 94 14.828 208 96 14.093 944 57 20 15.982 769 18 15.146 611 45— 14.375 185 30 2 16.329 585 75— 15.451 302 82 14.643 033 62 2 16.663 063 22 15.742 873 51 14.898 127 26 2% 16.983 714 63 16.021 888 53 15.141 073 53 : 17.292 033 30 16.288 888 54 15.372 451 O03 : 17.588 493 56 16.544 390 95+ 15.592 810 50+ ; 17.873 551 50— 16.788 890 86 15.802 676 67 ] 18.147 645 67 17.022 862 07 16.002 549 2I ; 18.411 197 76 17.246 757 96 16.192 904 OI . 18.664 613 23 17.461 0I2 40 16.374 194 29 I 18.908 281 95+ 17.666 040 58 16.546 831 71 3 19.142 578 80 17.862 239 79 16.711 287 34 ; 19.367 864 23 18.049 996 23 16.867 892 71 3 19.584 484 84 18.229 655 72 17.017 040 67 4) 19.792 773 88 18.401 584 42 17.159 086 35+ 4. 19.993 O51 8I 18.566 109 49 17.294 367 96 2 20.185 626 74 18.723 549 75+ 17.423 207 58 oF: 20.370 794 94 18.874 210 29 17.545 911 98 By 20.548 841 29 19.018 383 05+ 17.662 773 31 4, 20.720 039 70 19.156 347 42 17.774 069 82 495 20.884 653 56 19.288 370 74 17.880 066 50— 47 21.042 936 12 19.414 708 34 17.981 OI5 71 45 21.195 130 88 19.535 606 54 18.077 157 82 49 21.341 472 00 19.651 298 13 18.168 721 73 50 21.482 184 62 19.762 007 78 18.255 925 46 TAT: 8S TABLE 28. PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity receivable at end of each vear Naber > 4 per cent. 4% per cent. 5 per cent. 5I 21.617 485 21 19.867 950 03 18.338 976 63 52 21.747 581 93 19.969 330 17 18.418 072 98 i] 21.872 674 93 20.066 344 66 18.493 402 84 | 21.992 956 67 20.159 181 49 18.565 145 56 . 22.108 612 18 20.248 020 57 18.633 471 96 “i 22.219 819 40 20.333 034 04 18.698 544 73 ; 22.326 749 43 20.414 386 64 18.760 518 79 1 22.429 566 76 20.492 236 02 18.819 541 70 | 22.528 429 57 20.566 733 03 18.875 754 oo . 22.623 489 98 20.638 022 o4 18.929 289 53 a 22.714 894 21 20.706 241 18 18.980 275 74 22.802 782 89 20.771 522 66 19.028 834 04 22.887 291 24 20.833 992 98 19.075 080 03 22.968 549 27 20.893 773 19 19.119 123 84 [ 23.046 681 99 20.950 979 13 19.161 070 33 : 23.121 809 61 21.005 721 65+ 19.201 019 36 23.194 047 70 21.058 106 84 19.239 066 06 ¢ 23.263 507 40 21.108 236 21 19.275 30I 00 t 23.330 295 58 21.156 206 90 19.309 810 48 23.394 514 98 21.202 111 87 19.342 676 63 - 23.456 264 40 21.246 040 07 19.373 977 76 23.515 638 85-4 21.288 076 62 19.403 788 34 23.572 729 66 21.328 302 99 19.432 179 38 23.627 624 68 21.366 797 12 19.459 218 45+ 23.680 408 34 21.403 633 60 19.484 969 95+ 23.731 161 87 21.438 883 83 19.509 495 19 23.779 963 33 21.472 616 11 19.532 852 57 23.826 887 82 21.504 8935 80 19.555 097 68 23.872 007 52 21.535 785 45+ 19.576 283 51 23.915 391 85— 21.565 344 93 19.596 460 48 23.957 107 55— 21.593 631 51 19.615 676 65+ 23.997 218 79 21.620 700 O1 19.633 977 76 24.035 787 30 21.646 602 88 19.651 407 39 24.072 872 41 21.671 390 32 19.668 007 04 : 24.108 531 16 21.695 110 35+ 19.683 816 23 ¢ 24.142 818 42 21.717 808 95— 19.698 872 60 v 24.175 786 94 21.739 530 09 19.713 212 OO ? 24.207 487 45— 21.760 315 88 19.726 868 57 21 24.237 968 70 21.780 206 58 19.739 874 83 i 24.267 277 59 21.799 240 75— 19.752 261 74 Ly 24.295 459 23 21.817 455 26 19.764 058 8o 02 24.322 556 95— 21.834 883 42 19.775 294 10 ¢ 24.348 612 45— 21.851 564 99 19.785 994 38 o 24.373 665 82 21.867 526 31 19.796 185 12 ¢ 24.397 755 59 21.882 800 30 19.805 890 59 9 24.420 918 84 21.897 416 55+ 19.815 133 90 ec 24.443 191 I9 2I.9II 403 40 19.823 937 05- 0% 24.464 606 91 21.924 787 94 19.832 321 00 99 24.485 198 96 21.937 596 12 19.840 305 71 100 24.504 999 00 21.949 852 74 19.847 910 20 “BLL. 307 398 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 28. PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity receivable at end of each year Nuh or 51 per cent. 6 per cent. 64 per cent. : 0.947 867 30 0.943 396 23 0.938 967 14 1.846 319 71 1.833 392 67 1.820 626 42 2.697 933 38 2.673 or1 95— 2.648 475 51 3.505 150 I2 3.463 105 61 3.425 798 60 4.270 284 48 4.212 363 79 1-155 679 44 4.995 530 31 4.917 324 33 4.841 013 56 5.682 967 12 5.582 381 44 5.484 519 77 6.334 565 99 6.209 793 81 6.088 750 96 6.0952 195 25= 6.801 692 28 6.656 104 19 7.537 625 83 7.360 087 o5-+ 7.188 830 22 8.092 536 33 7.886 874 58 7.689 042 46 . 8.618 517 85— 8.383 843 94 8.158 725 32 9.117 078 53 8.852 682 96 8.599 742 o8 9.589 647 89 9.294 983 93 9.013 842 33 10.037 580 94 9.712 248 99 9.402 668 85 19 10.462 162 03 10.105 895 27 9.767 764 18 10.864 608 56 10.477 259 69 10.110 576 70 11.246 074 47 10.82% 603 48 10.432 466 38 19 11.607 653 52 11.158 116 49 10.734 710 22 27 11.950 382 48 11.469 921 22 11.018 507 25— ; 12.275 244 0b 11.764 076 62 11.284 983 33 27 12.533169 73 12.041 551 72 1T.5351105 62 12.875 042 39 12.303 378 98 11.770 136 73 13.151 698 95+ 12.550 357 53 11.990 738 71 13.413 932 66 12.783 356 16 12.197 876 73 2 J 13.662 495 41 13.003 166 19 12.302 372 5% 7 13.898 099 9I 13.210 534 I4 12.574 997 66 2 14.I21421 72 13.406 164 28 12.746 476 68 28) 14.333 IOI 16 13.590 721 02 12.907 489 84 14.533 745 17 13.764 831 15+ 13.058 675 91 14.723 929 OF 13.929 085 99 13.200 634 65+ 14.904 198 17 14.084 043 39 13.333 929 25+ 15.075 069 36 14.230 229 6I 13.459 088 50— 15.237 932 57 14.368 141 14 13.576 608 92 15.390 552 20 14.498 246 36 13.686 956 73 15.536 068 43 14.620 987 13 13.790 569 70 15.673 998 51 14.736 780 31 13.887 858 87 . 15.804 737 93 14.846 o19 17 13.979 210 2I 32 15.928 661 54 14.949 074 68 14.064 986 11 2v 16.046 124 69 15.046 296 87 14.145 526 87 ar 16.157 464 16 15.138 015 92 14.221 I5I 99 28% 16.262 999 20 15.224 543 32 14.292 I6I 49 4 16.363 032 42 15.306 172 94 14.358 837 08 41 16.457 850 63 15.383 182 02 14.421 443 27 4 16.547 725 72 15.455 832 09 14.480 228 42 40 16.632 915 37 15.524 369 90 14.535 425 75— 4: 16.713 663 86 15.589 028 21 14.587 254 22 4. 16.790 202 7I 15.650 026 61 14.635 919 46 49 16.862 751 39 15.707 57227 14.681 614 51 50 16.931 5I7 90 15.761 860 64 14.724 520 67 TABLES TABLE 28. PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity receivable at end of each vear Jone or | 5% per cent. 6 per cent. 63 per cent. 51 16.996 699 43 15.813 076 o7 14.764 808 14 52 17.058 482 87 15.861 392 52 14.802 636 75-4 £3 17.117 045 38 15.906 974 08 14.838 156 58 17.172 554 86 15.949 975 54 14.871 508 52 17.225 I70 49 15.990 542 97 14.902 824 go 17.275 043 II 16.028 814 12 14.932 229 96 17.322 315 75— 16.064 918 98 14.959 840 33 17.367 123 93 16.098 980 17 14.985 765 57 17.409 596 14 16.131 113 37 15.010 108 52 i 17.449 854 16 16.161 427 71 15.032 965 74 vo 17.488 013 43 16.190 026 14 15.054 427 93 C2 17.524 183 34 16.217 003 79 15.074 580 22 i 17.558 467 62 16.242 458 29 15.093 502 55— . 17.590 964 57 16.266 470 og 15.III 270 OO i 17.621 767 37 16.289 122 72 15.127 953 os } {9 17.650 964 33 16.310 493 14 15.143 617 89 17.678 639 17 16.330 653 90 15.158 326 66 Lo 17.704 871 25+ 16.349 673 49 15.172 137 71 t) 17.729 735'79 16.367 616 50+ 15.185 105 83 * 17.753 304 06 16.384 543 87 15.197 282 47 17.775 643 66 16.400 513 08 15.208 715 93 17.796 818 64 16.415 578 38 15.219 451 58 17.816 889 70 16.429 790 93 15.229 532 00 17.835 914 41 16.443 198 99 15.238 997 18 17.853 947 31 16.455 848 10 15.247 884 68 17.871 040 10 16.467 781 23 15.256 229 74 17.887 241 80 16.479 038 8g 15.264 065 49 17.902 598 87 16.489 659 33 15.271 422 99 17.017 155 32 16.499 678 62 15.278 331 45 : 17.930 952 9I 16.509 130 77 15.284 818 26 ‘ 17.944 O31 20 16.518 047 go +5.2090 909 17 17.956 427 67 16.526 460 28 5.296 628 32 17.968 177 89 16.534 396 49 55.301 998 43 ¢ 17.979 315 54 16.541 833 48 15.307 040 78 . 17.989 872 55— 16.548 946 68 5.311 775 38 8 17.999 879 19 16.555 610 08 5.316 221 or ¢ 18.009 364 16 16.561 896 30 -5.320 395 32 os 18.018 354 66 16.567 826 70 15.324 314 85-4 89 18.026 876 45+ 16.573 421 41 15.327 995 16 63 18.034 953 98 16.578 699 45— 15.331 450 86 18.042 610 41 16.583 678 72 15.334 695 64 2 18.049 867 69 16.588 376 154 15.337 742 39 18.056 746 62 16.592 807 69 15.340 603 18 18.063 266 94 16.596 988 39 15.343 289 37 18.069 447 34 16.600 932 44 15.345 811 62 « 18.075 305 53 16.604 653 25— 15.348 179 92 = 18.080 858 33 16.608 163 44 15.350 403 68 C3 18.086 121 64 16.611 474 94 15.352 491 72 99 18.091 1710 56 16.614 599 oo 15.354 452 32 100 18.095 839 39 16.617 546 23 15.356 293 26 EN 200 400 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 28. PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity receivable at end of each year Nuahe or 7 per cent. 8 per cent. 9 per cent. 0.934 579 44 0.925 925 93 0.917 431 19 1.808 018 17 1.733264 75 — 1.759111 IQ 2.624 316 04 2.577 096 99 2.531 294 67 3.387 211 26 3.312 126 84 3.239 719 88 4.100 197 44 3.992 7I0 04 3.889 651 26 4.766 539 66 4.622 879 66 4.485 918 59 5.389 289 40 5.206 370 06 5.032 952 84 5.971 298 51 5.746 638 94 5.534 819 II 6.515232 25= 6.246 887 91 5.995 246 89 i 7.023 581 54 6.710 081 40 6.417 657 70 ; 7.498 674 34 7-138 964 26 6.805 190 55+ ] 7.942 686 30 7.536 078 o2 7.160 725 28 1 8.357 650 74 7.903 775 94 7.486 903 92 ) 8.745 467 99 8.244 236 98 7.786 150 39 1 9.107 9I4 OI 8.559 478 69 8.060 688 43 : 9.446 648 60 8.851 369 16 8.312 558 19 ] 9.763 222 99 9.121 638 1X 8.543 631 37 J 10.059 086 91 9.371 887 14 8.755625 IT 3 10.335 595 24 9.603 599 20 8.950 114 78 2h 10.594 OI4 25— 9.818 147 41 9.128 545 67 “ 10.835 527 33 10.016 803 16 9.292 243 73 ; 11.061 240 50— 10.200 743 66 9.442 425 44 11.272 187 38 10.371 053 05— 9.580 206 83 11.469 334 00 10.528 758 28 9.706 611 77 11.633 533 18 10.674 776 19 9.822 579 60 bo 11.325 778 67 10.809 977 95-1 9.028 972 II 11.986 709 04 10.935 164 77 10.026 579 92 4 12.137 111 251 11.051 078 49 10.116/123 37 12.277 674 oF 11.158 406 o1 10.198 282 91 od 12.409 041 18 11.257733 34 10.273 654 04 12.531 814 19 11.349 799 39 10.342 8o1 87 12.646 555 32 11.434 999 44 10.406 240 25+ 12.753 790 02 11.513 888 37 10.464 440 60 12.854 009 36 11.586 933 67 10.517 835 4I 12.947 672 30 11.654 568 22 10.566 821 48 13.035 207 ‘76 11.717 192 79 10.611 762 82 13.117 016 60 I¥.775 173 51 10.652 993 42 13.193 473 45+ 11.828 868 99 10.690 819 65— 5 13.264 928 46 11.878 582 40 10.725 522 61 49 13.331 708 84 11.924 613 33 10.757 360 20 5 13.394 I20 4I 11.967 234 57 10.786 568 99 ‘ 13.452 448 98 12.006 698 67 10.813 366 04 ‘ 13.506 961 67 12.043 239 51 10.837 950 50— A 13.557 908 10 12.077 073 62 10.860 505 04 4 13.605 52I 59 12.108 401 50+ 10.881 197 29 46 13.650 020 18 12.137 408 80 10.900 181 00 47 13.691 607 64 12.164 267 41 10.917 597 25— 48 13.730 474 43 12.189 136 49 10.933 575 46 49 13.766 798 53 12.212 163 4T 10.948 234 36 50 13.800 746 29 12.233 484 64 10.961 682 go TABLES TABLE 28. PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR (Continued) For annuity receivable at end of each year Pamber or 7 per cent. 8 per cent. 9 per cent. 5I 13.832 473 17 12.253 226 52 10.974 02I OI 5° 13.862 124 46 12.271 506 04 10.985 340 38 5 13.889 835 94 12.288 431 52 10.995 725 12 ; 13.915 734 53 12.304 103 26 11.005 252 40 : 13.939 938 81 12.318 614 13 I1I.0I3 993 03 4 13.962 559 64 12.332 050 I2 11.022 OII 95~— 5 13.983 700 59 12.344 490 85— 11.029 368 76 5. 14.003 458 50— 12.356 o10 05— 11.036 118 13 14.021 923 83 12.366 675 97 11.042 3I0 2I {i 14.039 181 15+ 12.376 551 82 11.047 99I 02 14.055 309 49 12.385 696 13 11.053 202 77 14.070 382 70 12.394 163 o8 11.057 984 19 14.084 469 81 12.402 oo2 86 11.062 370 82 14.097 635 34 12.409 261 go 11.066 395 25— 14.109 939 57 12.415 983 24 11.070 087 38 j 14.121 438 85— 12.422 206 71 11.073 474 66 14.132 185 84 12.427 969 17 11.076 582 26 14.142 229 76 12.433 304 79 11.079 433 27 14.151 616 59 12.438 245 18 11.082 048 87 14.160 389 34 12.442 819 61 11.084 448 50+ 14.168 588 17 12.447 055 19 11.086 650 co 14.176 250 63 12.450 977 03 11.088 669 73 14.183 411 80 12.454 608 36 11.090 522 69 14.190 104 49 12.457 970 70 11.092 222 65— 14.196 359 33 12.461 083 99 11.093 782 25— 14.202 204 98 12.463 966 65+ 11.095 213 OF 14.207 668 21 12.466 635 79 11.096 525 75+ 14.212 774 03 12.469 107 21 11.097 730 05— 14.217 545 82 12.471 395 57 11.098 834 91 . 14.222 005 44 12.473 514 41 11.099 848 54 14.226 173 31 12.475 476 31 11.100 778 47 14.230 068 51 12.477 292 88 11.101 631 63 14.233 708 89 12.478 974 89 11.102 414 34 14.237 TIL 11 12.480 532 30 11.103 132 42 14.240 290 76 12.481 974 36 11.103 791 21 0) 14.243 262 39 12.483 309 59 I1.104 395 61 14.246 039 62 12.484 545 92 11.104 950 IO I) 14.248 635 16 12.485 690 66 11.105 458 81 3) 14.251 obo 89 12.486 750 61 II.I05 925 5I «9 14.253 327 94 12.487 732 o5— 11.106 353 68 t 14.255 446 67 12.488 640 79 11.106 746 49 14.257 426 8o 12.489 482 21 11.107 106 87 14.259 277 38 12.490 261 31 11.107 437 50— 14.261 006 go 12.490 982 69 11.107 740 83 \ 14.262 623 27 12.491 650 64 11.108 019 II C) 14.264 133 90 12.492 269 11 11.108 274 41 ot 14.265 545 70 12.492 841 77 11.108 508 63 6 14.266 8635 14 12.493 372 OI 11.108 723 52 99 14.268 098 26 12.493 862 97 11.108 920 66 100 14.269 250 71 12.494 317 57 II.I0Q IOI §2 4071 402 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 28. PRESENT VALUE OF AN ANNUITY OF ONE DOLLAR (Concluded) For annuity receivable at end of each year id on | 10 per cent. Re oy 10 per cent. 0.909 090 9I 51 9.922 558 62 1.735 537 19 Ie 9.929 598 75— 2.486 851 99 9.935 998 86 3.169 865 45— 3 9.941 817 15— 3.790 786 77 : 9.947 106 50— 4.355 260 70 9.95I 9I5 00— 4.868 418 82 9.956 286 36 5.334 926 20 ).960 260 33 5.759 023 82 9.963 873 03 2 6.144 567 11 f 9.967 157 30 11 6.495 ob1 oI 9.970 143 00 1. 6.813 691 82 9.972 857 27 ; 7.103 356 20 9.975 324 79 i 7.366 687 46 9.977 567 99 7.606 079 51 9.979 607 27 7.823 708 64 € 9.981 461 15+ So 3.021 553031 : 9.983 146 50+ . 3.201 412 IO ¢ 9.984 678 64 19 8.364 920 09 G1 9.986 071 49 20 8.513 563 72 3 9.987 337 72 g 8.648 694 29 : 9.988 488 83 8.771 540 26 9.989 535 30 8.883 218 42 9.990 486 64 8.984 744 02 : 9.991 35I 49 ? 0.077 040 02 9.992 137 72 2 9.160 945 47 : 9.992 852 47 2° 0.237 22316 ! 9.993 502 25— 25 9.306 566 51 9.994 092 95— 2. 9.369 603 91 9.994 629 96 Zs 9.426 914 47 ‘ 9.995 118 14 i 9.479 013 15+ : 9.995 561 95— 2 9.526 375 59 9.995 965 41 ; 9.569 432 36 ‘ 9.996 332 19 : 9.608 574 87 9.996 665 63 ; 9.644 158 97 ¢ 9.996 968 75— 3 9.676 508 16 & 9.997 244 32 : 9.705 916 51 « 3.997 494 83 2 9.732 631 37 oe 9.997 722 58 : 9.756 955 79 an 9.997 929 62 4 9.779 050 72 3 9.998 117 83 4 9.799 137 02 9.998 288 94 4 9.817 397 29 a 9.998 444 49 4 9.833 997 53 ( 9.998 585 90 4 9.849 088 67 ¢ 9.998 714 45+ 4 9.862 807 88 «, 9.998 831 32 4% 9.875 279 89 ub 9.998 937 57 47 9.886 618 08 ¢ 9.999 034 15+ 4% 9.896 925 53 C- 9.999 I2I 95+ 43 9.906 295 94 92 9.999 201 78 50 9.914 814 49 100 9.999 274 34 TADLES EXPLANATION OF TABLE 29 TEE ANNUITY WHICH ONE DOLLAR WILL PURCHASE The annuity receivable at the end of each year which $1 will purchase is noted in Table 29. This table contains the reciprocals of the numbers appearing in Table 28. It is based on the following formula: Let a," represent the annuity receivable at the end of each year which $1 will buy for # years. Let n represent any number of years, the term of the annuity. Let 7 represent the rate of interest expressed decimally; thus for 5 per cent, 7 = 0.05. Then: i (1 + 7)" fac) ” (x +32) — 1" And by reference to equations ( 19) and (22) wir 4 5 In other words the annuity receivable at the end of each year which $1 will buy for # years is the amount of $1 at compound interest divided by the amount of an annuity of $1 in » years. The annuity which $1 will purchase for any number of years is, therefore, ascertainable from Tables 22 and 26 by dividing the amount of $1 at compound interest found in Table 22, by the amount of an annuity of $1 found in Table 26. Example. — What annuity for 20 years can be purchased for $500 at 5 per cent interest? The amount of $1 at per cent compound interest for 20 years in Table 22 is found to be $2.653208. The amount of an annuity of $1 for 20 years at 5 per cent interest, as found in Table 26, is $33.06505; consequently the annuity which $1 will purchase for 20 years at 5 per cent is 2.653208 + 33.06505 = 0.0802426. And the annuity which can be purchased for $500 will be 0.0802426 X 500 = $40.12. ~ 13}. 403 \2Y 404 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 29. ANNUITY WHICH ONE DOLLAR WILL PURCHASE For annuity receivable at end of each year — — Years. I per cent. 13 per cent. 2 per cent. 1.010 000 00 I.0I5 OOO 00 1.020 000 OO 0.507 512 44 0. 5TT 277.92 0.515 049 501 0.340 022 II 0.343 382 96 0.346 754 67 0.256 281 09 0.259 444 79 0.262 623 75+ 0.206 039 80 0.209 089 32 0.212 158 39 0.172 548 37 0.175 525 2I 0.178 525 81 0.148 628 28 0.151 556 16 0.154 511 96 0.130 690 29 0.133 584 02 0.136 509 80 0.116 740 36 0.119 609 82 0.122 5I5 44 I. 0.105 582 08 0.108 434 18 0.111 326 53 : 0.096 454 08 0.099 293 34 0.102 177 94 12 0.088 848 79 0.091 679 99 0.094 559 60 mw 0.082 414 32 0.085 240 36 0.088 118 35+ I4 0.076 9o1 17 0.079 723 32 0.082 601 97 1. 0.072 123 78 0.074 944 36 0.077 825 47 I 0.067 944 60 0.070 765 08 0.073 650 13 1 0.064 258 0b 0.067 079 66 0.069 969 84 3 0.060 982 05 — 0.063 805 78 0.066 702 10 Iv, 0.038 o51 75+ 0.060 878 47 0.063 781 77 20 0.055 415 31 0.058 245 74 0.061 156 72 21 0.053 030 75+ 0.055 865 50— 0.058 784 77 27 0.050 863 72 0.053 703 32 0.056 631 40 2% 0.048 885 84 ©.0511730/ 75-1 0.054 668 10 it 0.047 073 47 0.049 924 IO 0.052 871 10 z 0.045 406 75+ 0.048 263 45+ 0.03 220 44 2 0.043 868 88 0.046 731 96 0.049 699 23 27 0.042 445 53 0.045 315 27 0.048 203 09 25 0.041 124 44 0.044 00I 08 0.046 989 67 2 0.039 895 02 0.042 778 78 0.045 778 36 : 0.038 748 11 0.041 639 19 0.044 649 92 ; 0.037 675 73 0.040 574 30 0.043 596 35— - 0.036 670 89 0.039 577 10 0.042 610 61 0.035 727 44 0.038 641 44 0.041 686 53 0.034 839 97 0.037 761 89 0.040 818 67 : 0.034 003 63 0.036 933 63 0.040 002 21 : 0.033 214 3I 0.036 152 40 0.039 232 85+ 0.032 468 o5— 0.035 414 37 0.038 506 78 0.031 761 50— 0.034 716 13 0.037 820 57 > 0.031 091 60 0.034 054 63 0.037 171 14 49 0.030 455 60 0.033 427 10 0.036 555 75— 41 0.029 851 02 0.032 831 06 0.035 971 83 42 0.029 275 63 0.032 264 26 0.035 417 29 2 0.028 727 37 0.031 724 65~ 0.034 889 93 4 0.028 204 41 0.031 210 38 0.034 387 94 4 0.027 705 O5— 0.030 719 76 0.033 909 62 46 0.027 227.75 0.030 251 25— 0.033 453 42 47 0.026772 1% 0.029 803 42 0.033 O17 92 4 0.026 333 84 0.029 375 00— 0.032 601 84 4u 0.025 914 74 0.028 964 78 0.032 203 96 50 0.025 5I2 73 0.028 571 68 0.031 823 2I TABLES J TABLE 29. ANNUITY WHICH ONE DOLLAR WILL PURCHASE (Continued) For annuity receivable at end of each vear Years. I per cent. 1; per cent. 2 per cent. 5I 0.025 126 80 0.028 194 69 0.031 458 56 5 0.024 756 03 0.027 832 87 0.031 109 09 5. 0.024 399 56 0.027 485 37 0.030 773 92 5 0.024 056 58 0.027 151 38 0.030 452 26 3 0.023 726 37 0.026 830 18 0.030 143 37 5) 0.023 408 24 0.026 521 06 0.029 846 56 . 0.023 101 56 0.026 223 41 0.029 561 20 ol 0.022 805 73 0.025 936 61 0.029 286 67 € 0.022 520 20 0.025 660 12 0.029 022 43 a 0.022 244 45- 0.025 393 43 0.028 767 97 0.021 978 co 0.025 136 04 0.028 522 78 0.02I 720 41 0.024 887 51 0.028 286 43 0.02I 471 25 + 0.024 647 41 0.028 058 48 0.021 230 13 0.024 415 34 0.027 838 55 ~- 0.020 996 67 0.024 I90 94 0.027 626 24 ) 0.020 770 52 0.023 973 86 0.027 421 22 0.020 551 36 0.023 763 76 0.027 223 16 0.020 338 89 0.023 560 33 0.027 031 73 Co 0.020 132 80 0.023 363 29 0.026 846 654 0.019 932 82 0.023 172 35+ 0.026 667 65— 0.019 738 70 0.022 987 27 0.026 494 46 ; 0.019 550 19 0.022 807 79 0.026 326 83 0.019 367 06 0.022 633 68 0.026 164 54 0.019 189 10 0.022 464 73 0.026 oo7 36 0.019 016 0g 0.022 300 72 0.025 855 08 0.018 847 84 0.022 141 46 0.025 707 51 0.018 684 16 0.021 986 76 0.025 564 47 0.018 524 88 0.021 836 45+ 0.025 425 76 ; 0.018 369 83 0.021 690 36 0.025 291 23 ; 0.018 218 85+ 0.021 548 32 0.0235 160 71 0.018 071 79 0.02I 4I0 19 0.025 034 05 0.017 928 51 0.021 275 83 0.024 9II IO o.o17 788 87 0.02I 145 09 0.024 791 73 0.017 652 73 0.021 017 84 0.024 675 81 . 0.017 519 98 0.020 893 96 0.024 563 21 b 0.017 390 50+ 0.020 773 33 0.024 453 81 0.017 264 18 0.020 655 84 0.024 347 50 a 0.017 140 89 0.020 541 38 0.024 244 16 8q 0.017 020 56 0.020 429 84 0.024 143 70 od 0.016 9o3 06 0.020 32I 13 0.024 046 02 CI o.o16 788 32 0.020 213 16 0.023 95I OI 02 0.016 676 24 0.020 III 82 0.023 858 59 0.016 566 73 0.020 OII 04 0.023 768 68 Cr 0.016 459 71 0.019 9I2 73 0.023 681 18 or, 0.016 355 II 0.019 816 81 0.023 596 o2 CJ 0.016 252 84 0.019 723 21 0.023 513 13 Cr 0.016 152 84 0.019 631 86 0.023 432 42 9J 0.016 055 03 0.019 542 68 0.023 353 83 99 0.015 959 36 0.019 455 60 0.023 277 29 100 0.015 865 74 0.019 370 57 0.023 202 74 40¢ 406 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 29. ANNUITY WHICH ONE DOLLAR WILL PURCHASE (Continued) For annuity receivable at end of each year Years. 2} perjcent. 3 per cent. 32 per cent. I 1.025 O00 00 1.030 000 00 1.035 000 00 0.518 827 16 0.522 610 84 0.526 400 49 0.350 137 17 0.353 530 36 0.356 934 18 0.265 817 88 0.269 027 05— 0.272 25I 14 0.215 246 86 0.218 354 57 0.221 481 37 0.181 549 97 0.184 597 50+ 0.187 668 21 0.157 495 43 0.160 506 35+ 0.163 544 49 0.139 467 35 - 0.142 456 39 0.145 476 65— 0.125 456 89 0.128 433 86 0.131 446 or i 0.114 258 76 0.117 230 5I 0.120 241 37 0.105 105 96 0.108 077 45 0.III O9I 97 }: 0.097 487 13 0.100 462 09 0.103 483 95— 0.091 048 27 0.094 029 54 0.097 061 57 0.085 536 52 0.088 526 34 0.091 570 73 ; 0.080 766 46 0.083 766 58 0.086 825 o7 To 0.076 598 99 0.079 610 85— 0.082 684 83 - 0.072 927 77 0.075 952 53 0.079 043 13 13 0.069 670 08 0.072 708 70 0.075 816 84 19 0.066 760 62 0.069 813 88 0.072 940 33 20 0.064 147 13 0.067 215 71 0.070 361 08 27 0.061 787 33 0.064 871 78 0.068 036 59 2% 0.059 646 61 0.062 747 39 0.065 932 07 2 0.057 696 38 0.060 813 90 0.064 018 80 2 0.055 912 32 0.059 047 42 0.062 272 83 2 0.054 275 92 0.057 427 87 0.060 674 04 2. 0.052 768 75— 0.055 938 29 0.059 205 40 2 0.051 376 87 0.054 564 2I 0.057 852 41 z 0.050 087 93 0.053 293 23 0.056 602 65— 2 0.048 891 27 0.052 114 67 0.055 445 38 : 0.047 777 64 0.051 019 26 0.054 371 33 ) 0.046 739 00 0.049 998 93 0.053 372 40 . 0.045 768 31 0.049 046 62 0.052 441 50+ : 0.044 859 38 0.048 156 12 0.051 572 42 y 0.044 006 75+ 0.047 321 96 0.050 759 66 : 0.043 205 58 0.046 539 29 0.049 998 35— : 0.042 451 58 0.045 803 79 0.049 284 16 : 0.041 740 90 0.045 III 62 0.048 613 25— ] 0.041 O70 12 0.044 459 34 0.047 982 14 3 0.040 436 15+ 0.043 843 85+ 0.047 387 75+ 4% 0.039 836 23 0.043 262 38 0.046 827 28 4 0.039 267 86 0.042 712 41 0.046 298 22 42 0.038 728 76 0.042 191 67 0.045 798 28 4 0.038 216 88 0.041 698 11 0.045 325 39 44 0.037 730 37 0.041 229 85— 0.044 877 68 45 0.037 267 51 0.040 785 18 0.044 453 43 43 0.036 826 76 0.040 362 54 0.044 051 08 47 0.036 406 69 0.039 960 51 0.043 669 19 48 0.036 005 99 0.039 577 77 0.043 306 46 4 0.035 623 48 0.039 213 14 0.042 961 67 50 0.035 258 0b 0.038 865 49 0.042 633 71 TAB ES / TABLE 29. ANNUITY WHICH ONE DOLLAR .WILL PURCHASE (Continued) For annuity receivable at end of each year Years. 2} per cent. 3 per cent. 33 per cent. 51 0.034 908 70 0.038 533 82 0.042 321 56 2 0.034 574 46 0.038 217 18 0.042 024 29 2 0.034 254 49 0.037 914 71 0.041 741 00 ; 0.033 947 99 0.037 625 58 0.041 470 90 - 0.033 654 19 0.037 349 07 0.04I 213 23 ©.033 372 43 0.037 084 47 0.040 967 30 0.033 102 04 0.036 831 14 0.040 732 45+ 0.032 842 44 0.036 588 48 0.040 508 10 © 0.032 593 OF 0.036 355 93 0.040 293 66 iH 0.032 353 40 0.036 132 96 0.040 088 62 0.032 122 94 0.035 919 08 0.039 892 49 0.03I gor 26 0.035 713 85— 0.039 704 80 0.031 687 90 0.035 516 82 0.039 525 13 0.031 482 49 0.035 327 6o 0.039 353 08 0.031 284 63 0.035 145 81 0.039 188 26 0.031 093 98 0.034 971 10 0.039 030 3I 0.030 9I0 2I 0.034 803 13 0.038 878 92 : 0.030 733 00 0.034 641 59 0.038 733 75+ t- 0.030 562 06 0.034 486 18 0.038 594 53 : 0.030 397 12 0.034 336 63 0.038 460 95+ 0.030 237 90 0.034 192 66 0.038 332 77 0.030 084 17 0.034 054 04 0.038 209 73 0.029 935 68 0.033 920 53 0.038 091 60 0.029 792 22 0.033 79I OI 0.037 978 16 0.029 653 58 0.033 667 96 0.037 869 19 0.029 519 56 0.033 548 49 0.037 764 50 0.029 389 97 0.033 433 31 0.037 663 90 0.029 264 63 0.033 322 24 0.037 567 21 , 0.029 143 38 0.033 2I5 10 0.037 474 26 i 0.029 026 O53 0.033 III 75~— 0.037 384 89 & 0.028 912 48 0.033 OI2 OI 0.037 298 94 ‘ 0.028 802 54 0.032 915 76 0.037 216 28 : 0.028 696 08 0.032 822 84 0.037 136 76 0.028 592 98 0.032 733 13 0.037 obo 25 i 0.028 493 10 0.032 646 50+ 0.036 986 62 £ 0.028 396 33 0.032 562 84 0.036 g15 76 ‘ 0.028 302 55— 0.032 482 02 0.036 847 56 ¢ 0.028 211 65+ 0.032 403 93 0.036 781 go os 0.028 123 53 0.032 328 48 0.036 718 68 Cs 0.028 038 og 0.032 255 56 0.036 657 81 o1 0.027 955 23 0.032 185 08 0.036 599 19 Co 0.027 874 86 0.032 116 94 0.036 542 73 C. 0.027 796 go 0.032 O5I O7 0.036 488 34 0.027 721 26 0.031 987 37 0.036 435 94 G; 0.027 647 86 0.031 925 77 0.036 385 46 96 0.027 576 62 0.031 866 19 0.036 336 82 (& 0.027 507 47 0.031 808 56 0.036 289 95— 93 0.027 440 34 0.031 752 81 0.036 244 78 99 0.027 375 17 0.031 698 86 0.036 201 24 100 0.027 311 88 0.031 646 67 0.036 159 27 2 ou 40° 408 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 29. ANNUITY WHICH ONE DOLLAR WILL PURCHASE (Continued) For annuity receivable at end of each year Years. 4 per cent. 43 per cent. 5 per cent. 1.040 000 00 1.045 000 00 1.050 000 00 0.530 196 08 0.533 997 55+ 0.537 804 88 0.360 348 54 0.363 773 36 0.367 208 56 0.275 490 05— 0.278 743 65— 0.282 o11 83 0.224 627 II 0.227 791 64 0.230 974 80 0.190 761 90 0.193 878 39 0.197 OI7 47 0.166 609 61 0.169 701 47 o.172 819 82 0.148 527 83 0.151 609 65-1 0.154 721 81 0.134 492 99 0.137 574 47 0.140 690 08 1 0.123 290 94 0.126 378 82 0.129 504 57 1 0.114 149 O4 o.117 248 18 0.120 388 89 3 0.106 552 I7 0.109 666 19 0.112 825 4I 0.100 143 73 9.103275 351 0.106 455 77 0.094 668 97 0.097 820 32 0.IOI 023 97 0.089 941 10 0.093 113 81 0.096 342 29 ] 0.085 820 00 0.089 015 37 0.092 269 91 0.082 198 52 0.085 417 58 0.088 699 14 l 0.078 993 33 0.082 236 90 0.085 546 22 ; 0.076 138 62 0.079 407 34 0.082 745 OI 2 0.073 581 75+ 0.076 876 14 0.080 242 59 70 0.071 280 II 0.074 600 57 0.077 996 II 2? 0.069 198 81 0.072 545 65— 0.075 970 51 : 0.067 309 06 0.070 682 49 0.074 136 82 - 0.065 586 83 0.068 987 03 0.072 4770 90 s 0.064 o11 96 0.067 439 03 0.070 952 46 2 0.062 567 38 0.066 021 37 0.069 564 32 : 0.061 238 54 0.064 719 46 0.068 291 86 a 0.060 012 98 0.063 520 81 0.067 122 53 2 0.058 879 93 0.062 414 61 0.066 045 5I 5 0.057 830 10 0.061 30I 54 0.065 O51 44 : 0.056 855 35+ 0.060 443 45— 0.064 132 12 0.055 948 59 0.059 563 20 0.063 280 42 0.055 I03 57 0.058 744 53 0.062 490 04 0.054 314 77 0.057 981 91 0.061 755 45- 0.053 577 32 0.087270 45— 0.061 O71 71 0.052 886 83 0.056 605 78 0.060 434 46 0.052 239 57 0.055 984 02 0.059 839 79 0.051 631 92 0.055 401 69 0.059 284 23 Lo! 0.051 060 83 0.054 855 67 0.058 764 62 47 0.050 523 49 0.054 343 I5— 0.058 278 16 . 0.050 017 38 0.053 861 58 0.057 822 29 4° 0.049 540 20 0.053 408 68 0.057 394 71 é 0.049 089 89 0.052 982 35— 0.056 993 33 4 0.048 664 54 0.052 580 71 0.056 616 25+ 4 0.048 262 46 0.052 202 02 0.056 261 73 4% 0.047 882 o5— 0.051 844 71 0.055 928 20 47 0.047 521 89 0.051 507 34 0.055 614 21 48 0.047 180 65— 0.051 188 58 0.055 318 43 44 0.046 857 12 0.050 887 22 0.055 039 65— 50 0.046 550 20 0.050 602 15— 0.054 776 74 TABLES J TABLE 29. ANNUITY WHICH ONE DOLLAR WILL PURCHASE (Continued) For annuity receivable at end of each year Years. 4 per cent. 43 per cent. 5 per cent. 51 0.046 258 85— 0.050 332 32 0.054 528 67 2 0.045 982 12 0.0350 076 79 0.054 204 50— 3 0.045 719 15— 0.049 834 69 0.054 073 34 { 0.043 469 10 0.049 6035 19 0.053 864 38 0.045 231 24 0.049 387 54 0.053 666 86 0.045 004 87 0.049 181 05-1 0.053 480 10 0.044 789 32 0.048 985 0b 0.053 303 43 0.044 584 o1 0.048 798 97 0.053 136 26 ) 0.044 388 36 0.048 622 21 0.052 978 02 : 0.044 201 85: 0.048 454 26 0.052 828 18 0.044 023 98 0.048 294 62 0.052 686 27 0.043 854 30 0.048 142 84 0.052 551 83 0.043 692 37 0.047 998 48 0.032 424 42 0.043 537 80 0.047 861 15- 0.052 303 65+ 0.043 390 19 0.047 730 47 0.052 189 15+ ¢ 0.043 249 21 0.047 606 08 0.052 080 57 0.043 114 5I 0.047 487 65— 0.05I 977 58 0.042 985 78 0.047 374 87 0.051 879 86 ti 0.042 862 72 0.047 267 45+ 0.051 787 15— : 0.042 745 06 0.047 165 11 0.051 699 15+ 0.042 632 53 0.047 067 59 0.051 615 63 0.042 524 89 0.046 974 65+ 0.051 536 33 0.042 421 gO 0.046 886 ob 0.051 461 03 0.042 323 34 0.046 8or1 359 0.051 389 53 0.042 229 00 0.046 721 04 0.051 321 61 . 0.042 138 69 0.046 644 22 0.035I 257 09 0.042 052 21 0.046 570 94 0.05I 195 80 0.041 969 39 0.046 501 04 0.051 137 56 0.041 890 07 0.046 434 34 0.051 082 22 Ls 0.041 814 08 0.046 370 69 0.051 029 62 : 0.041 741 27 0.046 309 95+ 0.050 979 63 : 0.041 671 50— 0.046 251 97 0.050 932 II 0.041 604 63 0.046 196 63 0.050 886 94 0.041 540 54 0.046 143 79 0.050 843 99 0.041 479 09 0.046 093 34 0.050 803 16 ¢ 0.041 420 18 0.046 045 16 0.050 764 33 7 0.041 363 70 0.045 999 15+ 0.0350 727 40 &3 0.04I 309 53 0.045 955 22 0.050 692 28 ¢ 0.041 257 58 0.045 913 25— 0.050 658 88 > 0.041 207 75+ 0.045 873 16 0.050 627 11 (1 0.041 159 95+ 0.045 834 86 0.050 596 89 tr 0.04I 114 IO 0.045 798 27 0.050 568 15— ¢ 0.041 070 10 0.045 763 31 0.050 540 80 ¢ 0.041 027 89 0.045 729 OI 0.050 514 78 Gl; 0.040 987 38 0.045 697 99 0.050 490 03 J] 0.040 948 50+ 0.045 667 49 0.050 466 48 97 0.040 QII 19 0.045 638 34 0.050 444 oF 98 0.040 875 38 0.045 610 48 0.0350 422 74 99 0.040 841 00 0.045 583 85— 0.050 402 45 100 0.040 808 oo 0.045 558 39 0.050 383 14 40C 410 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 29. ANNUITY WHICH ONE DOLLAR WILL PURCHASE (Continued) For annuity receivable at end of each year Years. 53 per cent. 6 per cent. 6% per cent. 1.055 000 00 1.060 000 00 1.065 000 00 0.541 618 oo 0.545 436 89 0.549 261 501 0.370 654 07 0.374 109 81 ©.377 575 7° 0.285 294 49 0.288 591 49 0.291 QO2 74 0.234 176 44 0.237 396 40 0.240 634 54 0.200 178 95 0.203 362 63 0.206 568 31 0.175 964 42 0.179 135 02 0.132 331 37 0.157 864 or 0.161 035 94 0.164 237 30 0.143 839 46 0.147 022 24 0.150 238 03 ] 0.132 667 77 0.135 867 96 0.139 104 69 3 0.123 570 65+ 0.126 792 94 0.130 055 2I 0.116 029 23 0.1101277 03 0.122 563 17 0.109 684 26 0.112 960 II 0.116 282 56 1 0.104 279 12 0.107 584 91 0.110 940 48 . 0.099 625 60 0.102 962 76 0.106 352 78 1 0.095 582 54 0.098 952 14 0.102.377.57 ) 0.092 04I 97 0.095 444 80 0.098 906 33 0.088 919 92 0.092 356 54 0.095 854 61 : 0.086 150 06 0.089 620 86 0.093 155 75+ ; 0.083 679 33 0.087 184 56 0.090 756 40 2 0.081 464 78 0.085 004 55— 0.088 613 33 . 0.079 471 23 0.083 045 57 0.086 691 20 0.077 669 65— 0.081 278 48 0.084 960 78 2 0.076 035 80 0.079 679 oo 0.083 397 70 : 0.074 549 35+ 0.078 226 72 0.081 981 48 2h 0.073 193 07 0.076 904 35— 0.080 694 8o Z 0.071 952 28 0.075 697 17 0.079 522 83 a 0.070 814 40 0.074 592 55+ 0.078 453 05+ Ze 0.069 768 57 0.073 579 61 0.077 474 40 a 0.068 805 39 0.072 648 91 0.076 577 44 0.067 916 65+ 0.071 792 22 0.075 753 93 0.067 095 19 0.071 002 34 0.074 996 65— 0.066 334 69 0.070 272 93 0.074 299 24 0.065 629 58 0.069 598 43 0.073 656 10 : 0.064 974 93 0.068 973 86 0.073 062 26 0.064 366 35— 0.068 394 83 0.072 5I3 32 . 0.063 799 93 0.067 857 43 0.072 005 34 3 0.063 272 17 0.067 358 12 0.071 534 80 ; 0.062 779 91 0.066 893 77 0.071 098 54 3 0.062 320 34 0.066 461 54 0.070 693 73 4 0.061 890 90 0.066 058 86 0.070 317 79 4 0.061 489 27 0.065 683 42 0.069 968 42 4 0.061 113 37 0.065 333 12 0.069 643 52 Z 0.060 761 28 0.065 cob 0b 0.069 341 19 4 0.060 431 27 0.064 700 50— 0.069 059 68 4) 0.060 121 75+ 0.064 414 85+ 0.068 797 43 47 0.0359 831 29 0.064 147 68 0.068 553 co 48 0.059 558 54 0.063 897 65+ 0.068.325 05+ 49 0.059 302 30 0.063 663 56 0.068 112 40 50 0.059 061 45+ 0.063 444 29 0.067 913 93 ‘TA ; ty TABLE 29. ANNUITY WHICH ONE DOLLAR WILL PURCHASE (Continued) For annuity receivable at end of each vear Years. J 5% per cent. 6 per cent. 63 per cent. 31 0.058 834 95+ 0.063 238 80 0.067 728 61 4 0.058 621 86 0.063 046 17 0.067 555 53 0.058 421 30 0.062 865 51 0.067 393 82 5 0.058 232 45+ 0.062 696 o2 0.067 242 67 ; 0.058 054 58 0.062 536 96 0.067 101 37 : 0.057 886 98 0.062 387 65- 0.066 969 23 0.0357 729 00 0.062 247 44 0.066 845 63 0.057 580 06 0.062 115 74 0.066 729 99 0.057 439 59 0.061 992 co 0.066 621 77 t 0.057 307 oF 0.061 875 72 0.066 520 47 0.057 182 02 0.061 766 42 0.066 425 64 [ 0.057 064 oo 0.061 663 66 0.066 336 84 0.056 952 58 0.061 567 04 0.066 253 67 0.056 847 37 0.061 476 154 0.066 175 77 0.056 748 oo 0.061 390 66 0.066 102 80 £1) 0.056 654 13 0.061 310 22 0.066 034 42 0.056 565 44 0.061 234 54 0.065 970 34 0.056 481 63 0.061 163 30 0.065 g10 29 . 0.056 402 42 0.061 096 25+ 0.0635 854 oo 0.056 327 54 0.061 033 13 0.065 8o1 24 0.056 256 75+ o.0o6o 973 70 0.0635 751 77 0.056 189 82 0.060 917 74 0.065 705 39 0.056 126 52 o.06o 865 o5— 0.065 661 go 0.056 066 65-4 0.060 815 42 0.065 621 12 0.056 o10 02 o.o0b6o 768 67 0.063 582 87 0.055 956 45+ 0.060 724 63 0.065 546 99 0.055 905 77 o.06o 683 15+ 0.065 513 35~ 0.055 857 81 0.060 644 07 0.0635 481 78 0.055 812 43 o.o6o 607 24 0.065 452 17 0.055 769 48 0.060 572 54 0.0635 424 40 0.055 728 84 0.060 539 84 0.065 398 33 ’ 0.055 690 36 0.060 509 03 0.0635 373 88 oN 0.055 653 95— 0.060 479 98 0.065 350 94 0.055 619 47 0.060 452 61 0.065 329 41 ‘ 0.055 586 83 0.060 426 81 0.065 309 21 $5 0.055 555 93 0.060 402 49 0.065 290 26 ’ 0.055 526 67 0.060 379 56 0.063 272 47 Pd 0.055 498 96 0.060 357 95— 0.065 255 77 89 0.055 472 73 0.060 337 57 0.065 240 10 9) 0.055 447 88 0.060 318 36 0.065 225 40 GI 0.055 424 35+ 0.060 300 25+ 0.0635 211 60 «2 0.055 402 07 0.060 283 18 0.065 198 64 ¢ 0.055 380 96 0.060 267 08 0.0635 186 49 eo 0.055 360 97 o.obo 251 89 0.065 175 07 G 0.055 342 04 0.060 237 58 0.0635 164 36 Co 0.0355 324 IO 0.060 224 o8 0.065 154 31 C 0.055 307 II o.06o 211 35+ 0.0635 144 87 03 0.055 29I OI o.06o 199 35+ 0.0635 136 or 99 0.055 275 77 0.060 188 03 0.0635 127 69 100 0.055 261 32 0.060 177 36 0.065 119 88 "ABLES 41 412 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 29. ANNUITY WHICH ONE DOLLAR WILL PURCHASE (Continued) For annuity receivable at end of each year Years. 7 per cent. 8 per cent. 9 per cent. 1.070 000 00 1.080 000 00 1.090 000 00 0.553 O9I 79 0.560 769 23 0.568 468 go 0.381 051 67 0.388 033 51 0.395 054 76 0.295 228 12 0.30I 920 80 0.308 668 66 0.243 890 69 0.250 456 45+ 0.257 092 46 0.209 795 80 0.216 315 39 0.222 919 78 0.185 553 22 0.192 072 40 0.198 690 52 0.167 467 76 0.174 014 76 0.180 674 38 0.153 486 47 0.160 079 71 0.166 798 80 s 0.142377 50+ 0.149 029 49 0.155 820 09 0.133 356 90 0.140 076 34 0.146 946 66 0.125 9OI 99 0.132 695 02 0.139 650 66 ; 0.119 650 85— 0.126 521 81 0.133 566 56 0.114 344 94 0.121 296 85+ 0.128 433 17 1 0.109 794 62 0.116 829 54 0.124 058 88 ” 0.105 857 65— 0.112 976 87 0.120 299 QI 0.102 425 I9 0.109 629 43 0.117 046 25— 0.099 412 60 0.106 702 10 0.II4 2I2 29 iy 0.096 753 oI 0.104 127 63 O.III 730 4I 20 0.094 392 93 0.101 852 2I 0.109 546 48 2 0.092 289 oo 0.099 832 25+ 0.107 616 63 oe 0.090 405 77 0.098 032 07 0.105 904 99 0.088 713 93 0.096 422 17 o.104 381 88 : 0.087 189 02 0.094 977 96 0.103 022 56 : 0.085 810 52 0.093 678 78 o.101 806 25 2 0.084 561 03 0.092 507 I3 0.100 715 36 : 0.083 425 73 0.091 448 10 0.099 734 9I 2s 0.082 39I 93 0.090 488 91 0.098 852 o5— 4 0.081 448 65+ 0.089 618 54 0.098 055 72 ) 0.080 586 40 0.088 827 43 0.097 336 35+ 0.079 796 91 0.088 107 28 0.096 685 60 0.079 072 92 0.087 450 81 0.096 096 19 0.078 408 o7 0.086 851 63 0.095 561 73 0.077 796 74 0.086 304 II 0.095 076 60 0.077 233 96 0.085 803 26 0.094 635 84 mT 0.076 715 31 0.085 344 67 0.0094 235 05— 0.076 236 85— 0.084 924 40 0.093 870 33 : 0.075 795 05+ 0.084 538 94 0.093 538 20 £4 0.075 386 76 0.084 185 13 0.093 235 55+ 4c 0.075 009 14 0.083 860 16 0.092 959 61 ‘ 0.074 659 62 0.083 561 49 0.092 707 89 ¢ 0.074 335 OI 0.083 286 84 0.092 478 14 3 0.074 035 89 0.083 034 14 0.092 268 37 4- 0.073 757 69 0.082 801 52 0.092 076 75— 4 0.073 499 57 0.082 587 28 0.091 9oI 65+ 4 0.073 259 96 0.082 389 91 0.091 741 60 4- 0.073 037 44 0.082 207 99 0.09I 595 25— 4 0.072 830 70 0.082 040 27 0.091 461 39 49 0.072 638 53 0.081 885 57 0.091 338 93 50 9.072 459 85— 0.031 742 86 0.091 226 87 T. 3 3 TABLE 29. ANNUITY WHICH ONE DOLLAR WILL PURCHASE (Continued) For annuity receivable at end of each vear Years. 7 per cent. 8 per cent. 9 per cent. 5I 0.072 293 65-4 0.081 611 16 0.09I 124 30 52 0.072 139 OI 0.081 489 59 0.09I 030 4I 5° 0.07I 995 09 0.081 377 35+ 0.090 944 43 0.071 861 10 0.081 273 70 o.0go 865 70 0.071 736 33 0.081 177 96 0.090 793 59 : 0.071 620 11 0.081 089 32 0.090 727 54 0.071 511 83 0.081 007 8o 0.090 667 o2 0.07I 4I0 93 0.080 932 27 0.090 611 57 0.071 316 89 0.080 862 47 0.090 560 76 5 0.071 229 23 0.080 797 95— 0.090 514 19 ‘ 0.071 147 49 0.080 738 30 0.090 471 5I - 0.071 O7I 27 0.080 683 14 0.090 432 40 0.07I 000 I9 0.080 632 14 0.090 396 54 0.070 933 88 0.080 584 97 0.090 363 66 0.070 872 03 0.080 541 35— 0.090 333 52 0.070 814 31 0.080 500 99 0.090 3035 89 0.070 760 46 0.080 463 67 0.090 280 56 0.070 710 21 0.080 429 14 0.090 257 32 th) 0.070 663 31 0.080 397 19 0.090 236 02 0.070 619 53 0.080 367 64 0.090 216 49 0.070 578 66 0.080 340 29 0.090 198 57 0.070 540 51 0.080 314 98 0.090 182 14 0.070 504 90 0.080 291 57 0.090 167 08 0.070 471 64 0.080 269 89 0.090 153 26 0.070 440 60 0.080 249 84 0.090 140 58 0.070 411 60 0.080 231 28 0.090 128 g6 0.070 384 53 0.080 214 10 0.090 118 30 0.070 359 24 0.080 198 20 0.090 108 52 0.070 335 63 0.080 183 49 0.090 099 55 3 0.070 313 57 0.080 169 87 0.090 O9I 32 0.070 292 97 0.080 157 26 0.090 083 77 0.070 273 73 0.080 145 59 0.090 076 85— 0.070 255 76 0.080 134 79 0.0Q0 070 50- 0.070 238 97 0.080 124 79 0.090 064 67 0.070 223 29 0.080 115 53 0.090 059 33 : 0.070 208 63 0.080 106 96 0.090 054 43 0.070 194 95 — 0.080 099 03 0.000 049 93 { 0.070 182 16 0.080 og1 68 0.090 045 81 8. 0.070 170 21 0.080 084 89 0.090 042 02 « 0.070 159 05+ 0.080 078 359 0.090 038 55+ ( 0.070 148 63 0.080 072 77 0.090 035 37 « 0.070 138 88 0.080 067 37 0.090 032 45~- ( 0.070 129 78 0.080 062 38 0.090 029 77 ¢ 0.070 121 28 0.080 057 75+ 0.090 027 31 2 0.070 I13 33 0.080 053 47 0.090 025 05+ 96 0.070 105 QO 0.080 049 51 0.090 022 98 97 0.070 098 97 0.080 045 84 0.090 021 09 98 0.070 092 48 0.080 042 44 0.090 019 34 99 0.070 086 43 0.080 039 30 0.090 017 75 100 0.070 080 76 0.080 036 38 0.090 016 28 ABLES 41° 414 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 29. ANNUITY WHICH ONE DOLLAR WILL PURCHASE (Concluded) For annuity receivable at end of each year Years. 10 per cent. Years. 10 per cent. I 1.100 O00 00 | 0.100 780 46 0.576 190 48 . 0.100 709 OC 0.402 114 80 | 0.100 644 13 0.315 470 80 5 0.100 585 23 0.263 797 48 : 0.100 531 75— 0.229 607 38 ; 0.100 483 17 0.205 405 50— 0.100 439 06 0.187 444 02 0.100 398 98 0.173 640 54 0.100 362 58 - 0.162 745 39 0.100 329 5I . 0.153 963 14 ; 0.100 299 46 0.146 763 32 i 0.100272 17 0.140 778 52 0.100 247 36 0.135 746 22 0.100 224 82 ©.131 47378 0.100 204 34 0.127 816 62 0.100 185 73 0.124 664 13 0.100 168 82 5 0.I2I 930 22 : 0.100 153 45— } 0.119 546 87 2 0.100 139 48 2h; 0.117 459 62 0.100 126 78 z 0.115 624 39 ; 0.100 II 24 0.114 005 0b x 0.100 104 76 ©. 112 571/31 0.100 005 22 0.IIT 299 78 0.100 086 56 0.110 168 07 0.100 078 68 Zz. 0.109 I59 04 7 0.100 O7I 53 o 0.108 257 64 i 0.100 065 02 2.4 0.107 45I OI 0.100 059 II zh 0.106 728 o7 0.100 053 73 : 0.106 079 25— «- 0.100 048 84 | 0.105 496 21 ‘ 0.100 044 40 0.104 971 72 : 0.100 040 36 0.104 499 4T ‘ 0.100 036 69 . 0.104 073 71 ¢ 0.100 033135 0.103 689 71 { 0.100 030 32 . 0.103 343 06 & 0.100 027 56 . 0.103 029 94 ¢ 0.100 025 06 0.102 746 92 & 0.100 022 78 2 0.102 490 98 { 0.100 020 7I 4c 0.102 259 41 ( 0.100 018 83 4 0.102 049 80 ( 0.100 O17 II 4 o.101 859 99 C 0.100 015 56 4 o.101 688 05— ¢ 0.100 O14 14 4 0.IOI 532 24 ¢ 0.100 012 86 A 0.IOI 39I OO ¢ 0.100 O11 69 4. o.101 262 95+ C 0.100 010 63 4 0.101 146 82 c 0.100 009 66 4 0.I0I 04T 48 Co 0.100 008 78 49 0.I00 045 90 9g 0.100 007 98 50 0.100 859 17 100 0.100 007 26 - 2S EXPLANATION OF TABLE 30 THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES OF THE CHARACTER Most FREQUENTLY ENCOUNTERED IN PusLic UTILITY VALUATIONS The probable life of any article does not depend merely upon its wearing qualities when in service, but upon a number of other factors as elsewhere explained. Its useful life under aver- age conditions is determinable with a greater or less degree of approximation from a study of all available experience. Without entering upon a full discussion of the basic available data, there is here presented a table in which the probable use- ful term of life for many articles, appliances, machinery and other things likely to be connected with industrial establish- ments or with public utilities is noted, due credit being given, so far as this is practicable, for the source of information in each case. Under ordinary conditions and particularly when used in connection with the Unlimited Life Method of procedure, the life terms here presented are given without any deduction due to failure caused by fortuitous events or by inadequacy and obsolescence. It is to be noted that in some of the sources from which infor- mation presented in this table was drawn, the depreciation was expressed in percentage by the Straight Line Method. This percentage has been translated into years of probable life. Summary of Authorities Quoted in Table 30 and Reference to Publication Alvord. John W. Alvord in Proceedings American Water Works Association, 1903. Arbitrators. Board of Arbitration in street lighting controversy at Atlanta, Georgia, 1899. Arnold. Bion J. Arnold. Coney Island and Brooklyn figures adopted by Public Service Commission of New York. Four Chicago appraisals quoted by H. A. Foster. Bryan. Wm. H. Bryan. “The Appraisal and Depreciation of Water Works.” Journal of Association of Engineer- ing Societies, Dec., 1907. Burdick. Chas. B. Burdick. Appraisal of Mt. Vernon Water Works, Illinois, 1906. "ABLE 415 416 VALUATION, DEPRECIATION AND THE RATE-BASE Cal. R. R. Com. California Railroad Commission — Reports 1913-4. Calistoga Electric Co. vs. Napa Valley Electric Co., May, 1914. Cuyamaca Water Co. Case, March, 1913. San Jose Water Co. Case, May, 1914. Stockton Terminal & Eastern R. R., April, 1913. Chi. Tele. Com. Chicago Telephone Commission. Published 1908. Chi. Trac. Com. Chicago Traction Commission. Quoted by G. W. Cra- vens, Electrical Review, April 23, 1910. Chi. U. T. Co. Chicago Union Traction Co. Quoted in Report Wisconsin R. R. Commission, Vol. 10, p. 220. Connette. E. G. Connette. 3rd Ave. Case figures adopted by Public Service Commission of New York. Cooley. Mortimer E. Cooley. Milwaukee 3¢ Fare Case. Report Wisconsin R. R. Com., Vol. 10, p. 226. Dodge. B. L. Dodge. Mt. Vernon Water Works Appraisal, Illinois, 1906. Floy. Trans. American Institute of Electrical Engineers, June, 1911. Third Avenue Case figures adopted by Public Service Commission of New York. Foster. H. A. Foster. “Engineering Valuation of Public Utilities and Factories,” Van Nostrand, 1912. Gillette. H. P. Gillette. Appraisal of Great Northern & Northern Pacific R. R.’s in Washington. Direction of Wash- ington Railroad Commission, 1906. Hammond. Robt. Hammond. Journal of Institute of Electrical En- gineers, England, April 25, 1907. Kiersted. W. Kiersted. Galena Appraisal, Kansas, 1905. Metcalf. Leonard Metcalf. Transactions American Society of Civil Engineers, 1909. Mil. E. R. & L. Co. Milwaukee Electric Railway and Lighting Co., in the Milwaukee 3¢ Fare Case, Aug., 1912. P. G. & E. Co. Pacific Gas & Electric Company. Figures used in rate hearings before Master in Chancery, San Francisco, 19134. Parsons. T. C. Parsons. Discussion of Mr. Hammond’s paper, Journal Institute Electric Engineers, England, April 25, 1907. Preece. Sir Wm. Preece. Report of Bristol Corporation, England, 1906. Rosecrans. W. H. Rosecrans. Galena Appraisals, Kansas, 1905. S.J. L.& DP. Corp. San Joaquin Light & Power Corporation. Rate hearing before California Railroad Commission, 1915. Starrett. Milton G. Starrett. Milwaukee 3¢ Fare Case. Report Wisconsin R. R. Commission, Vol. 10, p. 226. St. Louis P. S. C. St. Louis Public Service Commission. Case of Union Elec- tric Light & Power Co. TABLES 4d Stone & Webster. Figures for Chicago Union Traction Co. Case. Report Wisconsin Railroad Commission, Vol. 10, p. 220. Telephone “Data.” Compiled from practice A. T. & T. Co., Wisconsin R. R. Commission and others. Quoted by H. A. Foster. Trac. Val. Com. Traction Valuation Commission. Case of the Chicago Consolidated Traction Co. Wilgus. W. G. Wilgus. Appraisal of Lehigh Valley Railroad, January, 1914. Williams. Benezette Williams. Galena Appraisal, Kansas, 190s. Wis. R. R. Com. Wisconsin Railroad Commission. Quoted by Floy and by Foster and in published reports. Madison Electric Railway & Light Co. Case, March 8, 1910. Milwaukee Electric Railway & Lighting Co. Case, Nov. 25, 1913. Milwaukee 3¢ Fare Case. Aug. 23, 1912. Wisconsin Telephone Co. Case, Aug. 3, 190g. jr’ 418 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES Description. eee] Rogdus Authority. Remarks. Years Accumulators............... 15 Hammond Jour. Inst. Elec. Engrs. 15 Parsons Jour. Inst. Elec. Engrs. 15 10% Preece Report Bristol Corp., 1906. Airbrakes. ul lL JE 20 Wis. R. R. Com. Quoted by Henry Floy. Air compressors............. 20 5% P.G.&E. Co. S.F. rate hearing, 1913-14. 20-25 Trac. Val. Com. Chi. Con. Trac. Co. Case. Are lamps. iste ol 63 Arbitrators Ata. St. Lgt. Contrvsy, 1899. 12 5% Preece Report Bristol Corp., 1906. 121 St. Louis P. S.C. Union E. L. & P. Co. Case. 15 Wis. R. R. Com. Quoted by Henry Floy. 15 P. G.&E. Co. S. F. rate hearings, 1913-14. Arclamp posts. ............. 40 5% Preece Report Bristol Corp., 1906. Ammonia concentrators and IERES ied ST LR 15 Wis. R. R. Com. Quoted by H. A. Foster. Belling. tui ss ee 8 P. G.&E. Co. S. F. rate hearings, 1913-14. 20 Wis. R. R. Com Quoted by Henry Floy. 10-20 Wis. R. R. Com Mil. 3¢ Fare Case. with shafting and ropes... 15 Chi./U. 7. Co. Chi. Con. Trac. Co. Case. with shafting and ropes.... 20 Stone & Webs. Chi. Con. Trac. Co. Case. (eather). iv. Latah lil Ee g0-23 Foster ‘“ Eng. Valuation,’ etc. Benches (gas plant). ......... 25 Wis. R. R. Com Quoted by H. A. Foster. Blowers (gas plant) .......... 15 Wis. R. R. Com. Quoted by H. A. Foster. 20 P.G.& E. Co. S. F. rate hearings, 1913-14. BOIlers. cnr ere ar el 10 Arnold Coney Isl. & Brooklyn Case. 15 Chi. U. T. Co. Chi. Union Trac. Co. Case. 15 Alvord Aver. 32-Proc. A. W. W. A. 15 St. Louis P. S. C Union Elec. L. & P. Co. Case. 12-16 Metcalf Trans. Am. S. C. E., 1909. 16.7 Dodge Mt. Vernon W. W. Ill., 1906. 15-20 Wis. R. R. Com Milwaukee 3¢ Fare Case. 20 Stone & Webs. Chi. Union Trac. Co. Case. 20 o% P.G.&E. Co. S. F. rate hearings, 1913-14. 20 Hammond Jour. Inst. Elec. Engrs., 1907. 10-28 Chi. Trac. Com. Chicago Trac. Com., 1908. 25 Williams Galena Appraisal, Kan., 1905. 25 Burdick Mt. Vernon W. W. Ill., 1906. 28.57 Arnold 4 Chicago Appraisals. 25-30 Trac. Val. Com. Chicago Con. Trac. Co. Case. 30 Kiersted Galena Appraisal, Kan., 1905. 25-40 Rosecrans (Galena Appraisal, Kan., 1905. water-tube...... Ln 20 Floy ard Ave. Case, N. Y. water-tube.l.. LLL 00 20 | Wis. R. R. Com. Quoted by Henry Floy. water-tube.l.. 1.0 oa 25 5% Preece Report Bristol Corp., 1906. water-tube........ 0. LLL 20-30 Foster “ Eng. Valuation,” etc. fire-tube. if... kh 10 Arbitrators Ata. St. Lgt. Contrvsy, 1899. firestube. ll oi call EE To-15 Foster * Eng. Valuation,” etc. fire-tube electric light..... 16-30 Wis. R. R. Com Quoted by Henry Floy. fire-tube water works..... 20-25 Wis. R. R. Com. Quoted by Henry Floy. Lancashire. atl Sal 22 3% Preece Report Bristol Corp., 1906. boilers and accessories..... 20 S.J.L.&P. Cor. Cal. R. R. C. rate hearings. TAL _ES TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. Erooc Residual Authority. Remarks. Years Boilers (continued) steel breechings... . .... 10 Arnold 4 Chicago Appraisals. breechings and connections! 10-30 Trac. Val. Com. Chi. Con. Trac. Co. Case. Bonds yn 20 Trac. Val. Com. Chi. Con. Trac. Co. Case. 20 Wis. R. R. Com Quoted by Henry Floy. Bridges Howetruss R.R.......... 10 Gillette Gt. Nor. & Nor. Pac. apprais. trestles and wooden bridges 10 Cal. R. R. Com Stockton Term.& East. Case. Buildings. . ...... esate. 025-50 Wis. R. R. Com Quoted by Henry Floy. 50 St. Louis P.S. C Union Elec. L. & P. Case. 50 Connette 3rd Ave. Case, N. Y. City. railroad station............ 10 Cal. R. R. Com Stockton Term. & East R. R. Case. raflroad, iv... dae 33% Gillette Gt. Nor. & N. Pac. Appraisal. Street railway............. 50 Cooley Milwaukee 3¢ Fare Case. street railway............. 50 Starrett Milwaukee 3¢ Fare Case. Street railway ............. 50 Stone & Webs. Chi. Union Trac. Co. Case. Street railway ............) 50 Chi. U. T. Co. Chi. Union Trac. Co. Case. street railway............. 35-75 Wis. R. R. Com Milwaukee 3¢ Fare Case. street railway power plants. 20 Chi. U. T. Co. Chi. Union Trac. Co. Case. street railway power plants 25 Cooley Milwaukee 3¢ Fare Case. street railway power plants 50 Stone & Webs. Chi. Union Trac. Co. Case. street railway power plants 60 Wis. R. R. Com Milwaukee 3¢ Fare Case. sab-station............ 00 50 0% Preece Report Bristol Corp., 1906. SUb-Station ...... co. vens 50 1% Cal. R. R. Com. Calistoga E. Co. vs. Napa Val. E. Co. wooden, wood frame.......| 20 P. G.& E. Co. 8S. PF. rate hearings, 1913-14. wooden. tu is he 25 Rosecrans Galena Appraisal, Kan., 1903. wooden frame.... ........ 50 Arbitrators Ata. St. Lgt. Contrvsy, 1899. frame dwellings..........., 35 Wis. R. R. Com Quoted by H. A Foster. frame stables and sheds... 20-23 Wis. R. R. Com Quoted by H. A. Foster. corrugated iron... ......... 20 P. G. & E. Co. Wooden frame and floor. corrugated iron............ 25 P.G.&B. Co. Wooden frame, conc. floor. corrugated iron... ........ 30 P.G.&E. Co. Steel frame, wood floor. corrugated iron........... 36 P. G. & E. Co. Steel frame, conc. floor. BRICK. Js eins sn ak a 14 Rosecrans Galena Appraisal, Kan., 1905. yt AR i 30 Williams Galena Appraisal, Kan., 1905. bricks... edd 30 Kiersted Galena Appraisal, Kan., 1903. BECK. cies ves Fa a Se Caen 30 Dodge Mt. Vernon W. W., I11., 1906. Riel... te a 30 P.G.&E Co. Corr. roof, steel roof, frame, conc. floor. DECK... uo evion aise sin 30 P. G. & E. Co. Wood r., wood r-f., wood f. in RR 36 P. G. & E. Co. Slate r., wood r-f., and floor. BRIE see sik dis a) P. G. & E. Co. Corr. r., steel r-f., conc. f. brick... 50 P.G.&E. Co. Slate r., steel r-f., conc. f. BrICk eet ne ens 50 P. G. & E. Co. Rein. conc. r., steel r-f.,conc. f. Briel. ee ea) 35 Burdick Mt. Vernon W. W., Ill., 1906. brick. ois 60 Hammond Jour. Inst. E. E., 1907. Brack. 663 Trac. Val. Com. Chi. Union Trac. Co. Case. VL ES. 8 | “% Preece Renort Bristol Corp., 1906. fs 1 1 41Q 420 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. Erect] ST Authority. Remarks. Years Buildings (continued) brick gas retort. ........... 30 Wis. R. R. Com. Quoted by H. A. Foster. 1st class stone and brick... 75 Wis. R. R. Com. Quoted by H. A. Foster. 2nd class shops, etc........ 50 Wis. R. R. Com. Quoted by H. A. Foster. fireproof... alle 40 0% Chi. Tel. Com. Chicago Tel. Com., 1908. reinforced concrete. ....... 50 P. G. & E. Co. Steel r-f., conc. r., and floor. foundations... CLC RTO 0% Preece Report Bristol Corp., 1906. Cables mailing Aur Sc So 30 159% Parsons Jour. Inst. E. E., 1907. aisha La 20 Chi. Tel. Com. Chicago Telephone Com. armored mains. ........... 25 Hammond Jour. Inst. E. E., 1907. SONA TNAINS loa ls lle ale nla 30 Hammond Jour. Inst. E. E., 1g07. armored Lali tie LtL 1 35 15% Preece Report Bristol Corp., 1906. cables and feeders......... 20 Mil. E. R. & L. Milwaukee 3¢ Fare Case. cables and feeders......... I5-25 Wis. R. R. Com Milwaukee 3¢ Fare Case. main lead-covered......... 20 26% P. G. & E. Co. S. F. rate hearings, 1913-14. subsidiary cables.......... 15 40% Chi. Tel. Com. Chicago Telephone Com. aerial LL ak et 15 Chi. Tel. Com. Chicago Telephone Com. acrinlilines. a... J 20 St... P. S.C. Union Elec. L. & P. Case. aerial exchange. ........... I2-I5 30% Tel. “ Data" Quoted by H. A. Foster. aerial lead-covered......... 10-15 Foster “ Eng. Valuation,” etc. aerial lead-covered. ....... 15 Wis. R. R. Com Wisconsin Tel. Co. Case. aerial terminals........... 12 0% Chi. Tel. Com. Chicago Telephone Com. aerial terminals........... IO-I2 Tel. * Data” Quoted by H. A. Foster. underground lead covered 20 St. L.P.'S. C. Union Elec. L. & P. Co. Case. underground lead covered 25 Wis. R. R. Com. Quoted by Floy. underground lead covered. 20 Wis. R. R. Com. Quoted by H. A. Foster. underg’d mainexchange.... 20-25 40% Tel. “Data” Quoted by H. A. Foster. underground sub-exchange; 13-20 40% Tel. ““ Data” Quoted by H. A. Foster. Ol oA hel Ne 30 40% Tel. *“ Data” Quoted by H. A. Foster. SUDMATINE. . ue i= elev vives 10 Tel. Data?’ Quoted by H. A. Foster. Coal and ash machinery... .... 10 Wis. R. R. Com Quoted by Henry Floy. 10 Mil. E. R. & L. Milwaukee 3¢ Fare Case. 14 Trac. Val. Com. Chicago Con. Trac. Co. Case. 14.2 Arnold 4 Chicago Appraisals. 15 Wis. R. R. Com Milwaukee 3¢ Fare Case. 15 Chi. U. 2. Co- Chi. Union Trac. Co. Case. 20 Stone & Webs. Chi. Union Trac. Co. Case. 20 Henry Floy 3rd Ave. Case, N. Y. City. Compressors (Air) ............ 20 5% P..G.& BE. Co. S. F. rate hearings, 1913-14. , 20-25 Trac. Val. Com. Chi. Con. Trac. Co. Case. Compressor station Natural gas... lores dein 0 | 50% Cal. R. R. Com. Midway Gas Co., et al. CONGEUSEYS svi einiee alnis vivininimiminin 10 Arbitrators Ata. St. Lgt. Controversy. 15 $5.1... P. S.C. Union E. L. & P. Co. Case. 20 Wis. R. R. Com Quoted by Henry Floy. 20 Floy 3rd Ave. Case, N. Y. City. 20 Arnold Coney Isl. & Brooklyn Case. 20 0% P.G.&E. Co. S. F. rate hearings, 1913-14. 25 S.J.L.&P. Co. Cal R. R. Com. rate hear’gs. TABLES I TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. Erpect Residual" 4 thority. Remarks. Years - - Condensers (continued) old equipment. ........... 20 S.J. L. &. P. Co. Cal R. R. Com. rate hear’gs. 25 Trac. Val. Com. Chi. Union Trac. Co. Case. Conduis......0.... el all 50 Wis. R. R. Com Milwaukee 3¢ Fare Case. 50 St. L. P. S.C. Union Elec. L. &P. Co., Case. 100 Floy 3rd Ave. Case N. Y. City. mains... 0. 30 15% Parsons Jour. Inst. E. E., 1907. ucts. vais lr SE Hammond Jour. Inst. E. E., 1907. “solid ” system...........I 30 Hammond Jour. Inst. E. E., 1907. * ducts ” system..........| 30 Hammond Jour. Inst. E. E., 1907. ““solid ”’ sys. in wood... . . .. 40 12% Preece Report Bristol Corp., 1906. clay in concrete. .......... 50 0% Chi. Tel. Com. Chicago Telephone Com. fibre in concrete. .......... 20 0% Chi. Tel. Com. Chicago Telephone Com. subsidiary............ ...0 20 0% Chi. Tel. Com. Chicago Telephone Com. main-vitrified clay. ....... 50 0% Tel.“ Data” Quoted by H. A. Foster. main-concrete. ............ 53 0% Tel. “ Data” Quoted by H. A. Foster. main-fibre................ 20 0% Tel. * Data” Quoted by H. A. Foster, main-iron................ 20 0% Tel. “ Data” Quoted by H. A. Foster. main-creosoted wood. .. ... 20 0% Tel. “ Data” Quoted by H. A. Foster. subsidiary... .......000 I5 0% Tel. *“ Data Quoted by H. A. Foster. vitrified tile..............} 50 P.G.&E. Co. S.F. rate hearings, 1913-14. vitrified tile and fibre. . ... 40 P. G. & E. Co. S. F. rate hearings, 1913-14. fibre duct..............:: EE P.G.&E.Co. S.F.rate hearings, 1913-14. wrought iron pipe. ........ 20 P. G. &E. Co. S. F. rate hearings, 1913-14. Edison tube and fittings...: 20 15% P.G.&E.Co. S.F.rate hearings, 1913-14. paperconduit............) 25 P. G. & E. Co. S. F. rate hearings, 1913-14. wood conduit. ............ 25 P. G.&E. Co. S. F. rate hearings, 1913-14. w. i. lateral pipes.......... 15 P.G.&E. Co. S. F. rate hearings, 1913-14. conduit under tracks. . . ... 40 P. G.&E. Co. S. F. rate hearings, 1913-14. manholes and paving. ..... 40 P. G. & E. Co. S. F. rate hearings, 1913-14. service holes and paving. . 40 P. G.&E. Co. S. F. rate hearings, 1913-14. Converters static transformers. ....... 15 Hammond Jour. Inst. E. E., 1907. cs MNCRVRMIRG I feb loll 20 Hammond Jour. Inst. E. E., 1907. CONDENS. oo is cilia su is 10 Hammond Jour. Inst. E. E., 1907. Cranes... ivi ih rh 15 Chi. U. T. Co. Chi. Union Trac. Co. Case. 20 Stone & Webs. Chi. Union Trac. Co. Case. 50 Wis. R. R Com Milwaukee 3¢ Fare Case. 50 Arnold 4 Chicago Appraisals. Woolen, .... tu. dey 15 P. G.& E. Co. S. F. rate hearings, 1913-14. SUEEL..... 0s iii suv iiv same as bldg P. G. & E. Co. S. F. rate hearings, 1913-14. Culverts CRSEIION. oa vu. coun vss DR 16 Cal. R. R. Com Stockton Term.& East Case. log and timber. ........... 163 Gillette Gt. Nor. & N. P. R. R. Ap praisal. Dams arth... ie. i iris oR T00 Cal. R. R. Com Cuyumaca Water Co. Case. earth and loose rock.......i so S.J. L. & P. Co. Cal. R. R. Com. rate hear’gs. COMOTEEE. ars en 50 S.J. L. & P. Co. Cal. R. R. Com. rate hear'gs. concrete diverting........ | 100 Cal. R. R. Com. Cuyumaca Water Co. Case. fer dan A323; 422 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. pect] Residual Authority. Remarks. Years Distribution system street rallway...ooeeeneeenns 12} Cooley Milwaukee 3¢ Fare Case. street railway ............. 14 Starrett Milwaukee 3¢ Fare Case. distrib. and trans.......... 30.03 Wis. R. R. Com. Milwaukee 3¢ Fare Case. Ditches... da ae Salle miele 50 S.J. L. & P. Co: Cal. R. R. Com. rate hearing. concrete lining. ........... 20 S. J. L. & P. Co. Cal.R.R. Com. rate hearing. Economizers. ........---..... 10°20 Floy 4 Chicago Appraisals. 15 Chi. U. T- Co. Chi. Union Trac. Co. Case. 20 Stone & Webs. Chi. Union Trac. Co. Case. Electrical machinery dynamos and alternators. 25 Hammond Jour. Inst. Elec. E., 1907. dynamos and alternators. 30 8% Preece Report Bristol Corp., 1906. generators... ........oousre 10 Arbitrators Ata. St. Lgt. Controversy. generators. ..........ocxxos 15 St. LL. P. S.C. Union Elec. L. & P. Co. Case. Generators. .... ov vu-cnsrs 15 Chi. 0. T- Co. Chi. Union Trac. Co. Case. generators... ......c..cx-: 20 Stone & Webs. Chi. Union Trac. Co. Case. EENETAtOTS. . + « cisv sox an +» ij 15720 Wis. R. R. Com Milwaukee 3¢ Fare Case. generators. ....c.oveoss 20 2¢1b. P.G.&E. Co. S. F. rate hearings, 1913-14. generators... ......c.-en-- 1 20 Arnold Coney Isl. & Brooklyn Case. ZENETALOTS. .. «vn eunrnscners 20 Floy 3rd Ave. Case, N. Y. City. generators. ..........noveee 20 S.J.L.&P.Cor Cal.R.R. Com. rate hearing. generators. ................ 13733 Trac. Val. Com. Chicago Con. Trac. Co. Case. generators, modern types..; 20 Wis. R. R. Com. Quoted by Henry Floy. generators, obsolete types.. Is Wis. R. R. Com. Quoted by Henry Floy. generators belted.......... 10-20 Chi. Trac. Com. Quoted by G. W. Cravens. generators direct conn....., 20 Chi. Trac. Com. Quoted by G. W. Cravens. generators, telephone plant’ 20 20% Wis. R. R. Com Wisconsin Tel. Co. Case. ATIOLOTS 0 alint sia atato fu didiniote 10 Arbitrators Ata. St. Lgt. Controversy. NOLOTBY Luin tiatainisis re mnwiotn= SEN OO Hammond Jour. Inst. Elec. Eng., 1907. TIIOLOTE + ole inten we win re of AE 25 9% Preece Report Bristol Corp., 1906. INOLOTS Lele lalate a fa) fal i mied 25 9% Parsons Jour. Inst. Elec. Eng., 1907. EOtars Larter LOE ool od 1D. P. G.& E. Co. S. F. rate hearings, 1913-14. motors, modern types. .... 20 Foster “Eng. Valuation,” etc. motors, obsolete........... 15 Foster “ Eng. Valuation,” etc. motors, street railway. .... 20 Floy 3rd Ave. Case, N. Y. City. motors, street railway..... 20 Wis. R. R. Com Quoted by Henry Floy. motors, street railway. ... 30 Trac. Val. Com. Chi. Con. Trac. Co. Case. motors, small, misc....... 20 P. G.& E. Co. S. F. rate hearings, 1913-14. Engines. . atin rr 15 St. 1... B.'S. C. Union Elec. L. & P. Co. Case. 20 Arbitrators Ata. St. Lgt. Controversy. 25 Hammond Jour. Inst. E. E., 1907. engines and machinery... 25 6% Preece Report Bristol Corp., 1906. 10-33% Chi. Trac. Com. Quoted by G. W. Cravens. 13-20 Arnold Coney Isl. & Brooklyn Case. 20-33} Arnold 4 Chicago Appraisals. 15-20 Wis. R. R. Com Milwaukee 3¢ Fare Case. 20-33 Trac. Val. Com. Chicago Con. Trac. Co. Case. INACHINETY vss ova lels ia n'elels SE 2T, 67 Parsons Jour. Inst. Elec. E., 1907. stent ra RT Chi. U.T. Co. Chi. Union Trac. Co. Case. SECRTIY. «ve a visa ein alee wieleinins SER 20 Stone & Webs. Chi. Union Trac. Co. Case. TA 3 oo TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. Espoct| Ratu) Authority. Remarks. Years Engines (continued) SLeRIMN. ... vi. ia wnrc inn sai PO Mil. E. R. & L. Milwaukee 3¢ Fare Case. Steam... candle 20 5% P.G.& E. Co. S. F. rate hearings, 1913-14. Stearn. lala a 20 Floy 3rd Ave. Case, N. Y. City. Steamy, sues ind 20 S.J. L.&P. Cor Cal. R. R. Com. rate hearing, Steam... ...... kh. Jive 15-25 Metcalf Trans. Am. Soc. C. E., 1909. steam, slow speed......... 20 Wis. R. R. Com Quoted by Henry Floy. Corliss slow speed. ........ 25-30 Foster ‘“ Eng. Valuation,” etc. steam high speed. ......... 15-20 Foster ‘“ Eng. Valuation, etc. steam, high speed......... 15 Wis. R. R. Com Quoted by Henry Floy. E88... i dese dane sn uRIO-TS Foster ** Eng. Valuation," etc. AS La da aed Toa 15 Wis. R. R. Com. Quoted by Henry Floy. steam turbines............ 20 Stone & Webs. Chi. Union Trac. Co. Case, steam turbines............ 20 Mil. E. R. & L. Milwaukee 3¢ Fare Case. steam turbines............ 15 St. 1. P.S. C. Union Elec. L. & P. Co. Case, steam turbines........... 20 Wis. R. R. Com Quoted by Henry Floy. steam turbines........... 20 Hammond Jour. Inst. E. E., 1907. steam turbines........... 30 1¢lb. P.G. &E. Co. S. F. rate hearings, 1913-14. Exhausters gasplant. in uel! 25 1¢ Ib. Wis. R. R. Com Quoted by H. A. Foster. Fences Wooden. outs Lina iil 12 P. G. & E. Co. S. F. rate hearings, 1913-14. Wiremesh...............5. 12 P. G.&E. Co. S.F. rate hearings, 1913-14. railroad... ll nie ra 3 Gillette Gt. Nor. & N. P. Appraisal, ratlroad. ohn aa 15 Cal. R. R. Com Stockton Term. & East. Case. Filter beds water filters............... 15-20 - Bryan ‘* Appraisal of water works." water works............... 30-50 ! Foster *“ Eng. Valuation," etc. Flumes wooden... ia, dh da 30 Cal. R. R. Com. Cuyumaca Water Co. Case. ER ELS aE 25! S.J. L. & P. Cor, Cal. R. R. Com. rate hearing. concrete. vil dhe 50 S.J.L.&P. Cor. Cal.R.R. Com. rate hearing. Foundations Same as life] Trac. Val. Com. Chi. Con. Trac. Co. Case. of article sup-; Floy 3rd Ave. Case, N. Y. City. ported } Fire protection apparatus. . . . . 12 | P. G. & E. Co. S. F. rate hearings, 1913-14. Fuel oil handling apparatus... . 25 Trac. Val. Com. Chicago Con. Trac. Co. Fire hydrants. ...... NE. 40 Williams Galena Appraisal, Kan., 1905. 40-50 Metcalf Trans. Am. Soc. C. E., 1909. Furniture and fixtures. ... ..... 12% Cooley Milwaukee 3¢ Fare Case. 20 Starrett Milwaukee 3¢ Fare Case. 20 Mil. E. R. & L. Milwaukee 3¢ Fare Case. 20 Wis. R. R. Com Milwaukee 3¢ Fare Case. Gates and valves waterworks. ........0.0 40 Williams Galena Appraisal, Kan., 190s. water works............... 40-50 Metcalf Trans. Am. Soc. C. E., 1909. Gas Rolders...... 5.00 50 Wis. R. R. Com. Quoted by H. A. Foster. Governors gas plant... i). uu 0) 50 Wis. R. R. Com. Quoted by H. A. Foster. CONSUMETS. +vusuiuvenrsaas! 23 Wis. R. R. Com. Quoted by H. A. Foster. ABLES¢ 12 424 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. Hi oo Be hd | Authority. Remarks. Years Head gates oniditches... LLRs 30 S.J.L.&P. Cor. Cal. R.R. Com. rate hearing. Heaters (feed water) ......... 15 C. UT. Co. Chi. Union Trac. Co. Case. 20 Stone & Webs. Chi. Union Trac. Co. Case. 20 P. G.&E. Co. S. F. rate hearings, 1913-14. 16-25 Trac. Val. Com. Chicago Con. Trac. Co. Case. 15-30 Wis. R. R. Com Milwaukee 3¢ Fare Case. 30 Wis. R. R. Com Quoted by Henry Floy. 33% Arnold 4 Chicago Appraisals. Lamps ATCA i ah 63 Arbitrators Ata. St. Lgt. Controversy. ATC LAC Tai 12 5% Preece Report Bristol Corp., 1906. ATCA AE SLII Ls Sl 12% St. L. P. S.C. Union Elec. L. & P. Co. Case. arc un ni LTS P. G. & E. Co. S. F. rate hearings, 1913-14. BEC ER LA la 15 Wis. R. R. Com. Quoted by Henry Floy. Nernst. cL tu bhai 8-10 Foster “ Eng. Valuation,” etc. arc lamp posts. ............, 40 5% Preece Report Bristol Corp., 1906. Lighting systems incandescent street........ 15 P. G. & E. Co. S. F. rate hearings, 1913-14. arc (commercial & mun.).. 15 P. G. & E. Co. S. F. rate hearings, 1913-14. municipal street...........; 20 5% Cal. R. R. Com. Calis. E. C.vs. NapaVal.E. C. Lighting protection. ........... 10 P. G. & E. Co. S. F. rate hearings, 1913-14. 15 S.].L.&P. Cor. Cal. R.R. Com. rate hearing. 15-20 Foster “ Eng. Valuation,” etc. 10-12 Foster “ Eng. Valuation," etc. Machinery... iodine 27 6% Parsons Jour. Inst. Elec. E., 1907. engines and machinery... 25 6% Preece Report Bristol Corp., 1906. Meters electric, LL all 10 Hammond Jour. Inst. Elec. E., 1907. electric. (Liat Al iil, 12 29, Preece Report Bristol Corp., 1906. electric! fi. Jel de salah 12 59% Parsons Jour. Inst. Elec. E., 1907. electrict iia ve 32, 5 St... PS. C. Union Elec. L. &P. Co. Case. RleobTIC | Cd laine 15 P. G. & E. Co. S. F. rate hearings, 1913-14. electric il inet. 23.6 10% Cal. R. R. Com. Calis. E. C.vs.Napa Val.E. C. electric-switchboard. ...... 20 Wis. R. R. Com. Quoted by Henry Floy. electric Service. ...... out 15 Wis. R. R. Com. Quoted by Henry Floy. gas-station (drums).......1 20 Wis. R. R. Com. Quoted by H. A. Foster. gas-station (cases)......... 50 Wis. R. R. Com. Quoted by H. A. Foster. gAS-CONSUIMETS. ..«cuvneene- 25 Wis. R. R. Com Quoted by H. A. Foster. water. lal noob 20 Williams Galena Appraisal, Kan., 1905. Water! Lh dn i 20-30 Metcalf Trans. Am. Soc. C. E., 1909. water. . iu 50 Cal. R. R. Com. Cuyumaca W. Co. Case. POUND. Sie dats lls insinuate lets 10 Mil. E. R. & L. Milwaukee 3¢ Fare Case. 10 Cooley Milwaukee 3¢ Fare Case. 12.5 Starrett Milwaukee 3¢ Fare Case. 10-12.5 Wis. R. R. Com Milwaukee 3¢ Fare Case. 10-26 Stone & Webs. Chi. Union Trac. Co. Case. 10-25 Chi. U. T. Co: Chi. Union Trac. Co. Case. asphalt... Jol ee ey 10 Chi. U. T. Co. Chi. Union Trac. Co. Case. asphalt... lesser enisnn 10 Stone & Webs. Chi. Union Trac. Co. Case. TABLES i} TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. wig Revdual) Authority. Remarks. Years Paving (continued) asphalt, LL) lated 12 Wis. R. R. Com. Milwaukee E. R. & L. Case. brick... hn CTLs ne 12 Wis. R. R. Com Milwaukee E. R. & L. Case. cobble | oul i 25 Chi. U. T. Co. Chi. Union Trac. Co. Case. cobble, [Ca,L alls als 26 Stone & Webs. Chi. Union Trac. Co. Case. creosoted blocks........... 12 Wis. R. R. Com Milwaukee E. R. & L. Case. granite... 0 ga 16 Chi. U. T. Co. Chi. Union Trac. Co. Case. granite, oN on Ld 16 Stone & Webs. Chi. Union Trac. Co. Case. granite. ........ Liou oy Wis. R. R. Com. Mil. El. Ry. & Lt. Co. Case. Pipe water pipe: castiron................. ns Kiersted Galena Appraisal, Kan., 1905. cast fron. ls. Lil ial A es Williams Galena Appraisal, Kan., 1905. castiron... i... ....... 0 yon Burdick Mt. Vernon W. W., Ill., 1906. eastaron., lu lvl ron Dodge Mt. Vernon W. W., Ill., 1906. castro, LLL yon Alvord Proc. Am. W. W. Assoc., 1903. cast iron mains............ 50-75 Metcalf Trans. Am. Soc. C. E., 1909. cast iron mains............ 100 Cal. R. R. Com San Jose Water Co. Case, 1914. cast iron, small size........ 20-40 Metcalf Trans. Am. Soc. C. E., 1909. wrought iron. ......... 000 20 Kiersted Galena Appraisal, Kan., 190s. wrought jron.......... ... 20 Dodge Mt. Vernon W. W., Ill., 1906. wrought iron underground’ 30 Williams Galena Appraisal, Kan., 190s. wrought iron services...... 15-30 Metcalf Trans. Am. Soc. C. E., 1909. galv.wroughtironincl.fit's. 30-50 Foster ‘*“ Eng. Valuation,” etc. black w. iron and services, 25-35 Foster ** Eng. Valuation,” etc. steel pipe................. B25-50 Metcalf Trans. Am. Soc. C. E., 1909. Services... ol ol 20 Dodge Mt. Vernon W. W., Ill., 1906. wood-stave... lL ily 20-30 Metcalf Trans. Am. Soc. C. E., 19009. wood-stave.......... . 000 30 S.J.L.&P. Cor. Cal. R.R. Com. rate hearing, distributing system. ...... 16.5 Cal. R. R. Com Cuyumaca Water Co. Case. power-plant pen stocks... . 30 S.J]. L.&P. Cor. Cal. R. R. Com. rate hearing. gas pipe: w. i. & steel under3” diam. 20 Wis. R. R. Com. Quoted by H. A. Foster. w. iron & steel 3” and over 30 Wis. R. R. Com. Quoted by H. A. Foster. c. iron mains 3” & 4” diam. 50 Wis. R. R. Com Quoted by H. A. Foster. cast iron mains over 6”... 5 Wis. R. R. Com Quoted by H. A. Foster. Services. ..... lls Mon Wis. R. R. Com Quoted by H. A. Foster. miscellaneous: pipe and covering........ a I5 Chi. U. T. Co. Chi. Union Trac. Co. Case. pipe and covering. FPR Arnold Coney Isl. & Brooklyn Case. pipe and covering.........| 20 Stone & Webs. ~~ Chi. Union Trac. Co. Case. pipe and covering........." 20 Wis. R. R. Com Milwaukee 3¢ Fare Case. pipe and covering......... 20 Floy 3rd Ave. Case, N. Y. City. pipe and covering......... 28.5 Arnold 4 Chicago Appraisals. pipe and covering. ........ 22-25 Trac. Val. Com. Chicago Con. Trac. Co. Case. power stations............. 20 P. G.&E. Co. S.F. rate hearings, 1913-14. DOES, Sls bi 0 | % Chi. Tel. Com. Chicago Telephone Com. wooden... . 00 10 Arbitrators Ata. St. Lgt. Controversy, wooden, [0nd 13} Mil. E. R. & L. Milwaukee 3¢ Fare Case. wooden in earth. ......... 12-18 Wis. R. R. Com Quoted by Henry Floy. AZ 426 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. Ep Revidonl Authority. Remarks. Years Poles wooden in concrete........ 20 Wis. R. R. Com. Quoted by Henry Floy. cedar. lL Jl us hele ET | 167 ft. P. G. & E. Co. S. F. rate hearing 1913-14. cedar with cross arms..... I2 | 0% Wis. R. R. Com. Wisconsin Tel. Co. Case. cedar under 35’ long....... I0-I5 0% Tel. “Data” Quoted by H. A. Foster. cedar 35’ long and over.... 15-20 0% Tel. “ Data” Quoted by H. A. Foster. cedarinearth............. 10-18 Foster ‘ Eng. Valuation,” etc. cedar in concrete. ......... 12-20 Foster *“ Eng. Valuation,” etc. chestnut under 35’ long.... 8-12 Tel. Data” Quoted by H. A. Foster. chestnut 35’ and over...... I2-1I5 Tel. * Data” Quoted by H. A. Foster. pine-creosoted.............. 20 Tel. Data’ Quoted by H. A. Foster. FeGwOod.. iu asin tes navel 10 BiOf-z5g LP. G. & E. Co. S. F. rate hearing, 1913-14. LELOPIONR. vis vs 9s 55 0k =o REET] Wis. R. R. Com Quoted by H. A. Foster. telephone cross arms. .....| 8-12 Wis. R. R. Com. Quoted by H. A. Foster. average exchange.......... 10 0% Tel. “Data” Quoted by H. A. Foster. average toll... LLL 15 0% Tel. “Data” Quoted by H. A. Foster. ATROTY d eehule he adnate tibet une 20 Chi... -iCo. Chi. Union Trac. Co. Case. TOOT 4a af ela tare ales to Joule nis skal ete 40 Wis. R. R. Com Milwaukee 3¢ Fare Case. FTO lls lal ieteiale atatati tis mints EAC Arnold 4 Chicago Appraisals. Steel. on sa RA a EE SO Floy ard Ave. Case, N. Y. City Power plant equipment. ...... 12} Cooley Milwaukee 3¢ Fare Case. 20 Starrett Milwaukee 3¢ Fare Case. 21.0X Wis. R. R. Com Milwaukee 3¢ Fare Case. I I AE 15 St. [LiP.'S. C. Union Elec. L. & P. Co. Case. 20 Floy ard Ave. Case, N. Y. City. 20 Trac. Val. Com. Chi. Con. Trac. Co. Case. 20 Arnold Coney Isl. & Brooklyn Case. 20 Arnold 4 Chicago Appraisals. 20 Arbitrators Ata. St. Ltg. Controversy. 21.3 Alvord Proc. Am. W. W. Assoc., 1903. 22 Rosecrans Galena Appraisal, Kan., 1905. 25 Hammond Jour. Inst. Elec. E., 1907. 25 6% Preece Report Bristol Corp., 1906. 25-30 Williams Galena Appraisal, Kan., 1905. 30 Kiersted Galena Appraisal, Kan., 1905. 30 Burdick Mt. Vernon W. W., Ill., 1906. 40 Dodge Mt. Vernon W. W., Ill., 1906. and auxiliary machinery.. 20-30 Metcalf Trans. Am. Soc. C. E., 1909. and condensers............| I5-25 Wis. R. R. Com. Milwaukee 3¢ Fare Case. small steam...............| IS Wis. R. R. Com. Quoted by Henry Floy. general service.............1 16 | 5% P.G.&E. Co. S. F. rate hearings, 1913-14. centrifugal ou ties ioe nies 16 5% D.G.&E.Co. S.F.rate hearings, 1913-14. centrifugal ............... 20-30 Foster ‘Eng. Valuation," etc. geared pOWer.......:..... 20-30 Foster ‘“ Eng. Valuation,” etc. Botler feed... is al der ET 520 Foster “Eng. Valuation,” etc. of] Lr CS dtr 16 | 5% P.G.&E. Co. S. F. rate hearings, 1913-14. Purifiers gas—modern.......oeenn- 50 Wis. R. R. Com Quoted by H. A. Foster. ReServoirs. ......oovaveesess. 50-I00: Metcalf Trans. Am. Soc. C. E., 1909. 100 Burdick Mt. Vernon W. W., Ill., 1906. 1 3 / TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. Rapect] Residual, pythority, Remarks. Years Reservoirs (continued) €aTtheN «oii ives EI00 Cal. R. R. Com. Cuyumaca Water Co. Case. Retort house BOOMS... vas ii sis vis sir niv en BIS=30 Wis. R. R. Com Quoted by H. A. Foster. Rolling stock street railway............. 12.5 Cooley Milwaukee 3¢ Fare Case. street railway............. 16.7 Starrett Milwaukee 3¢ Fare Case. street railway............. 15-20 Wis. R. R. Com Milwaukee 3¢ Fare Case. ratlroad. . v.80 via 28 Gillette Gt. Nor. & N. P. Appraisal. railroad locomotives....... 20-35 Wilgus Lehigh Val. R. R. App. railroad passenger cars..... 35-40 30-40% Wilgus Lehigh Val. R. R. App. railroad freight cars........ 30-50 25% Wilgus Lehigh Val. R. R. App. street railway cars......... 30 Arnold Coney Isl. & Brooklyn Case. street railway bodies. ..... 15 Wis. R. R. Com Milwaukee 3¢ Fare Case. street railway open bodies. 25 Trac. Val. Com. Chi. Con. Trac. Co. Case. street ry. closed bodies... . 20 Trac. Val. Com. Chi. Con. Trac. Co. Case. street ry. bodies and trucks 13.3 M.E.R.&L. Co Milwaukee 3¢ Fare Case. street ry. bodies and wi 20 Chi. U. T. Co. Chi. Union Trac. Co. Case. street ry. bodies and trucks’ 20 Stone & Webs. Chi. Union Trac. Co. Case. street railway trucks...... 15-20 Wis. R. R. Com Milwaukee 3¢ Fare Case. street railway trucks...... 30 Trac. Val. Com. Chi. Con. Trac. Co. Case. street railway trucks...... 30 Arnold Coney Isl. & Brooklyn Case. street railway elec. equip. . 10 M.E.R.&L.Co. Milwaukee 3¢ Fare Case. street railway elec. equip.. 12-15 Chi. U. T. Co. Chi. Union Trac. Co. Case. street railway elec. equip.. 12-15 Stone & Webs. Chi. Union Trac. Co. Case. street railway elec. equip.. 10-20 Wis. R. R. Com Milwaukee 3¢ Fare Case. st. ry. fenders and registers 15 Wis. R. R. Com Milwaukee 3¢ Fare Case. Scrubbers and condensers. . . . . 30 Wis. R. R. Com. Quoted by H. A. Foster. Services (electric)........... 15 P. G.& E. Co. S. F. rate hearings, 1913-14. 20 S.J. L.&P. Cor. Cal. R.R. Com. rate hearing, 21.6 30% Cal. R. R. Com. Calis. E. Co. s. Napa Val. E.C. Snowsheds (R. R.)........... 25 Gillette Gt. Nor. & N. P. Appraisal. Stacks Brick... oii iis 33 Trac. Val. Com. Chi. Con. Trac. Co. Case. LT REE RL AT 33.3 Floy 4 Chicago Appraisals. steel... c. viodarda a pa 12 P. G. & E. Co. S. F. rate hearings, 1913-14. steel... dade BR Td 2 Floy 4 Chicago Appraisals. Sand Pipes. ..visveivauinin 25 Rosecrans Galena Appraisal, Kan., 1905. 30 Kiersted Galena Appraisal, Kan., 1905. 40 Williams Galena Appraisal, Kan., 1905. 25-40 Metcalf Trans. Am. Soc. C. E., 1909. Station buildings and R. R. SHUCIUYES . ...onvivive sins BRIO Cal. R. R. Com. Stockton Term & East Case. Steam vessels on Great Lakes............| 40 15% Wilgus Lehigh Val. R. R. Appraisal. on tide water..............| 32 | 15% Wilgus Lehigh Val. R. R. Appraisal. Stokers Bxed parts....... uc... ven “ry Trac. Val. Com. Chi. Con. Trac. Co. Case. MOVING parts. ......... Trac. Val. Com. Chi. Con. Trac. Co. Case. ~ABLEf 42" 428 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. Epoch Residual) Authority. Remarks. Years = Storage batteries. ............ 10 M.E.R.&L.Co Milwaukee 3¢ Fare Case. 10 Wis. R. R. Com Milwaukee 3¢ Fare Case. 12.5 6% P.G.&E. Co. S.F.rate hearings, 1913-14. 15 5% Wis. R. R. Com. Wisconsin Tel. Co. Case. 15 Chi. U./T. Co. Chi. Union Trac. Co. Case. 20 Stone & Webs. Chi. Union Trac. Co. Case. 20 St. Louis P. S. C. Union Elec. L. &P. Co. Case. 20 Floy ard Ave. Case, N. Y. City. Sub-station equipment. ....... 20 S.J. L.&P. Cor. Cal. R.R. Com. rate hearing. Z5 Preece Report Bristol Corp., 1906. 50 Cal. R. R. Com. Calis. E. C. vs. Napa Val E. C. Sum ps and wells at gas plant... LLL LEE 30 P.G.&E. Co. S.F. rate hearings, 1913-14. tar and ammonia. ........ 50 Wis. R. R. Com. Quoted by H. A. Foster. Surge tank concrete’... . avu d del I 30 S.J. L.& P. Co. Cal. R.R. Com. rate hearing. Superheaters..:... vedas 20 P.G.&E. Co. S.F. rate hearings, 1913-14. Switchboards. ......coevinnn 12} St. L. P.S. C. Union Elec. L. & P. Co. Case. 15 Chi. U.!T. Co. Chi. Union Trac. Co. Case. 16.7 Arnold Coney Isl. & Brooklyn Case. 20 Stone & Webs. Chi. Union Trac. Co. Case. 20 M.E.R.&L.Co Milwaukee 3¢ Fare Case. 20 Floy 3rd Ave. Case, N. Y. City. 20 P. G.&E. Co. S.F. rate hearings, 1913-14. 20 Hammond Jour. Inst. Elec. E., 1907. 15-20 S.J. L. & P. Co. Cal. R. R. Com. rate hearing. 15-20 Wis. R. R. Com Milwaukee 3¢ Fare Case. 33.3 Trac. Val. Com. Chi. Con. Trac. Co. Case. 50 Arnold 4 Chicago Appraisals. 50 Chi. Trac. Com. Quoted by G. W. Cravens. 50 Wis. R. R. Com. Quoted by G. W. Cravens. telephone, central. ........j 8 20% Chi. Tel. Com. Chicago Telephone Com. telephone, central. ....... | 8-10 15% Tel. * Data” Quoted by H. A. Foster. telephone, central. ........, 12 20% Wis. R. R. Com. Wisconsin Tel. Co. Case. telephone P. B. X......... 8 20% Chi. Tel. Com. Chicago Telephone Com. telephone P. B. X........ | 10 10% Tel. * Data” Quoted by H. A. Foster. telephone P. B. X......... 10 15% Wis. R. R. Com Wisconsin Tel. Co. Case. Systems and plants electric light and power.... 17.46 Wis. R. R. Com. Fon du Lac W. Co. Case aver. 6 plants. electric light and power.... 18 | Wis. R. R. Com Madison Gas & E. Co. Case. electric light and power.... 20 Mass. G. & E. Mass. Gas & Elec. Com. Com. electric light and power.... 20-25 Wis. R. R. Com. Jefferson Mun. E. L. & w. plant. electric light and power.... 22.0 P. G. & E. Co. S. F. rate hearing, 1913-14. electric railway............ 18.02 Wis. R. R. Com Fon du Lac W. Co. Caseaver. 7 plants. electric railway............ 18.6 Wis. R. R. Com Milwaukee 3¢ Fare Case. TABLES TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. Expo: Residual Authority. Remarks. Years Systems and plants (con.) electric railway............ 19.8 Wis. R. R. Com Duluth St. Ry. Co. Case. telephone.............v. «x. 10-25 Wis. R. R. Com. Oregon Telephone Co. Case. telephone..................| 14-15 Wis. R. R. Com Various cases in 1912-13. water supply.............. 50-65 Wis. R. R. Com Various cases in 1910-11. overhead system.........., 33% 35% Cal. R. R. Com Calis. E.C.s. NapaVal.E.C. st. ry. distrib. system.... | 12} Cooley Milwaukee 3¢ Fare Case. 14 Starrett Milwaukee 3¢ Fare Case. st. ry. distrib. & trans. sys. 30.03 Wis. R. R. Com Milwaukee 3¢ Fare Case. Tanks wooden... .... AL nae 12 P. G. & E. Co. S. F. rate hearings, 1913-14. Steel... ......... 0 30 P.G.&E. Co. S. F. rate hearings, 1913-14. Tar extractors P.& A. 0Gn1 GEE do Wis. R. R. Com. Quoted by H. A. Foster. Telephone equipment Street railway............. 10-12 Wis. R. R. Com. Milwaukee 3¢ Fare Case. Street railway............... 13.3 Mil. E. R. & L. Milwaukee 3¢ Fare Case. electric power plants.......| 12 P.G.& E. Co. S. F. rate hearings, 1913-74. elec. power plant lines. .... 20 S.J. L.&P. Cor Cal. R. R. Com. rate hearing. elec. power plant instrum’ts 20 S.J. L.&P. Cor Cal. R. R. Com. rate hearing. elec. power plant equipm’t. 8-14 S.J. L.&P. Cor. Cal. R. R. Com. rate hearing. farmersline. ....... i os. 15 Wis. R. R. Com Wautoma & Mt. Morris Tel, Line. subscribers instruments. . 8-10 10% Tel. * Data” Quoted by H. A. Foster. 10 5% Chi. Tel. Com. Chicago Tel. Commission. 10 5% Wis. R. R. Com Wisconsin Tel. Co. Case. telephone drop wires...... 8 15% Chi. Tel. Com. Chicago Tel. Commission. Testing instruments gleetrici. i. dol tol 10 20% Cal. R. R. Com Calis. E. C. vs. Napa Val. E. Co. Tools and shop machinery.... 5-25 Wis. R. R. Com Milwaukee 3¢ Fare Case. 12% Cooley Milwaukee 5¢ Fare Case. 14.2 Starrett Milwaukee 3¢ Fare Case. 13.3 Mil. E. R. & L. Milwaukee 3¢ Fare Case. 20 Chi. U. T. Co. Chi. Union Trac. Co. Case. 20 Stone & Webs. Chi. Union Trac. Co. Case tools, teams and furniture 4 10% Chi. Tel. Com. Chicago Telephone Com. tools and furniture........ 7 Wis. R. R. Com Quoted by H. A. Foster. tools and sundries......... 10 5% Preece Report Bristol Corp., 1906. Track rails, ties and bonding...... 12} Wis. R. R. Com Milwaukee 3¢ Fare Case. rails, ties and bonding..... 12} Cooley Milwaukee 3¢ Fare Case. rails, ties and bonding. ... 12} Starrett Milwaukee 3¢ Fare Case. rails, ties and bonding. ... 12.85 Chi. U. T. Co. Chi. Union Trac. Co. Case. rails, ties and bonding..... 13.86 Stone & Webs. Chi. Union Trac. Co. Case. rails, ties and bonding..... 13.33 Mil. E. R. & L. Milwaukee 3¢ Fare Case. Straight... il 18 Wis. R. R. Com Quoted by Henry Floy. special work..............0 8.3" Mil. E. R. & L. Milwaukee 3¢ Fare Case. Special work............... 10 Arnold 4 Chicago Appraisals. special work.............../BY2 Wis. R. R. Com. Quoted by Henry Floy. a 420 430 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Continued) Description. Bo Bestar Authority. Remarks. Track (continued) special work............... 12.85 Chi. UU. T-iCo- Chi. Union Trac. Co. Case. special work............... 13.86 Stone & Webs. Chi. Union Trac. Co. Case. EGR Sa Saba ata val ct Tea et 20 Trac. Val. Com. Chi. Con. Trac. Co. Case. railroad rails, new.........} 25 26% Cal. R. R. Com Stockton Term. & East. Case. railroad rails, relay ........ 15 48% Cal. R. R. Com. Stockton Term. & East. Case. R. R. rails and track fast.. 40 Gillette Gt. Nor. & N. P. Appraisal. railroad track fastenings.. | 123 Cal. R. R. Com. Stockton Term.& East. Case. railroad ties... Lod ni ES Gillette Gt. Nor. and N. P. Appraisal. railroad ties, redwood.....1 16 Cal. R. R. Com. Stockton Term.& East. Case. railroad ties, creosoted....., 19.35 O. Chanute Houston & Texas Cent. R. R. trestles and bridges....... | Io Cal. R. R. Com. Stockton Term.& East. Case. ballast CTO Cal. R. R. Com. Stockton Term. & East. Case. frogs and switches........., 25 367% Cal. R. R. Com. Stockton Term. & East. Case. cast-iron culverts.......... 16 Cal. R. R. Com. Stockton Term.& East. Case. Transformers... sisi sioioe iene 15 St. L. P. S.C. Union Elec. L. & P. Co. Case. 15 Wis. R. R. Com. Quoted by Henry Floy. station SETVice............. 20 Wis. R. R. Com. Quoted by Henry Floy. SEALION ale «ins Satan iete xis a hates 25 S.J. L.&P. Cor. Cal. R.R. Com. rate hearing. line. hl aia, he 20 10% Cal. R. R. Com. Calis. E. C. vs. Napa Val. E. Co. distribution... Lil. | 20 ($r.00kw. P. G. &E. Co. S. F. rate hearings, 1913-14. DOWELL tol byob leh ll oe 20 $ .50kw. P.G.&E. Co. S. F. rate hearings, 1913-14. static transformers. ....... 15 Hammond Jour. Inst. E. E., 1907. Tunnels powerplants. i... 0... LLL E50 S.J. L.&P. Cor. Cal. R.R. Com. rate hearing. Turbines SLEATTY | aleve halos lateretd oe JEERYS St. 1. P.:S.\C. Union Elec. L. & P. Co. Case. Shennan Sa es 20 Wis. R. R. Com. Quoted by Henry Floy. SEEATL a eale Tel otal] 20 Hammond Jour. Inst. Elec. E., 1907. LRAT Le ol le tebar el ainiale ata lates 30 1¢1b. P.G.&E. Co. S. F. rate hearings, 1913-14. VAULT nl sin a ae aia mol tal wa 30 Wis. R. R. Com. Quoted by Henry Floy. water-type prior 1900. ..... 25-40 Foster ‘“ Eng. Valuation,’ etc. water-type after 1900....... 30-50 Foster ‘ Eng. Valuation," etc. Washers (gas plant) CARLTON tals ae fr etal 40 Wis. R. R. Com. Quoted by H. A. Foster. Water gas machines. .......... 30 Wis. R. R. Com. Quoted by H. A. Foster. Watt meters SETVICE lv ool le di diatetiln tara ata tere MIT O=T5 Foster ‘“ Eng. Valuation,’ etc. Wells ; WALE «et ais aia dntora 30 S.J]. L..& P..Cor. Cal. R. R. Com. rate hearing. water, driven or drilled... 50-75 Foster ‘ Eng. Valuation,” etc. water, large open masonry. 75-100! Foster “Eng. Valuation,” etc. water well pumps.......... 10 S.].L.&P. Cor. Cal.R.R.Com.rate hearings. gas wells. Lire a0 0 LLL TO 0% Cal. R. R. Com. Midway Gas Co. et al. Case. gas well drilling equip... .. 10 25% Cal. R. R. Com. Midway Gas Co. et al. Case. Wharves and docks. ........... 33% Gillette Gt. Nor. & N. P. Appraisal. Wire BETIAY viet timate tot 20 St. .L.P. S.C. Union Elec. L. & P. Co. Case. Serial COPDET a ve oir sieininivi sins 15 Chi. Tel. Com. Chicago Telephone Com. Te J 1 TABLE 30. THE PROBABLE USEFUL LIFE OF VARIOUS ARTICLES (Concluded) Description. Pape Residual Authority. Remarks. Years Wire (continued) Bare... ise se dc ee ra IS 35% P.G.&E. Co. S.PF. rate hearings, 1913-14. insulated. co iianidl dl ud, 20 15% P.G.& E. Co. 8S. F. rate hearings, 1913-14. copper, weatherproof....... 13 Arbitrators Ata. St. Lgt. Controversy. copper, weatherproof....... 16 Wis. R. R. Com. Quoted by Henry Floy. copper, weatherproof....... I10-I5 Foster ‘“ Eng. Valuation,” etc. 2-kv. distribution......... 15 S.J]. L. &P. Cor. Cal. R. R. Com. rate hearing. 4-kv. distribution. ........| 15 S.J.L.&P. Cor. Cal. R. R. Com. rate hearing. 10-kv. distribution........| 20 S.J. L.&P. Cor Cal. R. R. Com. rate hearing, telephone, iron........... | 10 0% Wis. R. R. Com Wisconsin Tel. Co. Case. telephone, iron............| 8-15 Wis. R. R. Com. Quoted by H. A. Foster. telephone, weatherproof, fron. id die ii dR X85 Wis. R. R. Com. Quoted by H. A. Foster. telephone, copper. ........ 20 75% Wis. R. R. Com Wisconsin Tel. Co. Case. telephone exch., bare copper! 10-15 40% Tel. * Data” Quoted by H. A. Foster. telephone exch., insul. cop. 10 10% Tel. *“ Data” Quoted by H. A. Foster. telephone exch., bare iron. 8-10 o% Tel. * Data ™ Quoted by H. A. Foster. telephone toll, bare copper. 40 49% Tel. * Data” Quoted by H. A. Foster. telephone toll, bare iron. .. 15 % Tel. * Data” Quoted by H. A. Foster. telephone, distribution..... 10 15% Wis. R. R. Com. Wisconsin Tel. Co. Case. ABLES 43 432 VALUATION, DEPRECIATION AND THE RATE-BASE EXPLANATION OF TABLE 31 EXPECTANCY AND REMAINING VALUE Ari ARTICLES AssuMeED 70 Fam WitEIN A TERM EQUAL TO TWICE THEIR ORIGINAL EXPECTANCY (Approximate Values Only) The expectancy of any article in use, which is still in service- able condition, can be approximated from the following tables, when the probable life new of other articles of the same class is known. There is noted in these tables also the approximate remaining value, although this may also be obtained from the Amortization or Depreciation Table 33 by entering the same with the years of expectancy as elsewhere explained. The ex- pectancy noted in Table 31 is based on a reasonable assumption of the rate at which a large number of articles of the same prob- able life would go out of use (see Chapter VI)* and is in fair accord with the expectancy that would be found if all the articles were assumed to fail according to the law of probabilities within a period equal to twice the probable life term. The strict appli- cation of the law of probability under assumptions, relating not only to the probable life of any article in question, but also to the probability of survivals beyond some period, as, for ex- ample, twice the probable life, would be an unnecessary refine- ment not justified until a vastly greater mass of data than now available, relating to actual life of individual articles in each class, has been assembled. It may be claimed for this table in its present form that it will afford means of making much closer approximation to the actual remaining worth of any article than is possible by the use of the ordinary amortization tables in which age alone is taken into account and in which no distinction is made between actual and probable life. In this table the expectancy and remaining value are noted for any single article, whose probable life when new is known. The table has been computed for 4 per cent, 5 per cent, 6 per cent and 7 per cent interest per annum. For other interest rates, values may be interpolated. * Page 104 of “Valuation, Depreciation and the Rate-Base.” TABLES 433 In Tables 4 to 7, Chapter VL* the annual replacement re- quirement is noted for groups of numerous articles, all of the same probable life new. These tables cover the two cases of a plant which has attained its full growth and of a plant to which a uniform annual addition is being made. The annual replace- ment requirement is based on the probable annual number of failures. Similar tables can readily be prepared for other terms of usefulness than 5, 10 and 20 years covered by these tables and for any other hypothesis of the rate at which actual failures will take place. All figures noted in Tables 4 to 61 and in Table 31 are approx- imation figures derived from smoothed-out curves. They are, in fact, modifications of the values which were obtained as a result of the assumption already fully discussed that failures among any large group of articles will be greatest in number at or near the end of the probable life term, that practically no articles will survive twice the probable life term, and that there will be a uniform increase in the annual rate of failures from the beginning to the year of maximum number of failures and that the decrease in the number of annual failures will follow a similar law. To find the expectancy of any perishable article which has a probable life term new of # years, not covered by any of the subdivisions of the table here published, the ten-year life sub- division of Table 31 may be called to aid. Let e = the expectancy which is to be determined, m = the age of the article, n = the probable life new of the article, m’ = the relative age of an article whose probable life new was 10 vears such that ;. 4] 130. ZL = mr (31) Let ¢’ = the relative expectancy at the age m’ of an article whose probable life new was 10 years. * Page 104 of “Valuation, Depreciation and the Rate-Base.” t See pages 112-114 of “Valuation, Depreciation and the Rate-Base.” AT = 434 VALUATION, DEPRECIATION AND THE RATE-BASE Then the expectancy to be determined will be found from ne’ £i= (32) Example. — What is the expectancy of an article 8 years old, in fair condition, whose probable life new was 12 years? Here n = 12 and m = 8. 8 m = el 6.67. 12 For the age 6.67 years in the ten-year subdivision of Table 31 (this being in the seventh year) the expectancy 5.17 years is found by interpolation. The required expectancy is, therefore, — 517 X= =6 e = 5.17 X — = 06.2 years, which would be found in a twelve-year probable life table for the end of the eighth year or for the beginning of the ninth year. For general use the following formula are recommended which will be found to agree fairly well with the results presented in Table 31. They are applicable to any probable life term and any age to the limit beyond which the assumption is justified that no article will continue in service. When the age of an article is less than its probable life term new, that is, when m < n m2 ¢ =~ 003m + o30-". (33) When the age of an article is greater than its probable life term new, that is, when m > #» e =0.72% — 0.35 M. (34) Example. — What is the expectancy of an article whose probable term of usefulness when new was 12 years, which is 8 years old and apparently in good condition? Here n = 12 and m = 8. TAFLES By equation (33) € = 12 — 7.44 + 1.60 = 6.16 years. Example. — What is the expectancy of a similar article 1 5 years old, which has survived its probable term of usefulness but is still in service and in good condition? Here n = 12 and m = 13. By equation (34) e = 8.64 — 5.25 = 3.39 years. Example. — What is the expectancy of an article 40 years old, whose probable life new was 60 years and which is in good condition? Here n = 60 and m = 4o. By equation (33) e = 60 — 37.20 + 8.00 = 30.80 years. To find the remaining value of an original investment of $100 in any article or the accrued depreciation when the expectancy of the article is known and the probable life new is different from any covered by the tables here published, proceed as follows: Find the annuity which in # years will amount to $100. From tables, such as Tables 26 and 28 in this volume, or by calculation, find the amount of this annuity for (# — e) years. This amount will represent the accrued depreciation and $100 less this amount will be the remaining value of an original investment. Example. — What is the remaining value (6 per cent interest) of an article which cost $100, whose probable life new was 12 years, which is 8 years old and which is still in fair condition? The expectancy of this article as shown in a preceding example is about 6.2 years. The annuity which in 12 years at 6 per cent will amount to $100 is $5.93; this annuity in (12 — 6.2) years amounts to $40.44, the accrued depreciation. The present worth will be $100 — $40.44 = $359.56. By use of the ten- and fifteen-year subdivisions of the table and interpolation the procedure would be as follows: £2 435 436 VALUATION, DEPRECIATION AND THE RATE-BASE Eight years in a twelve-year probable life table is fairly com- parable with 6.67 years in a ten-year table and with 10 years in a fifteen-year table. Remaining value (at 6 per cent): For age 6.67 years from the ten-year table........... .... . $58.80 For age 10 years from the fifteen-year table................ _62.30 Difference... LLL coll LLL ad tc S12 SO or approximately 58.80 + 2 X 3.50 = $60.20. It remains to be noted that when remaining value is to be determined age may be entirely disregarded when expectancy can be ascertained by an inspection of the article in question. The condition of the article and all other circumstances affecting its serviceability being taken into consideration its probable remaining term of service or its expectancy is estimated. In this case it will be more convenient to use Table 33 than Table 31. Select the subdivision of Table 33, corresponding with the probable life new of the article, and use only the headings of the columns at the bottom of the page. For the expectancy noted in the right-hand column, the remaining value and the accrued depreciation will be found in their respective columns. Inter- polation may be resorted to for fractional years if this refinement be thought desirable. Because expectancy in the case of individualized articles which have been long in use can best be determined by inspection and by a consideration of local circumstances affecting continued serviceability, it has been thought sufficient to note values in the long-term subdivisions of Table 31 and for articles long in service only for every fifth or every tenth year. To find the current depreciation of any single article in any year by the use of Table 31 subtract from its remaining value at the beginning of that year the remaining value at the begin- ning of the following year. Example. — What is the current depreciation in the sixth year, at 6 per cent interest, of an article whose probable life is 15 years? Remaining value at the beginning of the sixth year........... $76.90 Remaining value at the beginning of the seventh year......... 2.60 Depreciation in the sixth year........ $4.30 TABLES +o / TABLE 3:1. EXPECTANCY AND REMAINING VALUE OF ANY ARTICLE WHOSE REPLACEMENT COST IS $100 All values in this table are based on the assumption that in a group of many articles, no article will survive twice its probable life and that the number of annual failures will increase at a uniform rate to a maximum at the end of the probable life term and will thereupon decrease at a uni- form rate. PROBABLE LIFE 5 YEARS 5 YEARS 5 YEARS Remaining value. Beginning Expectancy Ol vear. years. 4 per cent per 5 per cent per 6 per cent per 7 per cent per annum. annum. annum. annum. 5.00 $100.00 $100.00 $100.00 $100.00 4.15 84.30 84.60 84.90 85.20 3.40 70.00 70.50 | 71.00 71.50 2.75 57.30 57.90 58.40 59.00 “ 2.23 47.40 47.90 48.50 49.10 1.85 39.30 39.80 40.30 40.90 1.55 33.00 33.50 34.00 34.50 1.25 26.80 27.20 27.60 28.00 1.00 21.60 22.00 22.40 22.80 PROBABLE LIFE 10 YEARS 10 YEARS 10 YEARS T 10.00 100.00 100.00 100.00 100.00 9.10 92.50 92.90 93.20 93.50 8.25 85.20 | 85.80 86.40 | 87.00 7.50 78.50 79.30 80.10 81.00 6.80 72.10 73.10 74.00 75.00 : 6.10 65.60 66.70 67.70 68.80 5.50 59.90 60.90 62.00 63.10 5.00 54.90 56.10 57.20 58.40 : 4.50 49.80 51.00 52.20 53.30 10 4.10 45.90 46.90 48.10 49.20 II 3.70 41.60 42.70 43.90 45.00 12 3.35 37-90 | 39.00 40.10 41.20 1g 3.00 34.20 35.30 36.30 37.40 11 2.63 30.40 31.40 32.30 33.30 15 2.30 26.50 27.40 28.30 29.30 16 2.00 23.3008: 24.10 24.90 25.70 ry 1.63 19.50 20.20 20.90 21.60 18 1.33 15.70 | 16.30 16.90 17.50 19 1.00 11.90 12.30 12.80 12.20 AQ 438 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 31. EXPECTANCY AND REMAINING VALUE OF ANY ARTICLE WHOSE REPLACEMENT COST IS $100 (Continued) PROBABLE LIFE 15 YEARS 15 YEARS 15 YEARS Remaining value. Beginning Expectancy ; of year. years. 4 per cent per 5 per cent per 6 per cent per 4 per cent per annum. annum. annum. annum. 15.00 $100.00 $100.00 $100.00 $100.00 14.10 95.50 95.80 96.10 96.40 13.20 90.90 91.50 92.10 92.60 12.40 86.60 87.40 88.30 89.00 = 11.65 82.40 83.50 84.50 85.50 10.90 78.20 79.50 80.70 81.80 10.15 73.90 75.30 | 76.70 78.00 9.45 69.60 71.10 72.60 74.00 “ 8.85 65.90 67.50 69.10 70.60 10 8.25 62.10 63.80 65.50 67.10 II ES 58.90 60.60 62.30 64.00 12 wi. 2% 55.60 57.40 59.I0 60.80 13 6.75 52.30 54.00 55.80 57.50 14 6.30 49.20 5I.00 52.70 54.40 16 5.90 46.40 48.20 49.90 51.60 16 5.55 44.00 45.708 47 .40 49.10 17 5.20 AI.50 43.20 44.80 46.50 18 4.85 38.90 40.60 42.20 43.80 19 4.50 36.40 37.90 39.50 41.10 20 4.15 33.70 35.30 36.80 38.40 21 3.80 31.10 32.60 34.00 35.50 22 3-45 28.40 29.80 31.20 32.60 23 3.10 25.70 27.00 28.30 29.60 24 2.75 22.90 24.20 25.40 26.60 26 2.40 20.20 21.20 22.30 23.40 26 2.05 17.40 18.30 19.30 20.30 27 1.70 14.50 15.30 16.10 17.00 28 v.35 11.60 12.20 12.90 13.60 29 1.00 8.60 9.20 9.70 10.30 TABLES 439 TABLE 31. EXPECTANCY AND REMAINING VALUE OF ANY ARTICLE WHOSE REPLACEMENT COST IS $100 (Continued) PROBABLE LIFE 20 YEARS 20 YEARS 20 YEARS Remaining value. Beginning Expectancy of vear. years. 4 per cent per 5 per cent per 6 per cent per 7 per cent per annum. annum. annum. annum. 20.00 $100.00 $100.00 $100.00 $100.00 19.10 97.00 97.30 97.60 97.80 18.20 93.90 94.40 95.00 95.50 : 17.33 90.80 91.60 92.40 93.10 16.50 87.60 88.70 89.70 90.70 15.75 84.80 86.10 87.30 88.40 15.00 81.80 83.30 84.70 86.00 14.30 79.00 80.60 82.10 83.60 13.60 76.00 77.80 76.50 81.10 10 12.90 73.00 75.00 76.80 78.50 II 12.20 69.90 72.00 73.90 75.80 ¥3 11.60 67.20 69.30 71.40 73.30 v3 I1.00 64.50 66.70 68.80 70.80 14 10.50 62.10 64.30 66.350 68.50 156 10.00 59.70 62.00 64.20 66.30 16 9.50 57.20 59.50 61.70 63.90 i7 9.00 54.70 57.00 59.30 61.50 13 8.60 52.60 55.00 57.20 59.40 19 8.20 50.60 52.90 55.20 57.40 20 7.80 48.50 50.80 53.00 55.30 21 7.40 46.30 48.60 50.90 53.10 22 7.00 44.20 46.40 48.70 50.90 22 6.60 41.90 44.20 46.40 48.50 74 6.25 40.00 42.20 44.30 46.50 2b 5.90 38.00 40.10 42.30 44.40 26 5.53 36.00 38.00 40.10 42.20 27 5.20 33.90 35.90 38.00 40.00 28 4.85 31.90 33.90 35.80 37.70 2Q 4.50 29.70 31.60 33.50 35.30 30 4.15 27.60 29.40 31.20 33.00 31 3.80 25.40 27.10 28.80 30.50 22 3.45 23.30 24.80 26.40 28.00 23 3.10 21.10 22.50 24.00 25.50 24 2.75 18.80 20.10 21.50 22.90 35 2.40 16.50 17.70 18.90 20.20 36 2.05 14.20 15.30 16.40 17.50 #1 1.70 11.80 12.70 13.70 14.60 : 1.35 9.50 10.20 11.00 11.70 23 1.00 7.10 7.60 8.20 8 Ro 4 440 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 31. EXPECTANCY AND REMAINING VALUE OF ANY ARTICLE WHOSE REPLACEMENT COST IS $100 (Continued) ProBABLE LIFE 25 Years 25 YEARS 25 YEARS Remaining value. Beginning Expectancy _ of year. years. 4 per cent per 5 per cent per 6 per cent per 7 per cent per annum. annum. annum. annuin. 25.00 $100.00 $100.00 $100.00 $100.00 24.10 97.80 98.10 98.40 98.60 | 23.20 95.60 96.10 | 96.60 97.10 ; 22.30 93.30 94.10 94.80 95.40 5 21.45 91.00 92.00 92.90 93.80 6 | 20.60 88.70 90.00 91.10 92.10 7 19.80 86.40 87.90 | 89.20 90.50 3 19.05 84.20 85.90 87.40 88.80 9 18.30 81.90 83.80 85.50 87.20 10 | 17.60 79.80 81.80 83.60 85.30 11 16.90 77.60 79.70 81.70 83.50 12 16.20 75.20 77.50 79.60 81.60 13 15.55 73.00 75.45 | 77.70 79.80 14 14.90 70.80 73.30 75.60 77.80 16 14.30 68.70 71.20 73.70 76.00 16 13.75 66.70 69.30 71.90 74.20 17 | 13.20 6al90 8} 67.30 69.90 72.40 18 12.70 62.30 65.50 68.10 70.60 19 12.20 61.80 63.60 66.30 68.90 20 11.70 58.90 61.70 64.40 67.00 21 | 11.25 57.10 59.90 62.70 65.30 22 10.80 55.20 58.10 60.90 63.50 23 10.40 53.60 56.40 59.20 61.90 24 10.00 5I.90 54.80 57.60 60.30 2b 9.60 50.20 53.00 55.80 58.50 26 9.25 43.70% '% 5I.50 54.30 57.00 27 8.90 47.10 49.90 52.70 55.40 28 8.50 45.30 48.10 50.90 53.60 29 8.15 43.80 46.50 49.30 51.90 30 7.80 42.20 44.90 47.60 50.10 STE 7.40 40.30 43.00 45.60 48.20 36 5.60 31.50 33.90 36.30 38.60 41 3.80 22.10 24.00 25.90 27.80 46 2.05 12.40 13.50 14.70 15.90 49 1.00 6.20 6.80 7.40 8.00 TABLES na TABLE 31. EXPECTANCY AND REMAINING VALUE OF ANY ARTICLE WHOSE REPLACEMENT COST IS $100 (Continued) PROBABLE LIFE 30 YEARS 30 YEARS 30 YEARS Remaining value. Beginning ~~ Expectancy of vear. years. 4 per cent per 5 per cent per 6 per cent per 7 per cent per annum. annum. annum. annum. 30.00 $100.00 $100.00 $100.00 $100.00 29.10 98.40 98.60 98.90 99.00 28.20 96.70 97.20 97.70 | 98.00 27.30 95.00 95.80 96.40 97.00 b 26.45 93.30 94.30 95.20 95.90 25.60 91.60 92.80 93.80 94.70 24.80 89.90 91.30 92.50 93.60 24.00 88.20 89.80 91.20 92.40 ) 23.30 86.60 88.40 89.90 91.30 10 22.53 84.90 86.80 88.50 90.10 II 21.80 83.10 85.20 87.10 88.80 Iz 21.035 81.30 83.50 85.60 87.40 13 | 20.30 79.40 81.80 84.00 86.00 14 19.60 77.50 80.10 82.40 84.50 16 18.90 75.70 78.40 80.80 83.10 16 18.253 73.90 76.70 79.30 81.60 17 17.653 72.20 75.10 77.80 80.20 18 17.05 70.50 73.50 76.40 78.80 19 16.50 68.90 71.90 74.80 77 .40 20 15.95 67.20 70.40 73.30 76.00 21 15.40 65.50 68.70 71.770 74.50 22 14.90 64.00 67.20 70.30 73.10 23 14.40 62.40 65.70 68.70 71.70 24 13.95 60.90 64.20 67.40 70.30 25 13.50 59.40 62.70 65.90 68.90 26 13.05 57.60 60.90 64.50 67.50 27 12.60 56.50 59.70 62.90 66.00 28 12.20 55.00 58.40 61.60 64.70 29 11.80 53.60 56.90 60.20 63.30 30 11.45 52.30 55.70 58.90 62.00 31 | II.10 51.00 54.40 57.90 60.80 22 10.75 49.70 53.10 56.30 59.50 3 10.40 48.40 51.70 55.00 58.10 3 10.00 46.90 50.20 53.50 56.60 nd 442 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 31. EXPECTANCY AND REMAINING VALUE OF ANY ARTICLE WHOSE REPLACEMENT COST IS $100 (Continued) PROBABLE LIFE 30 YEARS 30 YEARS 30 YEARS Remaining value. Beginning Expectancy yea. years. 4 per cent per 5 per cent per 6 per cent per 7 per cent per annum. annum. annum. annum. 36 9.65 $45.50 $48.80 $52.10 $55.20 36 9.30 44.20 47 .40 50.60 53.70 37 8.95 42.80 46.00 49.20 52.30 38 8.55 41.20 44.30 47.50 50.50 39 8.20 39.70 42.90 46.00 49.00 40 7.95 38.30 41.40 44.40 47 .40 41 7.50 36.80 39.80 42.80 45.80 46 5.70 28.90 31.60 34.10 36.80 SE 3.90 20.50 22:60 24.60 26.70 50 2.10 11.40 12.70 13.90 15.20 59 1.00 5.60 6.20 6.90 7.50 PROBABLE LIFE 40 YEARS 40 YEARS 40 YEARS : 40.00 100.00 100.00 100.00 100.00 2 39.10 99.10 99.30 99.40 99.60 : 38.20 98.10 | 98.50 98.80 99.10 4 37.30 | 97.10 97.70 98.20 98.60 © 36.40 96.00 96.80 97.50 98.00 ‘ 35.50 94.90 95.90 96.80 ' 97.50 34.70 93.90 95.10 96.10 96.ga 33.90 92.90 94.30 95.40 96.40 L 32.10 91.80 93.40 94.70 95.80 10 32.30 90.70 92.50 93.90 95.10 II 31.50 89.60 91.50 93.10 94.40 12 30.75 88.50 go.60 92.30 93.80 13 30.00 87.40 89.60 91.50 93.10 19 29.30 86.30 88.60 90.70 |» 92.40 15 28.55 | 85.10 87.60 89.80 91.60 16 | 27.8 83.80 86.50 88.80 00.80 17 | 27.10 82.70 85.50 87.90 go .00 18 26.40 81.50 84.40 87.00 89.20 19 25.70 80.20 83.30 86.00 88.30 20 25.00 78.90 82.10 85.00 87.40 21 24.40 77.80 81.10 84.00 86.60 22 | 23.80 76.60 80.10 83.10 85.70 2% 23.20 75.50 79.00 82.10 84.90 24 22.60 74.20 747.90 81.10 83.90 TAL 5 443 TABLE 31. EXPECTANCY AND REMAINING VALUE OF ANY ARTICLE WHOSE REPLACEMENT COST IS $100 (Continued) PROBABLE LIFE 40 YEARS 40 YEARS 40 YEARS Remaining value. Beginning Expectancy of year. years, 4 per cent per 5 per cent per 6 per cent per 7 per cent per annum. annum. annum. annum. 25 22.00 $73.00 $76.70 $80.00 $83.00 26 21.48 71.80 75.60 79.00 82.00 27 20.95 70.80 74.60 78.10 81.20 28 20.45 69.70 73.60 | 77.310 80.30 29 19.95 68.60 72.50 76.10 79.40 30 19.45 67.40 71.40 75.10 78.40 31 | 19.00 66.40 70.40 74.20 77.50 36 16.80 60.90 65.20 69.10 72.80 41 14.80 55.60 59.90 64.00 67.80 46 12.83 50.00 54.30 58.40 62.20 5T 10.95 44.10 48.20 52.30 56.10 56 9.10 37.90 41.80 45.60 49.30 61 | 7.30 31.40 34.90 38.40 41.70 66 5.53 24.70 27.60 30.60 33.50 7% 3.80 17.50 19.70 22.00 24.30 79 2.08 9.70 11.10 12.50 13.90 79 1.00 4.90 5.60 6.30 7.00 PROBABLE LIFE 50 YEARS 50 YEARS 50 YEARS I 50.00 I00.00 I00.00 100.00 I00.00 49.05 99.40 99.50 99.70 99.80 . + 48.15 98.70 99.10 99.40 | 99.50 1 47.25 98.10 98.60 99.00 99.30 5 46.35 97.50 98.10 98.60 99.00 A 45.45 96.80 97.70 98.30 98.70 44.60 96.00 97.00 97.80 98.40 43.75 95.40 96.60 97.50 98.10 ] 42.90 94.70 96.00 97.10 97.80 10 42.10 94.10 95.50 96.60 97.50 Ir 41.30 93.30 94.90 96.20 | 97.20 12 40.50 92.60 94.40 95.80 | 96.80 13 39.75 91.90 93.80 95.30 96.50 14 39.00 91.20 93.20 94.80 96.10 5 38.23 90.40 92.60 04.40 95.70 RLES 444 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 31. EXPECTANCY AND REMAINING VALUE OF ANY ARTICLE WHOSE REPLACEMENT COST IS $100 (Continued) PROBABLE LIFE 50 YEARS 50 YEARS 50 YEARS Remaining value. Beginning Expectancy of year. years. 4 per cent per 5 per cent per 6 per cent per = 7 per cent per annum. annum. annum. annum. 16 37-350 $89.60 $92.00 $93.80 $95.30 17 36.75 88.80 91.30 93.30 94.90 18 | 36.00 88.00 | 90.60 92.80 94.50 19 35-30 87.20 90.00 92.20 94.00 20 34.60 86.40 89.30 91.70 93.50 21 33.90 85.60 88.60 9I.IO 93.10 22 33.20 84.70 | 87.90 00.50 92.60 23 32.50 83.80 87.10 89.80 92.00 24 31.80 82.90 86.30 89.20 91.50 25 31.13 82.10 85.60 88.50 90.90 26 30.50 81.20 84.80 87.90 90.40 27 29.90 80.30 84.10 87.20 89.80 28 29.30 79.50 83.30 86.60 89.20 29 28.70 78.60 82.50 85.90 88.70 30 28.10 77.770 81.70 85.20 88.00 31 27.50 76.80 80.90 84.40 87.40 36 24.85 72.50 77 .00 80.90 84.20 41 22.145 68.10 72.90 77-30 80.80 46 20.35 64.00 69.00 73.40 77.40 5I 18.50 60.00 65.10 69.70 73.90 oI 14.80 51.20 56.30 61.10 65.50 7y I1.10 41.10 | 45.80 50.30 54.60 81 7.50 29.60 | 33.50 37.40 41.20 91 3.90 16.50 19.00 21.50 24.00 99 1.00 4.50 5.20 6.00 6.80 PROBABLE LIFE 60 YEARS 60 YEARS 60 YEARS 60.00 100.00 100.00 100.00 100.00 59.I0 99.60 99.70 99.80 99.90 58.153 99.20 99.50 99.60 99.80 : 57-25 98.80 99.20 99.50 99.60 2 56.35 98.40 98.90 99.30 99.50 5 55.45 97.90 98.60 99.10 99.40 7 54.60 97.50 98.30 98.80 99.20 53.75 97.10 98.00 98.60 99.10 52.90 96.60 97.70 98.40 98.90 J 52.05 06.20 97.30 08.20 98.80 TABLES 445 TABLE 31. EXPECTANCY AND REMAINING VALUE OF ANY ARTICLE WHOSE REPLACEMENT COST IS $100 (Concluded) PROBABLE LIFE 60 YEARS 60 YEARS 6o YEARS Remaining value. Beginning Expectancy of year. YEars, 4 per cent per 5 percent per 6 per cent per 7 per cent per annum. annum. annum. annum. iI $51.20 $95.70 $97.00 $97.90 $98.60 12 50.40 95.20 96.60 97.70 98.40 13 49.50 94.60 96.20 97.40 98.20 14 48.75 94.10 95.90 97.10 98.00 16 48 .00 93.70 95.50 96.80 97.80 16 47.25 93.20 95.10 96.60 97.60 17 46.50 92.70 94.70 96.30 | 97.40 18 45.75 92.10 & 94.30 95.90 97.10 19 45.00 91.60 93.90 95.60 96.90 20 44.25 91.00 93.50 95.30 96.60 21 43.50 90.40 | 93.00 94.90 96.40 22 42.75 89.80 92.50 94.60 96.10 23 42.00 89.20 92.00 94.20 95.80 24 41.30 88.60 91.60 93.80 95.50 26 40.60 88.00 91.10 93.40 95.20 26 | 39.90 87.40 go.60 93.00 94.90 27 | 39.20 86.80 90.10 92.60 94.60 28 38.553 86.10 89.50 92.20 94.30 2Q 37.90 85.50 89.00 91.80 93.90 30 37.25 84.90 88.50 91.30 93.60 31 36.60 84.20 87.90 90.90 93.20 36 | 33.60 80.90 85.10 88.60 91.30 41 30.80 77.50 82.20 86.10 89.20 46 28.30 74.10 79.10 83.30 86.80 SI 26.10 70.80 76.10 80.60 84.30 56 24.10 67.60 73.10 77.80 81.80 61 22.20 64.20 69.90 74.80 79.10 71 18.50 57.00 62.80 68.00 72.60 81 14.80 48.70 54.30 59.60 64.40 91 | 11.10 39.00 44.20 49.10 53.10 101 7.50 28.10 32.40 36.50 40.50 Ir 3.90 15.70 18.30 21.00 23.60 119 1.00 4.30 5.00 5.80 6.70 446 VALUATION, DEPRECIATION AND THE RATE-BASE EXPLANATION OF TABLE 3:2 TABLE OF EXPECTANCY OF HUMAN LIFE In Table 32 there is shown the expectation of human life according to the Northampton, the Carlisle, the Combined or Seventeen Offices’ Experience, the American Experience and the Thirty Offices’ Experience tables of mortality. The Northampton table of mortality was constructed by Dr. Richard Price and is based on the mortality of the Parish of All Saints, Northampton, England, during the years 1741-1780. The number of male and female deaths were very nearly equal. This table probably has too great a proportion of the middle class as no precise information as to the members of the laboring class were obtainable. It was formerly much used in England but gives too great mortality especially in the younger ages. Census returns were not available to supplement the vital sta- tistics and the result has been a faulty construction. The Carlisle table is based on the observations of Dr. Heysham upon the mortality of Carlisle, England, in the years 1779-1787. It was constructed by Mr. Joshua Milne and published in 1815. The relative proportion of sexes is 8 males to 9 females. This is a well constructed table of healthy life in England. It has been extensively used in courts, in making estimates of annuities, damages, due to loss of life, etc. Its use for life insurance pur- poses is now practically ended. The Combined or Seventeen Offices’ Experience table was prepared by actuaries from the experience of seventeen impor- tant life insurance companies in England and Scotland. The data from 62,537 assurances were used in its construction and it was published in 1843 by Mr. J. Jones. This table has been and still is used for life insurance purposes. The American Experience table of Mortality was constructed by Mr. Shepard Hermans, from the experience of the Mutual Life Insurance Company about 1868. It has been largely used in the valuation of life insurance policies in the United States and is considered representative of the mortality of healthy insured lives in this country. TABLES £7 The Thirty Offices’ Experience table was constructed in 1873 under the supervision of the United States Chamber of Life Insurance. It is based on the experience of thirty leading companies of the United States and was published in 1881. Mr. Levi W. Meech was in charge of this study. The results have not yet been generally accepted as standard for life insurance purposes. The Expectancy of Human Life table which follows gives the remaining life or expectancy at any age based on the statistics given in the respective tables of mortality. The table used is indicated at the head of the column. The data are given in years of life. 14° 448 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 32. EXPECTANCY OF HUMAN LIFE As shown by various tables of mortality Explanation. — The names at the heads of the respective columns are the names of the tables of mortality, on which the figures in that column are based. Thirty offices’ expe- Combined or : rience Northamp-| Carlisle seventeen of- American ex- Age ton fices’ experience perience = fn Males | Females 1780 1815 1843 1868 1881 1 32.74 AZ. CSR oot eee ofan 1 2 37.79 AF ss Re dra sii rice ZN 30.55 49.82 Slant oC cr 4 © 40.58 SOL ZONE: (1. SL Rl bl ei . 40.84 Erol RC RR u 41.07 ST.T70 ee aia where fele lo BIER Tl TEL a LL BE Is a a i Leia 2 41.03 SOL SORE 0 ci 40.79 50.24 SRA RR LE rt Oe 0 a 40.36 49.57 rn A rie aE ver oR Co 10 39.78 48.82 48.36 48.72 49.99 48.05 +1 39.14 48.04 47.68 48.08 49.32 47.21 12 38.49 47-27 47.01 47.44 48.64 46.40 3 37-83 46.51 46.33 46.82 | 47.95 45.64 4 37-17 45.75 45.64 46.16 47.26 44.91 4 36.51 45.00 44.96 45.50 46.57 44.19 6 35.85 44.27 44.27 44.85 45.88 43.48 17 35.20 43.57 43.58 44.19 45.18 42.79 8 34.58 42.87 42.88 43.53 44.48 42.12 2 33-99 42.17 42.19 42.87 43.78 41.46 20 33.43 41.46 41.49 42.20 43.07 40.82 21 32.90 40.75 40.79 41.53 42.36 40.19 22 32.39 40.04 40.09 40.85 41.65 39.56 3 31.83 39.31 39-39 40.17 40.93 38.96 1 31.36 38.59 38.68 39.49 40.21 38.38 = 30.85 37.86 37.98 38.81 39.49 37.80 26 30.33 37-14 37-27 38.11 38.77 37-23 27 29.82 36.41 36.56 37-43 38.04 36.66 28 29.30 35.69 35.86 36.73 37-31 36.08 29 28.79 35.00 35.15 36.03 36.58 35.49 50 on 34.34 34.43 35.33 35.85 34.89 JI 27.76 33.68 33.72 34.62 35.12 34.29 2 27.24 33.03 33.01 33.92 34.38 33.69 3 26.72 32.36 32.30 33.21 33.65 33.06 sl 26.20 | 31.68 31.58 32.50 32.91 32.42 35H 25.68 31.00 30.87 31.78 32.17 31.73 TABLES TABLE 32. EXPECTANCY OF HUMAN LIFE (Continued) ) Thirty offices’ expe- Northamp- Carlisle sevortaemor American ex- Are ton fices’ experience perience = Males | Females 1780 1815 1843 1868 1881 35 25.16 30.32 30.15 31.07 31.43 31.13 37 24.64 29.64 29.44 30.35 30.70 30.47 23 24.12 28.96 | 28.72 29.62 29.96 29.81 29 23.60 28.28 28.00 28.90 29.22 29.16 ( J 23.08 27.61 27.28 28.18 28.48 °° 28.48 41 22.56 26.97 26.56 27.45 27.7% 27.82 az 22.04 26.34 25.84 26.72 27.01 27.1% a 21.54 25.71 25.12 25.99 26.28 26.45 £1 21.03 25.09 24.40 28.27 25.5% 25.74 or 20.52 24.46 23.69 24.54 24.82 25.02 42 20.02 23.82 22.97 23.80 24.09 24.30 47 19.51 23.17 22.29 23.08 23.38 23.57 43 19.00 22.50 21.56 22.36 22.66 22.33 (i 18.49 21.81 20.87 21.63 21.95 22.08 5. 17.99 ov, 11 20.18 20.91 21.24 21.33 17.50 20.39 19.50 20.20 20.54 20.59 : 17.02 19.68 18.82 19.49 19.84 19.87 16.54 18.97 18.16 18.79 19.15 19.15 . 16.06 18.28 17.50 18.09 18.47 18.44 : 15.58 17.58 16.86 17.40 17.80 17.73 ta 15.10 16.89 16.22 16.72 17.13 17.03 14.63 16.21 15.59 16.05 16.47 16.35 Le 14.15 15.55 14.97 15.39 15.83 15.67 Ty 13.68 14.92 14.37 14.74 15.19 15.02 €D 13.21 14.34 13.77 14.09 14.56 14.37 vl 12.75 13.82 13.18 13.47 13.94 13.73 "ot 12.28 13.31 12.61 12.86 13.34 13.10 [ 11.81 12.81 12.05 12.26 12.74 12.49 Ga 11.35 12.30 II.5I 11.68 12.16 II.90 a 10.88 11.79 10.97 II.IO 11.60 IT.31 €) 10.42 . 11.2% 10.46 10.54 11.04 10.74 €: - 9.96 | 0.75 9.96 10.00 10.50 10.19 €, 9.50 10.23 9.47 9.48 9.97 9.65 64 9.05 9.70 9.00 8.98 9.46 9.13 70 8.60 9.18 8.54 8.48 1 8.97 8.62 449 450 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 32. EXPECTANCY OF HUMAN LIFE (Concluded) Thirty offices’ expe- 3 Combined of American ex- rience Northamp- | 3 1 Age | ton Gatlin ame perience Males | Females 1780 1815 1843 1868 1881 7 8.17 8.65 8.10 8.00 8.49 3.13 72 Ta 8.16 7. 6y 7hsd 8.02 7.65 73 7.33 vio | 7.26 7.10 7.57 | 7.20 5 6.92 7.35 6.86 6.68 7.14 6.76 : , 6.54 | 7.01 6.48 6.28 6.72 6.34 2% 6.18 6.69 6.1% 5.88 6.32 5.93 7 5.83 | 6.40 5.76 5.48 5.93 5.55 55 5.48 | 6.12 5.42 5.10 5.57 5.18 2 5.1 5.80 5.09 4.74 5.231 4.82 ) 4375 | 5.51 4.78 4.38 4.87 4.49 oI 4-4 eat 4.48 4.04 4.55 4.17 «2 4.09 4.93 4.18 37% 4.24 3.88 3.80 4.65 3.90 3-39 3-95 3.59 2 3.58 4.39 3.63 3.08 3.67 3.33 o, 3-37 4.12 3.36 2.75 3.40 3.08 tH 3.19 3.90 3-10 2.47 3.14 2.84 7 , 3.01 3.73 2.84 2.19 2.89 2.62 «3 2.86 3.59 2.59 5.0 2.64 2.42 89 2.66 3-47 2.35 1.66 2.39 2.33 90 2.47 3.28 2.0 1.42 2 2.05% 33 2.09 3.26 1.89 1.19 1.98 1.89 C2 1.75 3-37 1.67 .98 1.81 1.73 $3 ¥.37 3.48 1.47 | .80 1.64 « 1.59 «1 1.05 3-53 v.28 : .64 ! 1.49 1.46 95 75 3-53 r.12 | .50 1.34 © 1.34 96 .50 3.46 .99 | main. | 1.18 1.23 OF slo 3.28 .89 Aaa 1.03 | 1.09 98 Shee ae 3.07 "75 a .83 .93 OOo hin 2.77 .50 Ban ans .50 2 BO 100 Bold i 1d oat oI a ts I che 101 dela TOMI ls a hob cn itl os OE tis ot os SR hs 102 RA 1.30 steely Sel wanted a PE aides all wis) co MII ey we Tw ul Ch 103 a td .83 El Ut NG Lh Je le al | bis Gs AE Airs 104 aap uk .50 rl uk TV EN | Er hh TA. ..23 TABLE 32. EXPECTANCY OF HUMAN LIFE (Continued) AMERICAN EXPERIENCE TABLE OF MORTALITY (Ultimate Type) Based on Mortality Experience of Mutual Life Ins. Co. of N. Y. Age | Number living - Number dying rary proba aly proba. Eoeciation ot 10 | I0O0 OOO 749 .007 490 .992 5I0 48.72 II 99 251 746 .007 516 .992 484 48.08 I2 98 505 743 | .007 543 .992 457 47.45 13 97 762 740 .007 569 .992 421 46.80 14 97 022 737 .007 596 .992 404 46.16 15 96 285 735 | .007634 .992 366 45.50 16 |, 95550 732 .007 661 -992 339 44.85 17 94 818 729 .007 688 .992 312 44.19 18 94 089 727 .007 727 .992 273 43.53 19 93 362 725 .007 765 .992 235 42.87 20 92 637 723 .007 80s .992 195 42.20 21 91 914 722 .007 855 -992 145 41.53 22 9I 192 721 .007 gob .992 094 40.835 23 Qo 471 720 .007 958 .992 042 40.17 24 89 751 719 .008 oI1 .991 989 39.49 25 89 032 718 .008 065 .99I 935 38.81 26 88 314 718 .008 130 .991 870 38.12 27 87 596 718 .008 197 .991 803 37-43 28 86 878 718 .008 264 .991 736 36.73 2Q 86 160 719 .008 345 .991 653 36.03 30 85 441 720 .008 427 .991 573 35.33 oe 84 721 221 .008 510 .99I 490 34.63 84 ooo 723 .008 607 .991 393 33.92 83 277 726 .008 718 .991 282 33.21 34 82 551 729 .008 831 .991 169 32.50 3s 81 822 732 .008 946 .99I 054 31.78 37 81 ogo 737 .009 089 .990 911 31.07 oF 80 353 742 .009 234 .990 766 30.35 25 79 611 749 .009 408 .990 592 29.62 39 78 862 756 .009 586 .090 414 28.90 40 78 106 765 .009 794 .990 206 28.18 41 77 341 774 .010 008 .989 992 27.45 42 76 567 785 .0IO 252 .989 748 26.72 43 75 782 797 .0I0 517 .989 483 26.00 44 74 985 812 .o10 829 .989 171 25.27 45 74 173 828 .0II 163 .988 837 24.54 46 73 345 848 .011 562 .988 438 23.81 47 72 497 870 .0I2 000 .988 ooo 23.08 (J 71 627 896 .0I2 509 .987 491 22.36 4) 70 731 927 .013 106 .986 894 21.63 "BLES 451 452 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 32. EXPECTANCY OF HUMAN LIFE (Concluded) Age Number living | Number dying poly puna Nrorly pros Ee a of 50 69 804 962 .013 781.986 219 20.91 5I 68 842 ~~ 1001 .014 541 i .985 459 20.20 52 67 841 I 044 ~ .o15 389 .984 611 19.49 53 66 797 | I 091 I .016 333 .983 667 18.79 54 65 706 I 143 .017 396 .982 604 18.09 55 64 563 I 199 .018 571 .981 429 17.40 56 63 364 1 260 .o19 885 .980 115 16.72 57 62 104 1.325 .021 335 | .978 665 16.05 58 60 779 I 394 .022 936 | 977 064 15.39 59 59 385 I 468 .024 720 .975 280 14.74 60 57917 : I 546 .026 693 .973 307 14.10 61 56371 1 1628 .028 880 .971 120 13-47 62 54 743 T7313 .031 292 .968 708 12.86 63 53 030 | 1 800 .033 943 .966 o57 12.26 64 5I 230 1 889 .036 873 .963 127 11.67 65 49341 | 1980 .040 129 + .959 871 11.10 66 47 361 |, 2070 .043 707 | .956 293 10.54 67 45291 | 2158 .047 647 | .952 353 10.00 68 43 133 | 2 243 .052 002 -947 998 9.47 69 40 890 2327 .056 762 .943 238 8.97 70 38 569 2 301 .061 993 .938 007 8.48 73 36 178 2 448 .067 665 .932 335 8.00 72 33 730 2 487 .073 733 -926 267 7-55 73 31 243 2 505 .080 178 .919 822 A 74 28 738 2 50I .087 028 .912 972 6.68 75 26 237 2 476 .094 371 .9o5 629 6.27 79 23 761 2 431 .102 3II .897 689 5.88 77 21 330 2 369 .III 064 .888 036 5.49 78 18 961 2 2901 .120 827 .879 173 5.17 79 16 670 2 196 131 734.868 266 4.74 8o 14 474 2 091 .144 466 .855 534 4.39 81 12 383 1 964 .158 605 .841 395 4.05 22 10 419 1 816 .174 297 .825 703 3-71 &3 8 603 1 648 .191 561 .808 439 3.39 84 6 955 I 470 .21I 359 .788 641 3.08 8s 5 435 I 202 .235 552 .764 448 2.77 86 4 193 I 114 .265 681 .734 319 2.47 87 3 079 933 .303 020 .696 980 2.18 88 2 146 744 .346 692 .653 308 1.91 89 I 402 555 .395 863 .604 137 1.66 90 847 385 -454 545 -545 455 I.42 91 | 462 246 .532 466 .467 534 1.19 92 216 137 .634 259 .365 741 .98 93 79 58 734 177 .265 823 | .80 94 | 21 18 .857 143 .142 857 .64 95 3 3 1.000 000 .000 000 .50 TABLES EXPLANATION OF TABLE 33 AMORTIZATION OR DEPRECIATION AND REMAINING OR PRESENT VALUE Table 33 is an amortization table or a set of tables computed for the interest rates 4 per cent to 7 per cent per annum and for all terms of indebtedness, terms of bonds or probable life terms of perishable articles, from 2 to 75 years, which are likely to come under consideration. By adding to this table headings at the bottom of the columns it has also been made convenient for use as a depreciation table. Care must be taken in its use to preserve the distinction indicated by the top and bottom headings and not to assume that the years of expectancy in the last column apply to the age or number of years noted in the first column. All values noted in this table are referred to $100 as the basic amount in order that the figures in the table may be used as percentages when so desired. The table has been computed by the use of the following formule which may be used when values are to be ascertained for interest rates or terms not covered by the table. Let a, be the amortization installment which must be in- vested annually in order to amount at compound interest to $100 in 7 years. Let 7 be the interest rate expressed decimally (thus o.05 for 5 per cent). Let A, be the accrued amortization in 7 years when the annual amortization installment is @, and the interest rate is s. Let m be any number of years. Let n represent the amortization term expressed in years. Let a, be the current amortization in the mth year, i.e., the amortization increment a, plus interest on the amortiza- tion fund already accumulated. Let ¢ be the remaining years of usefulness of any article whose probable life new is # years. = 453 454 VALUATION, DEPRECIATION AND THE RATE-BASE The basic formula for $100 derived from (28) from which all other formule are derived will be 100 7 n= (1 +0)" ogy (35) Note. — This formula is for the special case in which the amount of the annuity is $100 which fact should not be over- looked in applying it. The accrued amortization in m years will be: (1 +2) — ‘] An = re ————T Al roo] Gry: (36) The remaining investment at the end of the mth year will be 100 — Am = 100 |: i naan . 37) The current amortization a, in the mth year will be 0 i (1 + om! | Onl = wate al (38) For depreciation, as ordinarily though erroneously * deter- mined, these formule may be written for an original value of $100: 100 7 aq, = Gi —1 (35) The accrued depreciation will be a (1 +2) — !] An = 100 [oon = TL (39) The remaining or present value at the time when the expect- ancy is e years will be + iy —1 I rc 100 100| I ha (40) The current annual depreciation when the expectancy is e years will be i; | (1 + gyererl ] dp = 1007 i TH ay (41) The remaining value of any perishable article depends upon the cost, all circumstances considered, of replacing it when it * For a demonstration of error in the ordinary formule see p. 456. TABLES 455 ceases to be useful, and the time when the article will go out of use. But this value is dependent too upon the probable life of a new article of the same kind. The remaining value of several articles with the same expectancy of which one is in the 10-year life class, another in the 20-year class and another in the 4o-year class will not be the same, because the proportional serv- ice yet to be expected when compared with that of new articles will, in these cases, vary inversely as 10 to 20 to 40, and the remaining values will depart widely from each other. If the expectancy, for example, of each of three such articles is 5 years, and 6 per cent interest be made the basis of the calculation, the remaining values will be 57.23 per cent, 36.73 per cent and 28.00 per cent of the cost of replacement. The article with the prob- able life new of 10 years has the highest value for the reason that its remaining service years are a larger proportion of its probable life new than in the case of the other two articles with longer probable life new. Illustration of the Use of Table 27 What amount at the end of the 26th year will be in a sinking fund for the retirement of a bond issue of $100,000 running 40 years, if the money accumulating in the sinking fund earns 6 per cent per annum? On page 361 in the 4o-year life section of Table 27 at year 27 (beginning of year 27 is the end of year 26) in the left-hand column, the accrued amortization in the 6 per cent column for each $100 will be found to be $41.1637. Consequently, the amount in the sinking fund to retire $100,000 will be $41,163.70. The amount which will be added to the sinking fund in the 27th year will be $2939.60. Let it be assumed that by any means, such as inspection by experts, the probable remaining term of usefulness of an electric generator 13 years old has been found to be 11 years and that the type of generator to which it belongs has a probable life new of 20 years. What at 6 per cent interest is the accrued deprecia- tion if the cost of the generator was $3000 and what is its re- ni 456 VALUATION, DEPRECIATION AND THE RATE-BASE maining value if the cost of replacement at the end of its period of usefulness may be estimated at $2500? On page 465 in the 20-year life 6%, section of Table 33 at 11 years in the right-hand column there are found in the column with the bottom heading “ Present Value” the figures 68.7614 which represent percentage. The remaining value estimated from cost would be 0.687614 X 3000 = $2062.84; consequently the accrued depreciation, estimated from cost, would be 3oco — 2062.84 = $037.16. The remaining value estimated from the cost to replace will be 0.687614 X 2500 = $1719.04. The actual accrued depreciation, therefore, will be 3000 — 1719.04 = $1280.96. Demonstration of Error in Formule as Ordinarily Used in Estimating Current Depreciation That the ordinary depreciation formule based on expectancy or probable remaining life must be in error, even if it be supposed that the expectancy has been correctly ascertained, and that they should be regarded only as approximation formula, can be demon- strated as follows: Let it be assumed that the failures of a large number of articles, each representing an original investment of $100, which are all in the same life class and of the same age, can be grouped in couples such that for each article failing or going out of use s years before the end of the term of the originally predicted probable life, there will be another that fails s years after the end of this term. If the probable life as originally determined was # years, and some years of this life have already elapsed, the remaining actual years of service of the first of the two articles under consideration would be e — s years and of the second e -} s years, where e repre- sents the expectancy of all articles still in service and s is the de- parture in years from this expectancy by each of the two articles separately considered. If the actual failure of these two articles could be correctly forecast the current depreciation thereof would be estimated from the following formule based on equation (41). TABLES For the article failing early: ia] on]. Current Ann. Depr. = 100] Ciro (42) For the article failing late: soo Hi Current Ann. Depr. = too] EE: (43) For both articles together: evan EI + (1 4d) ne Current Ann. Depr. = 100: | PFE i (44) If estimated in the ordinary way this current annual deprecia- tion for the two articles would be estimated by formula (41) as follows: ou J2 (+l 2 dy = 100% BF: = (45 The estimate of current depreciation by formula (41) is too small, because as will be seen by comparison of equation (43) with equation (44): (1 + fy trie + (1 + {perl > 2 (1 + ol (46) "ne 1 (1 +79) GES ag > 2. (47) By the aid of formula (40) it can in a similar fashion be shown that the remaining value as ordinarily ascertained by such formule is too large. In further illustration of this fact let two identical articles of a group in the 40-year life class be compared, one of which is doomed to fail when 30 years and the other when 50 years in service. The difference in the present value of each $100 of investment in these two articles will be represented by the difference in the present value of each $roo required to re- place the one in 30 years and the present value of each $100 required to replace the other at the end of 50 years. If the actual 457 or 458 VALUATION, DEPRECIATION AND THE RATE-BASE life of both of these articles were in agreement with the group expectancy of 40 years, $9.72 would have to be invested at 6 per cent to produce $100 at the end of that period. The larger sum of $17.41 is actually required for the article which fails at 30 years and only $5.43 for the article which lasts 50 years. These figures show that the article which falls 10 years short of its expected life has a present value $7.69 less than if it would con- tinue in service 40 years and that the article which will serve 50 years exceeds the value which it would have if it were doomed to fail at 40 years by $5.43. These figures clearly show the greater effect of the years of service short of average life, than the effect of the years in excess of average life upon the present value of any group of articles all of which have the same expectancy. Or, looking at the matter in another way, the aggregate num- ber of service years which the short-lived articles are short of normal must be equal (by definition) to the number of service years by which the long-lived articles exceed the normal. For every failure of an article m years before the average or normal time of failure there will be a survival of some article m years beyond this time. But itis obvious that the m years of deficiency of service, being not so far in the future, represent a greater deficiency of value than m years of excess service, farther in the future, can make up. The aggregate number of years of defi- ciency of service, considered from the standpoint of present value, will always outweigh a like number of years of service beyond the normal term of life. The actual present or remaining value of such a group of articles will always, therefore, be smaller than the result found by such formule as (40) provided that the average probable life thereof has been correctly ascertained. Similarly the current depreciation by formula will be below the correct amount. The remedy for this defect, when sinking fund formule are to be used, will obviously lie in making the forecast of probable life con- servative — underestimating rather than overestimating the same. TABLES TABLE 33. AMORTIZATION AND DEPRECIATION The Current Annual and Total Amortization and the Remaining Invest- ment also the Current Annual and Accrued Depreciation and the Present Value for Each $100 of Bonds or of Investment. Computed by the compound interest sinking fund method Remaining | Amortiza- Total Remaining 5 oo. Total Your, rotons is my Toot SEE eet of year. year. | of year. of year. year. , of vear. 2 YEAR LIFE 2 YEAR LIFE i - 4 per cent. 5 per cent. $100.0000 |$49.0196 [849.0196 $100.0000 ($48.7805 ($48.7805 50.9804 | 50.9804 [100.0000 | 51.2195 | 51.2193 aL 6 per cent. 7 per cent. I3100.0000 |$48.5437 948.5437 F100. 0000 $48.3092 $48.3092 | 51.4563 | 51.4563 (100.0000 51.6908 | 51.6908 WI 3 YEAR LIFE 3 YEAR LIFE 4 per cent. 5 per cent. 1 |$100.0000 1$32.0349 [832.0349 $100.0000 $31.7209 [$31.7209 | 67.9651 33.3162 | 65.3511 | 68.2791 | 33.3069 | 65.0278 34.6489 34.6489 [100.0000 34.9722 | 34.9722 [100.0000 6 per cent. 7 per cent. i |$100.0000 $31.4110 [Fat sere $100.0000 $31.1052 $31.1052 . 68.5890 33.2956 | 64.7066 | 68.8948 33.2825 ' 64.3877 5 35.2934 35.2034 100.0000 35.6123 | 35.6123 .100.0000 | 4 YEAR LIFE 4 YEAR LIFE 4 per cent. 5 per cent. ; 3100.0000 $23.3490 '$23.5490 B$100.0000 $23.2012 '$23.2012 76.4510 24.4910 48.0400 76.7988 24.3612 47.5624 51.9600 25.4706 73.5106 ~~ 52.4376 25.5793 73.1417 26.4894 26.4894 100.0000 26.8583 | 26.8583 100.0000 6 per cent. 7 per cent. 100.0000 $22.8591 $22.8591 $100.0000 $22.5228 $22.5228 77.1409 24.2307 47.0898 | 77-4772 24.0994 46.6222 52.9102 25.6845 72.7743 53.3778 25.7864 72.4086 27.2257 27.2257 100.0000 27.5914 27.5914 ,[00.0000 | Current Current Expecte Present SL Present ee pec value |Jepreciaton vale. [fepreeaion iy . 450 460 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining 5, oo. Total Remaining | Elz Total Year. ry fonduring| ARONA Amen’ tondunng hori: of year. year. of year. of year. year. of year. 5 YEAR LIFE 5 YEAR LIFE 4 per cent. 5 per cent. I Buasieom |$18.4627 $18 .4627 $100.0000 |$18.0975 [$18.0975 S1.53730 19.20120 37.6639 81.9025 | 19.0023 | 37.0998 4 . 62.3361 19.9693 « 57.6332 62.9002 | 19.9525 | 57.0523 3 : 42.3668 20.7680 78.4012 42.9477 | 20.9501 78.0024 2 v 21.5988 21.5988 ‘100.0000 ‘ 21.9976 21.9976 100.0000 6 per cent. : 7 per cent. 1 $100.0000 [$17.7396 |$17.7396 ($100.0000 |$17.3891 i$17.3801 J 2 82.2604 | 18.8041 | 36.5437 82.6109 | 18.6063 | 35.9954 4 5 63.4563 19.9322 ' 56.4759 | 64.0046 ' 19.9087 | 55.9041 + 43.5241 21.1282 77.6041 44.0959 21.3024 77.2065 2 b 22.3959 22.3959 |100.0000 22.7935 ' 22.7935 100.0000 | i 6 YEAR LIFE 6 YEAR LIFE 4 per cent. 5 per cent. 1 |$100.0000 [$15 .0762 [$15.0762 $100 .0000 But vous [ft 6 3 84.9238 ' 15.6792 ' 30.7554 85.2083 | 15.4368 | 30.1385 b 3 69.2446 16.3064 47.0618 '' 69.8615 16.2087 | 46.3472 4 4 52.9382 16.9587 64.0205 53.6528 | 17.0191 | 63.3663 3 5 35.9795 17.6370 81.6573 36.6337 17.8701 ! 31.2364 : a 18.3425 18.3425 100.0000 18.7636 18.7636 100.0000 : 5 6 per cent. 7 per cent. I [00 coe $14.3363 $14.3363 [$100.0000 $13.9796 |$13.9796 5 2 85.6637 ' 15.1964 29.5327 86.0204 | 14.9581 | 28.9377 J 3 70.4673 16.1082 45.6409 71.0623 | 16.0052 | 44.9429 3 q 54.359I 17.0747 62.7156 55.0571 | 17.1256 | 62.0685 i 37.2844 18.0992 80.8148 37.9315 | 18.3244 | 80.3929 2 19.1852 19.1852 100.0000 ! 19.6071 | 19.6071 |100.0000 | 1 Current Current | Expect- P t a P t en: value. | depreciation A gear Eo TARLES TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining 5 ooo Total Remaining 5 oe. Total Year. [ment donduring (HT MIStmen don during erie of year. year. of year. of year. | year. of vear. 7 YEAR LIFE 7 YEAR LIFE 4 per cent. 5 per cent. $100.0000 '$12.6610 '$12.6610 $100.0000 '$12.2820 $12.2820 | 87.3390 13.1674 | 25.8284 87.7180 | 12.8961 25.1781 74.1716 13.6941 39.5225 74.8219 13 5409 38.7190 | 60.4775 14.2419 53.7644 61.2810 14.2179 52.9369 | 46.2356 14.8115 68.5759 47.0631 14.9288 67.8657 31.4241 15.4040 83.9799 32.1343 15.6753 83.5410 16.0201 16.0201 100.0000 16.4590 16.4590 100.0000 6 per cent. 7 per cent. 4 $100.0000 '$11.9135 $11.9135 $100.0000 $11.5553 $11.5553 | 88.0865 12.6283 24.5418 88.4447 12.3642 23.9195 75.4582 13.3860 37.9278 76.0805 13.2297 37.1492 - . 62.0722 14.1892 52.1170 62.8508 14.1558 51.3050 4 47.8830 15.0405 67.1575 48.6950 15.1467 66.4517 32.8425 15.9430 83.1003 33.5483 16.2069 82.6586 16.8995 16.8995 [00.0000 17.3414 17.3414 100.0000 8 YEAR LIFE 8 YEAR LIFE 4 per cent. 5 per cent. [Segciance $10.8528 $10.8528 $100.0000 $10.4722 $10.4722 | 2 89.1472 11.2869 22.1397 89.5278 10.9958 28.4050) v 77.8603 11.7384 33.8781 78.5320 11.5456 33.0136 a . ' 66.1219 12.2079 46.0860 66.9864 12.1229 45.1365 | b . 53.9140 12.6962 58.7822 54.8635 12.7290 57.8655 | 4 41.2178 13.2041 71.9863 42.1345 13.36,4 71.2309 28.0137 13.7322 85.7183 28.7601 14.0337 85.2646 14.2815 14.2815 100.0000 14.7354 14.7354 100.0000 | Current Current .Expect-~ P t i P: t eh Vor | petion valve, | Jepreciation | Years. Fw 461 462 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining | ap ovens Total Remaining | Ariortizds Total Year, | FVCSmON ion during here RYSImOnt | donduring {horeed of year. eat of year. of year. Year. of year. 8 YEAR LIFE 8 YEAR LiFe 6 per cent. 7 per cent. 1 |[$100.0000 $10.1036 Bio $100.0000 ® 9.7468 s 9.7468 8 2 89.8964 | 10.7098 | 20.8134 = 90.2532 | 10.4290 | 20.1758 7 3 79.1866 11.3524 32.1658 79.8242 11.1591 ' 31.3349 3 4 67.8342 12.0335 44.1993 68.6651 11.9402 43.2751 O J | 55.8007 12.7556 56.9549 56.7249 12.7760 356.05II 1 ; 43.0451 13.5209 70.4758 43.9489 13.6704 69.7215 ; ? 29.5242 14.3321 | 84.8079 30.2785 14.6273 84.3488 3 15.1921 I5.I92I [100.0000 15.6512 15.6512 100.0000 ' 9 YEAR LIFE 9 YEAR LIFE 4 per cent. 5 per cent. { ramen ® 9.4493 S 9.4493 $100.0000 3 9.06090 [$ 9.0600 | 9 . 90.5507 9.8273 ' 19.2766 90.9310 9.5225 | 18.5915 3 y 80.7234 10.2204 29.4970 81.4085 9.9986 | 28.5901 7 4 70.5030 10.6292 40.1262 71.4099 10.4985 | 39.0886 a 5 . 59.8738 11.0543 51.1803 60.9114 11.0234 | 50.1120 & 3 48.8195 11.4965 62.6770 49.8880 11.5746 61.6866 1 ¥ 37.3230 11.9564 74.6334 | 38.3134 12.1533 73.8399 3 25.3666 12.4346 87.0680 26.1601 12.7610 86.6009 9 12.9320 12.0320 TI00.0000 13.3991 13.3991 100.0000 : 6 per cent. 7 per cent. 1 [$100.0000 $ 8.7022 :$ 8.7022 $100.0000 s 8.3486 |$ 8.3486 © 9 ; 91.2978 | 9.2244 17.9266 | 91.6514 8.9330 | 17.2816 5 5 82.0734 9.7778 27.7044 : 82.7184 9.5584 | 26.8400 7 4 72.2956 10.3645 38.0689 = 73.1600 10.2275 37.0675 J 35 61.9311 10.9864 49.0553 62.9325 10.9434 48.0109 J ; 50.9447 11.6455 60.7008 51.9891 11.7004 59.7203 4 39.2992 12.3443 73.0451 40.2797 12.5291 72.2494 , 26.9549 13.0849 86.1300 27.7506 13.4061 85.6555 | 2 13.8700 13.8700 100.0000 14.3445 14.3445 100.0000 i I Current Current | Expect- P t Ca P: ca Led WH fpr WE pel jg TABLES TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining poo Total Remaining 5, ooo Total Year. !nvestment [oo qn amortiza- investment [oq amortiza- EO og rT ion Bl begin TRE Meats 10 YEAR LIFE 10 YEAR LIFE 4 per cent. 5 per cent. [$100.0000 $ 8.3291 $ 8.3291 $100.0000 $ 7.9505 $ 7.9505 . 1. 91.6709 | 8.6623 16.9914 92.0495 | 8.3480 + 16.2085 | gu 83.0086 | 9.0088 26.0002 83.7015 8.7654 1 25.0639 | & i 73.9998 | 9.3690 35.3692 74.9361 9.2037 34.2676 | ¥ 64.6308 9.7439 45.1131 65 7324 9.6638 43.9314 Cl 54.8869 10.1336 55.2467 56.0686 10.1470 354.0784 - 44.7533 10.5389 65.7856 45.9216 10.6544 64.7328 34.2144 10.9606 76.7462 35.2672 11.1871 75.9199 23.2538 11.3989 88.1451 24.0801 11.7464 87.6663 : 11.8549 11.8549 100.0000 12.3337 12.3337 100.0000 6 per cent. 7 per cent. _ $100.0000 $ 7.5868 $ 7.5868 S$100.0000 $ 7.2377 $ 7.2377 10 92.4132 8.0420 15.6288 92.7623 7.7444 | 14.9821 t 84.3712 8.5245 24.1533 85.0179 + 8.2865 23.2686 & 75.8467 9.0360 33.1893 76.7314 8.8666 32.1352 . 66.8107 9.5782 42.7675 67.8648 9.4872 41.6224 57.2325 10.1528 52.9203 58.3776 10.1513 51.7737 47.0797 10.7620 63.6823 48.2263 10.8619 62.6356 36.3177 11.4078 75.0901 37.3644 11.6223 74.2579 24.9099 12.0922 87.1823 25.7421 12.4358 86.6937 i, 12.8177 12.8177 100.0000 13.3063 13.3063 100.0000 15 YEAR LIFE 15 YEAR LIFE 4 per cent. 5 per cent. $100.0000 |$ 4.9941 '$ 4.9941 $100.0000 $ 4.6342 |$ 4.6342 1B 95.0059 5.1939 10.1880 95.3658 4.8660 9.5002 14 89.8120 5.4016 15.5896 90.4998 5.1092 | 14.6004 13 84.4104 | 5.6177 21.2073 85.3906 5.3646 | 19.9740 12 78.7927 5.8424 27.0497 80.0260 5.6330 | 25.6070 Ti 72.9503 6 760 33.1257 74.3930 5.9146 31.5216 '. 66.8743 ©.3192 39.4449 68.4784 6.2103 37.7319 ] Current Current Expect- Present ih Present os di t d t y value. | an value. | al on | To 463 464 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining Aortisa. Total Remaining Amortiza. J Lotal Vear, {VSN ion Guring| Oris Smvesment | on uring amortizy "of year. | Ye. | of vear. of year. Fear. of year. 15 YEAR LIFE 15 YEAR LIFE 4 per cent. 5 per cent. 8 $60.5551 $6.5719 Bat out $62.2681 $6.5209 [$44.2528 8 9 53.9832 6.8348 | 52.8516 55.7472 6.8468 | 51.0996 7 10 47.1484 7.1081 59.9597 48.9004 7.1892 58.2888 6 IX 40.0403 7.3925 67.3522 41.7112 7.5487 65.8375 3 12 32.6478 7.6882 45.0404 34.1625 7.9261 | 73.7636 | 13 24.9596 7.9957 83.0361 26.2364 8.3224 82.0860 14 | 16.9639 3.31560F g1 .3517 17.9140 8.7385 90.8245 15 8.6483 8.6483 100.0000 9.1755 9.1753 (100.0000 1 6 per cent. 7 per cent. L [100.0000 $4.2963 i$ 4.2063 $100. 0000 # 3.9795 ($ 3.9795 1b 2B 95.7037 4.55408" 8.8503 96.0205 | 4.2580 | 8.2375 14 3 01.1497 4.8273 13.6776 gr .76250 4.5561 ‘12.7936 13 4 86.3224 5.1170 18.7946 87.2064 4.8750 17.6686 12 b 81.2054 5.4239 24.2183 82.3314 + 5.2162 22.8848 II 6 , 75.7815 5.7493 29.9678 77.1152 5.5814 28.4662 10 7 70.0322 6.0944 36.0622 71.5338 5.9722 34.4384 ) o 63.9378 6.4601 42.5223 65.5616 6.3901 40.8285 9 | 57-4777 6.8476 49.3699 59.1715 6.8375 47.6660 : 10 50.6301 7.2584 56.6283 52.3340 7.3160 54.9820 J YIN 43.3737 7.6041 64.3224 45.0180 7.8282 62.8102 i 12 35.6776 8.1555 72.4779 37.1898 8.3762 71.1864 .3 27.5221 8.6450 81.1229 28.8136 8.9625 80.1489 TA 18. 8751 9.1636 90.2865 19.8511 9.5899 | 89.7388 15 9.7135 9.7I35 100.0000 10.2612 10.2612 {100.0000 i 20 YEAR LIFE 20 YEAR LIFE 4 per cent. 5 per cent. ! |$100.0000 $3.3582 |$ 3.3582 $100.0000 | $3.0243 |$ 3.0243 | 20 "© 96.6418 | 3.4925 ' 6.8507 | 96.9757 1 3.1755 | 6.1998 ' 19 03.1493 3.6322 10.4829 93.8002 3.3342 9.5340 18 89.5171 3.7775 14.2604 90.4660 3.5010 ! 13,0350 17 85.7396 | 3.9286 18.1890 86.9650 3.6760 16.7110 16 81.8110 4.0857 22.2747 83.2800 3.8598 20.5708 16 Current | . Current Expect- P. t i P t : fee. {deprecation tee. depreciation fe TABLES TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining oo Total Remaining poo Total Year, ' \nvestment oo to A amortiza- Investment oo "300 amortiza- aE ea 20 YEAR LIFE 20 YEAR LIFE 4 per cent. 5 per cent. : 877.7253 84.2492 $26.5239 $79.4292 $4.0528 $24.6236 | 14 73-4761 4.4191 30.9430 75.3764 4.2554 28.8790 1; 9 69.0570 4.5959 35.5389 7I.1210 4.4682 33.3472 | 12 10 ' 64.4611 4.7797 40.3186 66.6528 4.6916 38.0388 ' 11 11 59.6814 4.9709 45.2895 61.9612 4.9262 42.9650 © 10 12 | 54.7105 5.1608 50.4503 57.0350 5.1725 48.1375 13 49.5407 5.3766 55.8359 51.8625 5.4311 53.5686 . 14 44.1641 5.5916 61.4275 46.4314 5.7027 59.2713 15 38.5725 5.8152 67.2427 40.7287 5.9878 65.2591 16 | 32.7573 6.0479 73.2906 34.7409 6.2872 71.5463 17 26.7094 6.2898 79.5804 28.4537 6.6016 78.1479 18 20.4196 6.5414 86.1218 21.8521 6.9317 85.0796 19 | 13.8782 6.8031 92.9249 14.9204 7.2782 | 92.3578 20 7.0751 | 7.0751 [00.0000 7.6422 | 7.6422 '100.0000 6 per cent. 7 per cent. $100.0000 $2.7185 § 2.7185 S$100.0000 $2.4393 $ 2.4393 20 | 97.2815 2.88153 5.6000 97.5607 2.6100 | 5.0493 19 94.4000 3.0545 8.6545 94.9507 2.7928 | 7.8421 18 | 01.3455 3.2377 11.8922 92.1579 2.9882 10.8303 17 : 88.1078 3.4320 15.3242 89.1697 3.1974 14.0277 ' 16 84.6758 3.6379 18.9621 85.9723 3.4213 17.4490 1b 81.0379 3.8562 22.8183 82.5510 3.6607 21.1097 14 77.1817 4.0875 26.9058 78.8903 3.9170 25.0267 13 73.0942 4.3328 31.2386 74.9734 4.1011 29.2178 12 10 | 68.7614 4.5928 35.8314 70.7822 4.4846 33.7024 II II 64.1686 4.8683 40.6998 66.2076 4.7984 38.5008 10 12 59.3002 5.1604 45.8602 61.4992 5.1344 43.6352 . 13 54.1398 5.4701 51.3303 56.3648 5.4937 49.1289 “ 14 48.6697 5.7982 57.1283 50.8711 5.8783 55.0072 156 42.8715 6.1462 63.2747 44.9928 6.2898 61.2970 16 36.7253 6.5149 69.7896 38.7030 6.7301 68.0271 17 30.2104 6.9058 76.6954 31.9729 7.2012 75.2283 * 23.3046 7.3202 84.0156 24.7717 7.7053 82.9336 1 15.9844 7.7594 91.7750 17.0664 8.2446 91.1782 2. 8.2250 8.2250 100.0000 8.8218 8.8218 100.0000 Current Current Expect- P: t Eg P t , Expec value. [Jeprecistion value, |Jepreciation he 465 466 VALUATION , DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining A tial Total Remaining | Arortizas Total Year, | VeSment on during| ATiortiza: investment Gor amortisa of year. | year. of year. of year. year. of year. 25 YEAR LIFE 25 YEAR LIFE 4 per cent. 5 per cent. , ($ro0.0000 $2.4012 3 2.4012 $100.0000 $2.0952 |$ 2.0952 2b 2 97.5988 2.4972 4.8984 | 97.9048 2.2001 4.2952 24 3 95.1016 2.5972 7.4956 95.7047 2.3100 | 6.6053 23 4 02.5044 2.70I0 10 1966 93.3947 2.4254 | 9.0307 22 b 89.8034 | 2.8091 13.0057 90.9693 2.5468 11.5775 21 6 86.9943 2.9214 15.9271 88.4225 2.6742 14.2517 20 : 84.0729 3.0383 1 18.9654 85.7483 2.8078 17.0595 19 : 81.0346 3.1598 | 22.1252 82.9405 2.9482 20.0077 18 9 77-8748 3.2862 | 25.4114 79.9923 3.0057 23.1034 :7 10 74.5886 3.4176 28.8290 76.8966 3.2504 | 26.3538 6 II 71.1710 3.5544 32.3334 73.6462 3.4129 , 29.7667 1b 12 ' 67.6166 3.6965 36.0799 70-2333 3.5836 33.3503 14 13 + 63.9201 3.8444 39.9243 66.6497 3.7627 37.1130 13 14 | 60.0757 3.9982 43.9225 62.8870 3.9509 41.0639 Tz 16 ' 56.0775, 4.1581 48.0806 58.0361 4.1485 45.2124 1 16 | 51.9194 4.3244 52.4050 54.7876 4.3559 49.5683 10 17 | 47.5950 4.4974 56.9024 50.4317 4.5736 | 54.1419 ) 18 43.0976 4.6773 61.5797 45.8581 4.8024 | 58.9443 19 38.4203 4.8643 66.4440 41.0557 5.0424 63.9867 20 33.5560 5.0590 71.5030 36.0133 5.2046 69.2813 . 21 28.4970 5.2613 76.7643 30.7187 5.5593 74.8406 J 22 23.2357 5.4718 82.2361 25.1594 5.8373 80.6779 23 17.7639 5.6906 87.9267 19.3221 6.1291 1 86.8070 24 12.0733 5.9183 93.8450 13.1930 6.4356 | 93.2426 25 6.1550 6.1550 100.0000 6.7574 6.7574 100.0000 6 per cent. 7 per cent. ~ (200, 0000 $ 1.8227 $ 1.8227 $100.0000 $1.5811 $ 1.5811 2b z 98.1773 | 1.9320 3.7547 | 98.4189 1.60178 i 32728 24 3 06.2453 2.0480 5.8027 = 96.7272 1.8101 5.0829 23 1 94.1973 2.1708 7.9735 94.9171 | 1.9369 ' 7.0198 22 J 92.0265 2.30I1 10.2746 92.9802 2.0724 9.0922 21 ’ 89.7254 2.4301 12.7137 90.9078 2.2175 11.3097 20 87.2863 2.5855 15.2992 88.6903 2.3728 13.6825 19 84.7008 2.7406 18.0398 86.3175 2.5388 16.2213 18 81.9602 2.905 20.9449 83.7787 2.7165 18.9378 17 — 79.0551 3.0794 24.0243 81.0622 2.9067 21.8445 16 Current Current J Expect- P t on] P t Hs ) Var | Qerecistion verde. Jepreciation) pe TAFE". 75 TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining Ariortizas Total Remaining Amortiza: Total Year, WVSUMENt (onuring Sori DUSTER gion dunng| $ertin of year. eal. of year. of vear. Year: of year. 25 YEAR LIFE 25 YEAR LIFE 6 per cent. 7 per cent. 11 | $75.9757 $3.2641 '$27.2884 $78.1555 83.1102 1$24.9547 15 12 72.7116 3.4600 30.7484 75.0453 3.3279 28.2826 14 13 69.2516 3.6675 34.4159 71.7174 3.5608 31.8434 ' 13 14 | 65.5841 3.8877 38.3036 68.1566 3.8101 35.6535 12 16 61.6964 4.1208 42.4244 64.3465 4 0768 39.7303 IT 16 . 57.5756 4.3682 46.7926 6o 2697 4.3622 44.0925 10 17 53.2074 4.6302 51.4228 55.9075 4.6675 48.7600 ( 18 48.5772 4.9081 56.3309 51.2400 4.9942 53.7542 | i 19 43.6691 5.2025 61.5334 46.2458 5.3439 59.0981 20 38.4666 5.5147 67.0481 40.9019 5.7179 64.8160 L. 21 32.9519 5.8455 72.8936 35.1840 6.1181 70.9341 22 | 27.1064 6.1963 79.0899 29.0659 6.5465 77.4806 23 20.9101 6.5681 85.6580 22.5194 7.0047 84.4853 24 | 14.3420 6.9621 92.6201 15.5147 7.4950 91.9803 26 7.3799 7.3799 100.0000 8.0197 8.0197 (00.0000 30 YEAR LIFE 30 YEAR LIFE 4 per cent. 5 per cent. : $100.0000 $1.7830 8 1.7830 $100.0000 $1.5051 $ 1.5051 30 98.2170 1.8543 3.6373 98.4949 1.35804 3.0855 29 > 96.3627 1.9283 5.5658 96.9145 1.6595 4.7450 28 4 94.4342 2.0057 7.35715 95.2550 1.7424 6.4874 27 ° 92.4285 2.0859 9.6574 93.5126 1.82953 8.3169 26 0 90.3426 2.1693 11.8267 91.6831 1.9210 10.2379 2b 88.1733 2.2560 14.0827 89.7621 2.0170 12.2549 24 85.9173 2.3463 16.4290 87.7451 2.1179 14.3728 23 ty 83.5710 2.4402 18.8692 85.6272 2.2238 16.5966 2 10 81.1308 2.5378 21.4070 83.4034 2.3349 18.9313 21 11 78.5930 2.6393 24.0463 81.0685 2.4517 21.3832 20 12 75.9537 2.7449 26.7912 78.6168 2.5743 23.9575 19 : 73.2088 2.8545 29.6457 76.0425 2.7031 26.6606 18 70.3543 2.9689 32.6146 73.3394 2.8381 29.4987 17 67.3854 3.0877 35.7023 70.5013 2.9801 32.4788 16 64.2977 3.2111 38.9134 67.5212 3.1291 35.6079 i 61.0866 3.3395 42.2529 64.3021 3.2855 38.8034 ia Accrued Accrued Current hat Current + Expect- Present ald tion] Present ry | t Pec whe. lien veke: Joes RUS SLES 467 468 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining A tiga. Total Remaining A rari Total Year. NCSMENt gion during 3portiza- | imvestment ond fl) amortisa. of year. Year. of year. of year. Year of year. 30 YEAR LIFE 30 YEAR LIFE | 4 per cent. 5 per cent. 18 $57.7471 $3.473 843.7260 $61.1066 $3.4499 fos on 13 19 54.2740 3.6121 | 49.3381 57.6567 3-6223 | 45.9656/ 12 20 50.6619 3.7565 53.0046 54.0344 3.8031 49.7690 II 21 46.9054 3.9068 57.0014 50.2310 3.9936 - 53.7626 10 22 42.9986 4.0631 | 61.0645 46.2374 4.1932 | 57.9358 3 23 38.9355 4.2256 ' 65.2901 42.0442 4.4030 | 62.3588 3 24 34.7099 4.3946 69.6847 37.6412 4.6231 | 66.9819 7 26 30.3153 4.5704 74.2551 33.0181 4.8542 71.8361 ; 26 25.7449 4.7532 79.0083 28.1639 5.0969 76.9330 J 27 20.9917 4.9433 83.9516 23.0670 5.3518 82.2848 : 28 16.0484 5.I4I1 89.0927 17.7152 5.6194 87.9042 29 10.9073 5.3467 94.4394 12.0958 5.9004 | 93.8046 30 5.5606 5.5606 100.0000 6.1954 6.1954 .100.0000 | 6 per cent. 7 per cent. ~ i |$100.0000 $1.2649 $ 1.2649 $100.0000 $1.0586 (® 1.0586 30 2 1 98.7351 1.3408 [ 2.6057 08.9414 1.1328 2.1914 29 3 97.3943 1.4212 4.0269 97.8086 1.2120 3.4034 28 4 ' 95.9731 1.5065 | 5.5334 96.5966 1.2969 4.7003 27 2 94.4666 1.5069 7.1303 95.2997 1.3877 6.0880 26 . 02.8697 1.60927 8.8230 03.9120 1.4848 | 7.5728 2b 91.1770 1.7943 10.6173 92.4272 1.5887 9.1615 24 J 89.3827 1.90I9 I2.5I92 90.8383 1.6999 . 10.8614 23 Y 87.4808 2.0161 14.5353 89.1386 1.8190 12.6804 22 10 85.4647 2.137008 16.6723 87.3196 1.9462 14.6266 21 II 85-3277 2. 26520018 .0375 85.3734 2.0825 16.7091 20 12 81.0625 2.4011 21.3386 83.2909 2.2283 18.9374 19 13 78.6614 2.5452 23.8838 81.0626 2.334321. 3217 18 14 76.1162 2.6980 26.5818 78.6783 2.551200123.8720 17 16 73.4182 2.8597 29.4415 76.1271 2.7297 26.6026 16 16 70.5585 3.0314 32.4720 73.3974 2.9208 29.5234 | 1b 17 67.5271 3.2133 | 35.6862 70.4766 3.1253 32.6487 | 14 13 64.3138 3.4061 39.0923 67.3513 3.3440 35.9927 13 IY 60.9077 3.6104 42.7027 64.0073 3.5782 39.5709 12 20 57.2973 3.8271 46.5208 60.4291 3.8286 43.3995 II Present Current a Present d Curcens section Bape ois valve. [dren ae, | Joecistien wr TAET ES TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining Ammortizas Total Remaining Amortiza Total Vor, vegan oo re Loum rwesmem SERIE, amend of year. year. {of year. of year. year, of year. { . 30 YEAR LIFE 30 YEAR LIFE 6 per cent. 7 per cent. 21 | $53.4702 $4.0566 $50.5864 $56.6005 $4.0966 $47.4961 22 49.4136 4.3001 54.8863 52.5039 4.3883 | 51.8704 23 45.1135 4.5581 59.4446 48.1206 4.6902 56.5696 3 24 40.5554 4.8316 64.2762 43.4304 5.0186 | 61.5882 | 2b 35.7238 5.1214 69.3976 38.4118 5.3608 66.9580 26 30.6024 5.4288 74.8264 33.0420 5.7457 72.7037 27 25.1736 5.7544 80.5808 27.2963 6.1479 78.8516 28 19.4192 6.0998 86.6806 21.1484 6.5782 85.4298 24 13.3194 6.4657 93.146 14.5702 7.0387 92.4683 30 6.8537 6.8537 100.0000 7.5315 7.5315 [00.0000 | 35 YEAR LIFE 35 YEAR LIFE 4 per cent. 5 per cent. © [$100.0000 81.3577 81.3577 S100.0000 $1.1072 $1.1072 3B 98.6423 1.4121 2.7698 98.8928 1.1625 2.2607 34 - 97.2302 1.4685 4.2383 97.7303 1.2207 3.4994 33 4 95.7617 1.5273 5.7656 96.5096 1.2816 4.7720 2 i] 04.2344 1.5884 7.3540 95.2880 1.3458 6.1178 b 92.6460 1.6519 9.0059 93.8822 1.4131 7.5309 30 90.9941 1.7179 10.7238 92.4691 1.4837 9.0146 29 89.2762 1.7867 12.5103 90.9854 1.5579 10.5725 28 y 87.4895 1.8581 14.3686 89.4275 1.6358 12.2083 27 10 ' 85.6314 1.9325 16.3011 87.7917 1.7176 13.9259 26 I 83.6089 2.0098 18.3109 86.0741 1.8035 15.7204 2b 12 81.6891 2.0002 20.4011 84.2706 1.8936 17.6230 24 13 79.5989 2.1737 22.5748 82.3770 1.9883 19.6113 23 14 77.4252 2.2607 24.8355 80.3887 2.0877 21.6990 22 15 75.1645 2.3512 27.1867 78.3010 2.1922 23.8912 21 16 72.8133 2.4452 29.6319 76.1088 2.3017 26.1929 20 17 70.3681 2.5430 32.1749 73.8071 2.4168 28.6097 19 3 67.8251 2.6447 34.8196 71.3903 2.5377 31.1474 1% 19 65.1804 2.7505 37.5701 68.8526 2.6645 33.8119 17 20 62.4299 2.8605 40.4306 66.1881 2.7978 36.6097 15 21 59.5604 2.9750 43.4056 ~~ 63.3903 2.9376 39.5473 13 v- 56.5944 3.0939 46.4995 60.4527 3.0845 42.6318 1. os 53.5005 3.2178 49.7173 57.3682 3.2388 45.8706 Accrued Accrued Current Tee Current Hae Expect- Present rary t Pp: t | Sor t = mm NE mm Te “3a! 469 470 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining pou Total Remaining + 5 oo Total Year. [507 SImentilsiin during 2 or HEn SnVOstmentily oy dirt | amortiza- a re 35 YEAR LIFE 35 YEAR LIFE 1 = : -— ! 4 per cent. 5 per cent. 24 $50.2827 $3.3464 $53 .0637 $54.1204 | $3.4007 $49.2713 ' 12 2b |. 46.9363 3.4803 56.5440 50.72378l1 3.5708 | 52.8421 In 26 | 43.4560 3.6195 60.1635 47.1579 | 3.7492 56.5913 | 10 27 , 39.8365 3.7642 63.9277 43.4087 ' 3.9367 60.5280 | J 28 36.0723 3.9149 67.8426 39.4720 4.1337 64.6617 ' 3 29 32.1574 4.0714 7I.9I40 35.3383 4.3403 69.0020 ! 30 28.0860 4.2343 76.1483 30.9980 4.5572 73.5592 J 3I 23.8517 4.4037 80.5520 26.4418 4.7851 © 78.3443 J 32 19.4480 4.5798 85.1318 21.6557 5.0244 83.3687 ; 33 14.8682 4.7630 89.8048 16.6313 5.2756 1 88.6443 34 10.1052 4.9535 94.8483 11.3557 5.5394 04.1837 3b 5. I5E7 5.15I7 100.0000 5.8163 5.8163 100.0000 6 per cent. 7 per cent. 1 $100.0000 $0.8974 $ 0.8974 $100.0000 $o.7234 ' $o0.7234 3b 2 99.1026 0.9512 1.8486 99.2766 0.7740 1.4974 34 3 08.1514 1.0083 2.8569 | 08.5026 0.8282 2.325633 4 97.1431 1.0688 53-9257 97.6744 + 0.8862 33-2718 32 5 96.0743 1.1320 5.0586 06.7882 0.9483 | 4.1601 3I 6 04.9414 1.2010 6.2596 05.8399 1.0146 . 5.1747 30 7 93.7404 1.2729 7.5325 | 04.8253 | 1.0856 6.2603 29 8 92.4675 1.3493 8.8818 93.7397 , 1.1616 7.4219 28 9 91.1182 1.4303 10.3121 02.5751 I.2429 8.6648 27 10 89.6879 1.5162 11.8283 01.3352 1.3300 0.9948 26 II 88.1717 1.6071 13.4354 00.0052 | 1.4230 11.4178 2b 12 86.5646 1.7034 15.1388 | 88.5822 1.5226 12.9404 24 13 84.8612 1.8058 | 16.9446 87.0596 1.6293 14.5697 23 14 83.0554 1.9140 «+ 18.8586 85.4303 1.7432 16.3129 22 15 81.1414 2.0289 20.8875 83.6871 * 1.8653 18.1782 21 16 vg.1125 2.1506 23.0381 81.8218 1.9959 . 20.1741 20 17 76.9619 2.270708 25.3173 | 79.8259 2.1356 | 22.3097 : 19 rs 74.6822 2.4165 27.7343 77.6903 2.2851 24.5048 ' 18 19 72.2657 2.5614 30.2957 75.4052 2.4450 1 27.0398 . 17 20 69.7043 2.7152 33.0109 72.9602 2.6162 29.6560 ! 16 21 66.9891 | 2.8780 35.8889 70.3440 2.7993 32.4553 | 15 22 64.1111 3.0507 38.9396 67.5447 2.0953 , 35.4506 14 Current Current i Expect- P. t NEA Present en a Jomecation. aus. |Jemreciation EL TL 5 TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining, Total Remaining, .. Total Year. ming. (ton during jmortizs- investment (Gf, amortiza- of year. | year. of year. of vear. Feat. of year. 35 YEAR LIFE 35 YEAR LIFE 6 per cent. 7 per cent. 23 $61 .0604 $3.2338 $42.1734 $64.5494 $3.2049 $38.6555 13 24 57.8266 3.4278 45.6012 | 61.3445 3.4293 42.0848 12 20 54.3988 3.6334 49.2346 57.9152 3.6603 45.7541 ' II 26 50.7654 3.8515 53.0861 54.2450 3.9262 49.6803 10 27 | 46.9139 4.0826 57.1687 50.3197 4.2010 53.8813 a 28 | 42.8313 4.3275 61.4962 46.1197 4.4951 58.3764 by 29 38.5038 4.5871 66.0833 41.6236 4.8097 63.1861 z 30 33.9167 4.8624 70.9457 36.8139 5.1464 68.3323 : 31 29.0543 5.1541 76.0998 31.6675 5.5067 73.8392 - a7 23.9002 5.4634 81.5632 26.1608 5.8922 79.7314 = 18.4368 5.7911 87.3543 20.2686 6.3046 86.0360 34 | 12.6457 6.1387 93.4930 13.9640 6.7459 | 92.7819 36 6.5070 6.5070 100.0000 7.218 7.2181 100.0000 40 YEAR LIFE 40 YEAR LIFE 4 per cent. 5 per cent. 3100.0000 $1.0524 $ 1.0524 $100.0000 $0.8278 $ 0.8278 40 98.9476 1.0944 2.1468 99.1722 0.8692 1.6970 39 97.8532 1.1382 3.2850 98.3030 0.9127 | 2.6097 38 96.7150 1.1838 4.4688 97.3903 0.9583 3.5680 37 : 95.5312 1.2311 5.6999 96.4320 1.0062 4.5742 36 94.3001 1.2803 6.9802 95.4258 1.0565 5.6307 3b 93.0198 1.3316 8.3118 94.3693 1.1093 6.7400 34 91.6882 1.3848 9.6966 93.2600 1.1648 7.9048 33 . 90.3034 1.4402 11.1368 92.0952 1.2230 9.1278 32 10 88.8632 1.4978 12.6346 90.8722 1.2842 10.4120 31 II 87.3654 1.5577 14.1923 89.5880 1.3484 11.7604 30 12 85.8077 1.6201 15.8124 88.2396 1.4158 13.1762 29 13 84.1876 1.6848 17.4972 86.8238 1.4866 14.6628 28 4 82.5028 1.7523 19.2495 85.3372 1.5610 16.2238 27 15 80.7505 1.8223 21.0718 83.7762 1.6390 17.8628 26 16 78.9282 1.8952 22.9670 82.1372 1.7210 19.5838 2b 17 | 77.0330 1.9710 24.9380 80.4162 1.8070 21.3908 24 r- 75.0620 2.0499 26.9879 78.6092 1.8074 23.2882 23 73.0121 2.1319 29.1198 76.7118 1.9923 25.2805 22 70.8802 2.21710031.3369 74.7195 2.0019 27.3724 | 21 Prost Curent Present Current Ee ae: 0! € ation . value. Fi oh aor value. — oo fo ABLES 471 472 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining poo. Total Remaining, Total Year. Dvetment on dunng Gertz imvestment {ionduring amortica of year. year of year. of year. | vear. of year. 40 YEAR LIFE 40 YEAR LIFE 4 per cent. 5 per cent. 21 $68.6631 $2.3059 $33.6428 | $72.6276 $2.1965 [$29.5689 | 20 22 66.3572 2.3980 36.0408 | 70.4311 |, 2.3063 | 31.8752 19 23 63.9592 2.4940 38.5348 68.1248 | 2.4216 | 34.2968 | 18 24 61.4652 2.5937 41.1285 65.7032 2.5427 | 36.8395 17 26 58.8715 2.6975 43.8260 63.1605 | 2.6698 39.5093 16 26 56.1740 2.8054 46.6314 60.4907 | 2.8033 | 42.3126 1b 27 | 53.3686 2.9176 49.5490 57.6874 | 2.9434 45.2560 14 28 50.4510 3.0343 52.5333 54.7440 | 3.0006 48.3466 13 29 47.4167 3.1557 55.7390 51.6534 3.2451 51.5917 I2 30 - 44.2610 3.2819 59.0209 48.4083 3.4074 54.9991 II 31 40.9791 3.4132 62.4341 45.0009 3.5778 58.5769 10 32 37-5659 3.5498 65.9839 41.4231 3.7567 62.3336 | 1 33 34.0161 3.6016 69.6755 37.6664 3.9445 66.2781 34 30.3245 3.8393 73.5148 33.7219 4.1417 70.4198 : 3b 26.4852 3.9930 77.5078 29.5802 4.3488 74.7686 : 36 22.4922 4.1526 81.6604 25.2314 4.5662 79.3348 u 37 18.3396 4.3189 85.9793 20.6652 4.7946 84.1204 28 14.0207 4.4915 90.4708 15.8706 5.0343 89.1637 39 9.5292 4.6712 - 95.1420 10.8363 5.2860 04.4497 40 4.8580 4.8580 100.0000 5.5503 5.5503 ‘100.0000 6 per cent. 7 per cent. ($100.0000 $0.6462 $ 0.6462 $100.0000 $o.5009 '$ 0.5009 40 © 99.3538 | 0.6849 | 1.3311 | 099.4901 - 0.5360 | 1.0365 39 3 98.6689 | 0.7260 ; 2.0571 08.9631 | 0.5735 1.6104 38 4 | 97.9429 | 0.7696 2.8267 08.3896 | 0.6136 | 2.2240 37 b 97.1733 | 0.8157 3.6424 97.7760 0.6566 2.8806 36 6 96.3576 0.8647 4.5071 97.1194 0.7026 3.5832 3b 7 95.4929 0.9166 5.4237 96.4168 0.7517 4.3349 34 3 94.5763 0.9716 6.3953 95.6651 0.8044 5.1393 33 9 93.6047 1.0299 7.4252 94.8607 + 0.8606 5.9999 ! 32 10 ' 092.5748 1.0016 8.5168 94.0001 0.9210 6.9209 31 IT 91.4832 1.15720K 0.6740 93.0791 0.9853 | 7.9062 30 i go.3260 1.2266 10.9006 92.0938 1.0544 8.9606 29 £3 89.0994 1.3002 12.2008 91.0394 1.1281 10.0887 28 £4 87.7992 | 1.3782 13.5790 89.9113 I.2071 11.2958 27 16 86.4210 1.4609 15.0399 88.7042 1.2017 12.5875 26 Current Current Expect- P t CE) P t en. value, [debreeation vane, [depron = TABLES TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining oc Total Remaining Amortiza Total Year. Hytment omdunng ortif petment (iden omort of year. | year | of year of year. year. of year. 40 YEAR LIFE 40 YEAR LIFE 6 per cent. 7 ver cent. 16 | $84.9601 $1.5485 [$16.5884 $87.4125 $1.3820 $13.9695 26 17 83.4116 1.6415 18.2299 86.0304 1.4788 15.4483 24 r8 81.7701 1.7399 19.9698 84.5517 1.5823 17.0306 23 19 80.0302 1.8443 21.8141 | 82.9694 1.6930 18.7236 22 20 78.1859 1.9550 23.7691 || 81.2764 1.8116 20.5352 21 71 76.2309 2.0724 25.8415 : 79.4648 1.9384 22.4736 20 22 74.1585 2.1966 28.0381 77.5264 2.0741 24.5477 19 ol 71.9619 2.3284 30.3665 75.4523 2.2192 26.7669 18 24 69.6335 2.4682 32.8347 73.2331 2.3746 29.1415 17 25 67.1653 2.6162 35.4509 ' 70.8585 2.5408 31.6823 16 26 | 64.5491 2.7732 38.2241 + 68.3177 2.7187 34.4010 ' 1b 27 . 61.7759 2.9396 41.1637 65.5990 2.9090 37.3100 14 28 58.8363 3.1160 44.2797 ' 62.6900 3.1126 40.4226 13 29 55.7203 3.3029 47.5826 | 59.5774 3.3305 43.7531 12 30 52.4174 3.5011 51.0837 56.2469 3.5636 47.3167 IT 31 48.9163 3.7112 54.7949 52.6833 3.8131 51.1208 10 32 45.2051 3.9339 58.7288 48.8702 4.0800 55.2008 “ 3 41.2712 4.1699 62.8987 44.7902 4.3656 59.5754 3 34 | 37.1013 4.4200 67.3187 ' 40.4246 4.6712 64.2466 : 35 32.6813 4.6853 72.0040 35.7534 4.9982 69.2448 6 36 27.9960 4.9664 76.9704 30.7552 5.3480 74.5028 © . i 7 23.0206 5.2644 82.2348 25.4072 5.7225 80.3153 : 17.7652 5.5802 87.8150 19.6847 6.1229 86.4382 ad | 12.1850 5.9151 93.7301 13.5618 6.35516 92.9898 40 6.2699 | 6.2699 100.0000 7.0102 | 7.0I02 [00.0000 45 YEAR LIFE 45 YEAR LIFE 4 per cent. 5 per cent. 3100.0000 $0.8262 $0.8262 $100.0000 $0.6262 $0.6262 46 99.1738 0.8593 1.6855 | 99.3738 0.6575 1.2837 | 44 | 98.3145 ' 0.8937 2.5792 98.7163 0.6903 1.9740 | 43 ‘ 97.4208 | 0.9204 3.5086 98.0260 0.7249 2.6989 42 , | 96.4914 0.9666 4.4752 97.3011 0.7611 3.4600 41 95.5248 1.0053 5.48053 96.5400 0.7992 4.2592 4 94.5195 1.0455 6.5260 95.7408 0.8392 5.0084 3: 93.4740 , 1.0872 7.6132 94.9016 0.8810 5.9794 3u Current Current Expect- Present § A Present Rs d t di t . value, [depreciation value. [depreciation] gaey. 473 474 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) " Remaining | Amoriiza. Total Remaining Amiortizo Total Year, VOSUmENt fon Gunny Goris investment | fon, gmortiag- of year. years of year. of year. year. of year. 45 YEAR LIFE 45 YEAR LIFE 4 per cent. 5 per cent. 9 $92.3868 $1.1308 $ 8.7440 $94.0206 | $0.9251 $ 6.9045 | 37 10 | gr.2560 1.1760 | 9.9200 93.0955 0.9714 | 7.8759 36 aT 90.0800 1.223008 I1.3430 92.1241 1.0200 8.8959 | 3b 12 88.8570 1.272000 12.4150 OI.IO4I 1.0710 | 9.9669 34 13 87.5850 1.322000 1377379 00.0311 1.12458 17.0014 33 14 86.2621 1.375700 N5-1136 88.9086 1.13078 22721 32 15 84.8864 1.4308 16.5444 87.7270 1. 23030 73. 51 10M ¥ 16 83.4556 1.4880 18.0324 86.4881 1.3018 14.8137 30 17 81.9676 1.5476 19.5800 85.1863 1.3668 16.1805 29 1% 80.4200 1.6094 21.1804 83.8195 1.435200 17.6157 28 19 78.8106 1.6738 22.8632 82.3843 1.5070 19.1227 27 20 77.1368 1.7408 24.6040 80.8773 1.5823 20.7050 26 21 75.3960 1.8104 26.4144 79.2050 1.6614 22.3664 2b 22 73.5856 1.8828 28.2972 77.6336 1.7445 24.1109 24 23 71.7028 1.9581 30.2553 75.8891 1.8317 25.9426 23 24 69.7447 2.0365 32.2918 74.0574 1.922300 27. 86500-0022 26 67.7082 2.1180 34.4098 72.5347 2.0195 29.8854 I 26 65.5902 2.2026 36.6124 70.1146 2.1205 32.0059 20 27 63.3876 2.2907 38.9031 67.9941 2.226400 31.2323 19 28 61.0969 2.3824 41.2855 65.7677 2.3378 36.5701 ' 18 29 58.7145 2.4777 43.7632 63.4209 2.4548 39.0249 | 17 30 56.2368 2.5768 46.3400 60.9751 2.5773 41.6022 ' 16 3I 53.6600 2.6798 49.0198 58.3978 2.7062 44.3084 1b 32 50.9802 2.7870 51.8068 55.6916 2.8417 47.1501 14 33 48.1932 2.8986 54.7054 52.8499 2.9837 50.1338 3 34 45.2946 3.0144 57.7198 49.8662 3.1328 53.2666 I2 3b 42.2802 3.1350 60.8548 46.7334 3.2806 56.5562 iI 36 39.1452 3.2605 64.1153 43.4438 3.4539 60.0101 10 37 35.8847 3.3909 67.5062 39.9899 3.6267 63.6368 7 a8 32.4938 + 3.5264 71.0326 36.3632 3.8081 67.4449 ¢ 39 28.9674 3.6676 74.7002 32.5551 3.9983 71.4432 40 25.2098 3.8142 78.5144 28.5568 4.1984 75.6416 ) 41 21.4836 3.9669 82.4813 | 24.3584 4.4083 80.0499 J 42 17.5187 4.1255 - 86.6068 19.9501 4.6286 84.6785 43 13.3932 4.2905 90.8973 15.3215 4.8600 89.5385 44 9.1027 4.4621 95.3594 10.4615 5.1032 94.6417 | 456 4.6406 4.6406 100.0000 5.3583 5.3583 100.0000 | * p hy Current P tg | Current | Expect- Soe (Joma value, [depreciation | Fears. TAL TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining poo Total Remaining | 4 oreion Total Your Trot vel Soon iver on dung i of vear. year. of year. of year. year. |, ‘of vear. 45 YEAR LIFE 45 YEAR LIFE 6 per cent. 7 per cent. $100.0000 $0.4700 $ 0.4700 $100.0000 $o0.3500 |$ 0.3500 4b 99.5300 0.4983 | 0.9683 99.6500 0.3744 | 0.7244 44 99.0317 0.5281 ' 1.4964 99.2756 0.4007 1.1251 43 : 98.5036 0.5599 | 2.0563 98.8749 0.4287 1.5538 42 2? 97.9437 0.5934 2.6497 98 .4462 0.4587 2.0125 Wh 4y : 97.3503 0.6200 3.2787 97.9875 0.4908 | 2.5033 40 96.7213 © 0.6668 3.9455 97.4967 0.5252 3.0285 39 96.0545 , 0.7068 4.6523 96.9715 0.5620 3.5905 38 : 95.3477 ©.7492 5.4015 96.4095 0.6013 4.1918 37 10 94.5985 0.7941 6.1956 95.8082 0.6434 4.8352 36 II 93.8044 0.8418 7.0374 95.1648 0.6884 5.5236 3b 12 92.9626 0.8923 7.9297 94.4764 0.7366 6.2602 34 13 92.0703 0.9458 8.87553 93.7398 0.7882 7.0484 3; 14 91.1245 1.0026 9.8781 92.9516 0.8433 7.8917 34 15 90.1219 1.0628 10.9409 92.1083 0.9024 8.7941 31 6 89.0591 1.1265 12.0674 91.2059 0.9655 9.7596 | 30 17 87.9326 1.1941 13.2613 00.2404 1.0331 10.7927 ° 29 8 86.7383 1.2657 14.5272 89.2073 1.1055 11.8982 28 Ly 85.4728 1.3417 15.8689 88.1018 1.1828 13.0810 27 20 84.1311 1.4222 17.2911 ' 86.9190 1.2657 14.3467! 26 21 82.7089 1.5075 18.7986 85.6533 1.3542 15.7009 2b 22 81.2014 1.5979 20.3965 84.2991 1.4490 17.1499 24 7 79.6035 1.6939 22.0904 82.8501 1.5504 18.7003 23 z4 77.9096 1.7954 23.8858 81.2997 1.6590 20.3593 22 26 76.1142 1.9032 25.7890 79.6407 ' 1.7751 22.1344 1 21 26 74.2110 2.0174 27.8064 77.8656 1.8994 24.0338 20 27 72.1936 2.1385 29.9449 75.9662 2.0323 26.0661 19 28 70.0551 - 2.2667 32.2116 73.9339 | 2.1746 28.2407 18 29 67.7884 2.4028 34.6144 71.7593 2.3268 30.5675 17 30 65.3856 2.35469 37.1613 69.4325 2.4897 33.0572! 16 31 62.8387 ' 2.6997 39.8610 66.9428 2.6640 35.7212 1B 22 60.1390 2.8617 42.7227 64.2788 2.8504 38.5716 14 31 57.2773 3.0334 45.7561 61.4284 3.0499 41.6215 13 5% 54.2439 | 3.2154 48.9715 58.3785 3.2635 44.8850 12 35 51.0285 | 3.4083 52.3798 55.1150 3.4920 48.3770 1x C t C t Present deer Present ES 3 Expect- value. tion during value. , tion during ay year. year. : : BLES 475 476 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining : A iortizan Total Remaining | Arnortizes Total Year. MESON iionduring hori vestment oon during SEY of year. | year. | of year. . of year. year. of year. 45 YEAR LIFE 45 YEAR LIFE is 6 per cent. 7 per cent. 36 $47.6202 $3.6129 855-9927 $51.6230 $3.7363 |$s52.1133 10 37 | 44.0073 3.8296 | 59.8223 47.8867 3.9979 | 56.1112 9 39 10.1777 4.0594 63.8817 43.8888 4.2777 | 60.3889 | 8 39 36.1183 4.3030 68.1847 39.6111 4.5772 | 64.9661 7 40 31.3153 4.56110 72. 7458 35.0339 4.8976 | 69.8637 3 41 27.2542 4.8348 77.5806 30.1363 5.2404 | 75.1041 J 42 22.4194 5.1249 82.7055 24.8959 5.6073 ! 80.7114 43 17.2045 5.4324 88.1379 19.2886 5.9997 | 86.7111 44 11.8621 5.7583 1 93.8962 13.2889 6.4197 93.1308 4b 6.1038 6.1038 100.0000 6.8692 6.8692 100.0000 | I 50 YEAR LIFE 50 YEAR LIFE 4 per cent. 5 per cent. + |[$100.0000 $o.6550 $ 0.6550 ($100.0000 $o.4777 I$ o.4777 b0 2 99.3450 0.6812 | 1.3362 99.5223 0.5015 0.9792 49 3 098.6638 0.7085 2.0447 99.0208 0.5267 1.5059 48 4 97.9553 ©.7368 2.7815 98.4941 0.5529 2.05838 47 d 97.2185 0.7663 3.5478 97.9412 0.5806 2.6394 46 3 06.4522 0.7969 4.3447 97.3606 0.6097 3.2491 4b 7 95.6553 0.8288 5.1735 96.7509 0.6401 3.8802 44 0 94.8265 0.8620 6.0355 06.1108 0.6722 4.5614 43 9 93.9645 0.8964 6.9319 95.4386 0.7057 5.2671 42 10 93.0681 0.9323 7.8642 04.7329 0.7410 6.0081 41 iI 92.1358 0.9606 8.8338 93.9919 0.7781 6.7862 40 12 91.1662 1.0084 9.8422 93.2138 0.8170 7.6032 39 13 90.1578 1.0487 10.8909 92.3968 0.8578 8.4610 38 14 89.1001 | 1.0906 11.9813 9I.5300 0.9008 9.3618 37 16 88.0185 1.1343 13.1153 90.6382 0.9457 , 10.3075 36 16 86.8842 1.1797 14.2955 89.6925 0.9931 ' 11.3006 3b 17 | 85.7045 1.226301 .5223 88.6994 1.0427 12.3433 34 18 84.4777 1.2759 16.7982 87.6567 ' 1.0048 13.4381 33 19 | 83.2018 1.327000 18.1252 86.5619 1.1496 14.5877 32 20 81.8748 1.3800 19.5052 85.4123 1.2071 15.7948 I 21 80.4948 1.4353 20.9405 84.2052 1.2674 17.0622 30 22 79.0595 1.4926 22.4331 82.9378 1.3307 18.3929 | 29 23 77.5669 1.5523 | 23.9854 81.6017 1.3974 19.7903 28 Current Current Expect- Dp t a P t hi 1 value, |Qepreciation Ce pitien | goer TABLES TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining A 1 ortiza- Total Remaining 5 ooo Total Year, | iBVeStment (onuring amortize: investment on quring 4MOTHZy of year. year. | of year. of year. year. | of year. so YEAR LIFE 50 YEAR LIFE 4 per cent. 5 per cent. 24 ~~ $76.0146 $1.6144 $25.5998 $80.2097 81.4672 $21.2575 27 26 74 .4002 1.6791 27.2789 78.7425 1.5405 22.7980 26 26 72.7211 1.7461 29.0250 77.2020 1.6176 24.4156 | 26 27 70.9750 1.8161 30.8411 | 75.5844 1.6084 26.1140 24 28 69.1589 1.8887 32.7208 73.8860 1.7834 27.8974 23 29 67.2702 1.9642 34.6940 72.1026 1.8726 29.7700 22 30 ' 65.3060 2.0427 36.7367 70.2300 1.9661 31.7361 21 31 63.2633 2.1245 38.8612 68.2639 2.0645 33.8006 20 32 61.1388 2.2095 41.0707 66.1994 2.1677 35.9683 19 74 58.9293 2.2979 43.3686 ' 64.0317 2.2761 38.2444 13 34 56.6314 2.3897 45.7583 | 61.7556 2.3899 40.6343 17 36 54.2417 2.4854 48.2437 | 59.3657 2.5095 43.1438 16 36 51.7563 2.5847 50.8284 56.8562 2.6347 45.7785 1b 37 49.1716 2.6882 53.5166 54.2215 2.7666 48.5451 14 2d 46.4834 2.7957 56.3123 + 51.4549 2.9050 S5I.4501 13 sy 43.6877 2.9075 359.2198 48.5499 3.0501 54.5002 12 40 40.7802 3.0238 62.2436 45.4998 3.2027 57.7029 II 41 37.7564 3.1448 65.3884 42.2971 3.3629 61.0658 10 42 34.6116 3.2706 68.6390 38.9342 3.5309 64.5947 | ¢ 43 31.3410 3.4013 72.0603 35.4033 3.7075 08.3042 44 27.9397 3.5375 75.5978 31.6958 3.8929 72.1971 | 4b 24.4022 3.6789 79.2767 27.8029 4.0875 76.2846 : 46 20.7233 3.8261 83.1028 23.7154 4.2919 80.5763 47 | 16.8972 3.9791 87.0819 19.4235 4.5065 85.0830 48 12.9181 4.1383 01.2202 14.9170 4.7319 89.8149 35 8.7798 4.3038 95.5240 10.1851 4.9683 94.7832 60 | 4.4760 4.4760 100.0000 5.2168 5.2168 100.0000 6 per cent. 7 per cent. $100.0000 $0.3444 $0.3444 $100.0000 $0.2460 $o0.2460 50 99.6556 0.3651 0.7095 99.7540 0.2632 0.5092 49 99.2905 0.3870 1.0965 99.4908 0.2816 0.7908 48 98.9035 0.4102 | 1.35067 99.2092 0.3014 1.0922 | 47 98.4933 0.4349 | 1.9416 98.9078 0.3224 1.4146 | 4% 98.0584 0.4609 , 2.4025 98.5854 0.3450 1.7596 | Present ~~, Current Present | Current Expect- vale, depron ee, | demeatin = Vo 477 478 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining | pnortimn Total | Remaining Amortizs. Total Year, nvestment oo ogo amortiza- investment fiondur: amortiza- = Tepe [S030 Sneddon dual ind 50 YEAR LIFE 50 YEAR LIFE 6 per cent. 7 per cent. ~ $97.5975 $0.4886 |$ 2.8911 $98.2404 ' $0.3692 '$ 2.1288 a4 z 97.1089 0.5179 3.4090 1 97.8712 0.3950 | 2.5238 43 9 96.5910 0.5489 | 3.9579 97.4762 0.4226 | 2.9464 42 10 96.0421 0.5819 4.5398 97.0536 0.4522 3.3986 41 II | 95.4602 0.6169 5.1567 96.6014 0.4839 3.8825 40 12 94.8433 0.6538 5.8105 96.1175 0.5178 4.4003 39 13 94.1895 0.6931 | 6.5036 95.5997 ©.5540 4.9543 38 14 93.4964 « 0.7346 | 7.2382 95.0457 0.5928 5.5491 37 15 92.7618 0.7787 8.0169 94.4529 0.6343 6.1814 36 16 91.9831 0.8255 8.8424 93.8186 0.6786 6.8600 3b 17 91.1576 | 0.8749 9.7173 93.1400 = 0.7262 7.5862 34 18 go. 2827 0.9275 10.6448 02.4138 | o.7771 8.3633 33 19 89.3552 0.9831 11.6279 91.6367 0.8314 9.1947 32 20 88.3721 1.0421 12.6700 90.8053 0.8896 10.0843 iI 21 | 87.3300 1.1046 13.7746 89.9157 0.9519 11.0362 30 22 | 86.2254 1.1710 14.9456 88.9638 1.0185 12.0547 29 23 ' 85.0544 1.2411 16.1867 87.9453 1.0898 13.1445 28 24 83.8133 1.31560 17 's023 86.8555 1.1661 14.3106 27 26 82.4977 1.3946 18.8969 85.6804 1.2477 15.5583 26 26 81.1031 1.473200 20.3751 84.4417 1.3351 16.8934 2b 27° 70.6240 1.5670 21.9421 83.1066 1.423500 18.3210 24 28 78.0579 1.6610 23.6031 81.6781 1.5285 19.8504 23 29 | 76.3969 I.7606 25.3637 80.1496 | 1.6355 21.4859 22 30 74.6363 1.8662 27.2299 78.5141 3.750023. 2350 21 3I 72.7701 1.9783 29.2082 76.7641 1.8725 25.1084 20 32 | 70.7918 2.0969 3I.305I 74.8916 2.0036 27.1120 19 33 68.6949 2.22278 833.5273 72.8880 2.1438 29.2558 18 34 66.4722 2.3561 | 35.8839 | 70.7442 | 2.2030 31.5497 || 17 36 64.1161 2.4975 38.3814 68.4503 | 2.4545 34.0042 ' 16 36 61.6186 2.6473 41.0287 65.9958 2.6263 36.6305 1b 37 58.9713 2.8061 43.8348 63.3695 2.8101 38.4406 | 14 2 56.1652 2.9745 46.8003 60.5504 3.0068 42.4474 ' 13 53.1907 3.1530 49.9623 = 57.5526 | 3.2173 1 45.6647 | 12 50.0377 3.3422 53.3045 54.3353 3.4425 | 49.1072 2 46.6955 3.5427 56.8472 50.8928 = 3.6835 ' 52.7907 | 10 C t C t Present Sn Present dor Re value. tion during value. | tion during | Years: year. year. TABLES TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining Aportiza- Total Remaining A ..ortiza- Total Year. investment tion duri amortiza- investment tion dur amortiza- =I TEES ar me yer ase so YEAR LIFE so YEAR LIFE 6 per cent. 7.per cent. 42 $43.1528 83.7553 $60.6025 $47.2093 ' $3.9414 856.7321 43 39.3975 3.9805 64.5830 43.2679 4.2172 | 60.9493 44 35.4170 4.2194 68.8024 | 39.0507 4.5124 65.4617 | - 45 31.1976 4.4726 73.2750 34.5383 4.8284 70.2001 | 46 26.7250 4.7410 78.0160 29.7099 5.1662 75.4563 | 47 21.9840 5.0253 83.0413 24.5437 5.5280 80.9843 48 16.9587 5.3270 88.3683 19.0157 5.9149 86.8992 ar 11.6317 5.6465 04.0148 13.1008 6.3289 03.2281 bu 5.9852 5.9852 100.0000 6.7719 | 6.7719 100.0000 6o YEAR LIFE 60 YEAR LIFE 4 per cent. 5 per cent. $100.0000 $0.4202 $ 0.4202 $100.0000 $0.2828 $ 0.2828 60 99.5798 ©0.4370 ©0.8572 = 99.7172 ©0.2970 0.5798 59 99.1428 0.4544 1.3116 99.4202 0.3118 | 0.8916 58 ) 98.6884 0.4727 | 1.7843 99.1084 0.3274 | 1.2190 5 2 08.2157 0.4916 2.2750 98.7810 0.3437 1.5627 ! 56 a 97.7241 0.5112 2.7871 08.4373 0.3610 1.9237 bb 97.2129 O.5317 3.3188 98.0763 0.3790 2.3027 sh 96.6812 0.5529 3.8717 97.6973 0.3980 2.7007 5 ~ 96.1283 0.5750 4.4467 97.2993 0.4178 3.11853 52 10 95.5533 0.5981 | 5.0448 06.8815 0.4388 3.5573 51 11 94.9552 0.6220 5.6668 06.4427 0.4606 4.0179 60 12 04.3332 | 0.6468 6.3136 95.9821 0.4837 4.5016 49 13 93.6864 0.6728 6.9864 95.4984 0.5079 5.0095 48 14 93.0136 0.6996 7.6860 94.9905 ©.5333 5.5428 47 156 92.3140 0.7276 8.4136 94.4572 0.5600 6.1028 46 16 91.5864 0.7567 9.1703 93.8972 0.5880 6.6908 4b 17 90.8297 0.7870 9.9573 93.3092 0.6174 7.3082 44 18 go.og427 0.8185 10.7758 92.6918 0.6481 7.9563 43 19 89.2242 0.8512 11.6270 92.0437 ©0.6807 8.6370 42 20 88.3730 0.8853 12.5123 91.3630 0.7146 9.3516 4I 21 87.4877 0.9207 13.4330 90.6484 0.7504 10.1020 | 40 2 86.5670 ©.9575 14.3905 89.8980 0.7880 10.8900 3. . 85.6005 0.9958 15.3863 89.1100 0.8273 11.7173 | 36 Present ac Present PAC gi n Bape: : 1at10: W value. oe roar. value. i ng | Too. 479 480 VALUATION , DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining [UAThortiza. Total Remaining Aerartiznh Total Year. | 'PUSiice: | fon during! gots investment (REL | amortizy of year. Feat. of year. of year. | year. of year. 60 YEAR LIFE 60 YEAR LIFE ! 4 per cent. 5 per cent. 24 + $84.6137 ' $1.0356 [$16.4219 $88.2827 ' $0.8686 (812.5859 | 37 26 83.5781 1.0771 17.4990 87.4141 0.9122 ' 13.4981 36 26 | 82.5010 1.1201 18.6101 86.5019 0.9577 14.4558 3b 27 ! 81.3809 1.1650 19.7841 85.5442 1.0056 15.4614 34 28 80.2159 1.2115 20.9956 84.5386 | 1.0559 16.5173 3 29 79.0044 I.26000 22.2556 83.4827 1.1087 | 17.6260 2 30 77.7444 1.3104 23.5660 82.3740 © 1.1641 18.7901 oY 31 76.4340 1.3629 24.9289 81.2009 1.2223 20.0124 30 32 75.0711 ° 1.4173 26.3462 79.9876 1.2835 21.2059 29 33 73.6538 1.4741 27.8203 | 78.7041 1.3476 22.6435 28 34 72.1797 1.5329 29.3532 77-3505 1.4149 24.0584 27 3b 70.6468 1.5044 30.9476 75.9416 1.4858 25.5442 26 36 69.0524 1.6580 32.6056 74.4558 1.5600 27.1042 2b 37 67.3944 1.7245 34.3301 72.8958 1.6380 28.7422 24 38 65.6699 1.7934 36.1235 71.2578 1.7200 30.4622 23 39 63.8765 1.8651 37.9386 69.5378 1.8059 32.2681 22 40 62.0114 1.9397 39.9283 67.7319 1.8962 34.1643 21 41 60.0717 2.0173 41.9456 65.8357 1.9911 36.1554 20 42 58.0544 2.0980 44.0436 63.8446 2.0006 38.2460 19 43 55.9564 2.1820 46.2256 61.7540 2.1951 40.4411 18 44 53.7744 2.2692 48.4948 59.5589 2.3049 42.7460 17 45 5I.5052 2.3599 50.8547 57.2540 2.4201 ! 45.1661 | 16 46 . 49.1453 2.4544 53.3001 54.8339 2.5411 47.7072 1B 47 46.6909 2.5526 55.8617 52.2028 2.6682 50.3754 14 48 44.1383 2.6546 58.5163 49.6246 2.8016 53.1770 zs 49 41.4837 2.7609 61.2772 46.8230 | 2.9416 , 56.1186 | 12 60 38.7228 2.8712 64.1484 43.8814 3.0888 59.2074 1 I 5I 35.8516 2.9861 67.1345 | 40.7926 3.2432 62.4506 10 52 32.8655 3.1056 70.2401 37.5494 3.4053 65.8559 ) 53 29.7599 3.2298 73.4699 = 34.1441 1 3.5756 © 69.4315 ? 54 26.5301 3.3590 76.8289 30.5685 3.7544 73.1859 | 65 23.1711 3.4933 80.3222 26.8141 3.9421 77.1280 : 56 19.6778 3.6331 83.9552 22.8720 4.1392 81.2672 © J 57 16.0447 3.7784 87.7337 18.7328 4.3462 85.6134 ; 58 12.2663 3.9205 01.6632 14.3866 4.5635 + 90.1769 59 | 8.3368 4.0867 95.7499 9.8231 4.70917 94.9686 | 60 4.2501 4.2501 100.0000 5.0314 5.0314 I0O.0000 iP: GE Current Present Current asa Bape. TE draton we fqameton $= TABLES TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining A ortiza- Total Remaining Amortiza- Total Year. VOOR. Gon orn, AO nr tion during Aortiza: of year. year. | of year. of year. | year. , of year. 60 YEAR LIFE 60 YEAR LIFE 6 per cent. 7 per cent.’ '$100.0000 $0.1876 $ 0.1876 $100.0000 $0.1229 $ 0.1229 60 99.8124 0.1988 0.3864 | 99.8771 0.1316 0.2545 59 3 99.6136 0.2108 0.5972 - 99.7455 ©.I407 0.3952 58 & | 99.4028 0.2234 0.8206 99.6048 0.1506 0.5458 57 o 99.1794 ' 0.2368 1.0574 09.4542 0.1611 0.7069 56 6 98.9426 0.2510 1.3084 99.2931 ©.1724 ©.8793 Bb 7 98.6916 0.2661 1.5745 99.1207 0.1845 1.0638 5, ] 98.4255 0.2820 1.8565 98.9362 0.1974 1.2612 ‘ y 98.1435 0.2989 2.1554 98.7388 0.2112" 1.4724 g 10 | 97.8446 0.3169 2.4723 98.5276 0.2260 1.6984 sf II 97.5277 ©.3360 2.8083 98.3016 0.2418 1.9402 60 12 | 97.1917 0.3560 3.1643 98.0598 0.2587 2.1989 49 13 ' 96.8357 0.3775 3.5418 97.8011 0.2768 2.4757 43 14 96.4582 0.4000 3.9418 97.5243 0.2963 2.7720 4 16 96.0582 0.4241 4.3659 ° 97.2280 0.3169 3.0839 4b 16 95.6341 0.4495 4.8154 06.9111 0.3392 3.4281 4b 17 | 95.1846 0.4765 5.2919 96.5719 0.3629 3.7910 44 8 94.7081 0.5051 5.7970 96.2090 0.3882 4.1792 43 £9 94.2030 ©.5354 6.3324 95.8208 0.4154 4.5947 42 20 93.6671 ©0.5675 6.8999 95.4053 0.4446 5.0393 4I 21 93.1001 0.6016 7.5015 94.9607 0.4756 5.5149 40 22 92.4985 0.6377 8.1392 94.4851 0.5089 6.0239 39 23 91.8608 0.6759 8.8131 93.9761 0.5446 6.5685 38 24 91.1849 0.7165 9.5316 93.4315 0.5827 7.1512 37 26 90.4684 0.7594 10.29I0 92.8488 0.6235 7.7747 36 26 89.7090 0.8051 11.0961 92.2253 0.6672 8.4419 3b 27 88.9039 0.8533 11.9494 91.5581 0.7138 9.1557 34 28 88.0506 0.9045 12.8539 90.8443 0.7638 9.9196 33 29 87.1461 0.9589 13.8128 go.0804 0.8173 10.7369 32 30 86.1872 1.0163 14.8291 89.2631 0.8745 11.6114 31 31 85.1709 1.0773 15.9064 88.3886 0.9357 12.5471 30 32 84.0936 1.1420 17.0484 87.4529 1.0012 13.5483 29 : 82.9516 1.2104 18.2588 86.4517 1.0713 14.6196 28 3a 81.7412 1.2831 19.5419 85.3804 | 1.1463 15.7659 27 36 80.4581 1.3601 20.9020 84.2341 1.2265 16.9924 26 , 79.0980 1.4417 22.3437 | 83.0076 1.3174 18.3048 2b or 77.6563 1.5282 23.8719 81.6952 1.4043 19.7091 24 Present 4 Current Present 4 Curent | Expect- epreclation epreciation . value. | a year. value. hn sn] J Se 481 482 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining 5 ou. | Total Remaining [ Amortiz Total Vear, investment tion during amortiza- investment tion a, amortiza- Cefrant | Cree RE aR [han pe 60 YEAR LIFE 60 YEAR LIFE Sa Tein, on - an) ay _ 6 per cent. 7 per cent. ] 38 | $76.1281 $1.6199 825.4918 . $80.2909 | $1.5025 jour. 2ra | 23 39 | 74.5082 1.717181. 27.20800 78.7384 1.6078 | 22.8194 22 40 © 72.7911 1.8201 29.0290 77.1806 1.7203 24.5397 21 41 70.9710 1.9203 30.9533 75.4603 1.8407 | 26.3804 | 20 42 69.0417 | 2.0452 33.0035 73.6196 | 1.9695 | 28.3499 LE 43 66.9965 | 2.1677 35.1712 71.6501 | 2.1074 | 30.4573 | 18 44 64.8288 2.2978 37.4690 ' 69.5427 ' 2.2550 | 32.7123 | 17 45 62.5310 2.4357 39.9047 67.2877 2.432700 35-1250 16 46 60.0953 2.5819 42.4866 64.8750 2.5817 37.7067 | 1B 47 57.5134 2.7367 i 45.2233 62.2033 2.7624 40.4691 © 14 43 54.7767 2.9010 48.1243 59.5300 2.9557 43.4248 | 13 49 51.8757 3.0750 51.1993 56.5752 3.1627 | 46.5875 | 12 60 48.8007 3.2596 54.4589 53.4125 3.3841 49.9716 © 1 51 45.5411 3.4551 57.9140 50.0284 3.6209 | 53.5925 10 52 42.0860 3.6624 61.5764 46.4075 3.8744 | 57.4669 9 53 38.4236 3.8821 65.4585 42.5331 4.1456 61.6125 3 54 34.5415 4.1151 69.5736 38.3875 4.4358 66.0483 65 30.4264 4.3620 73.9356 33.9517 4.7463 70.7946 = 56 26.0644 4.6237 78.5593 29.2054 5.0786 45.8732 J 57 21.4407 4.9012 83.4605 24.1268 | 5.4340 81.3072 8 16.5395 5.1952 88.6557 18.6928 5.8144 87.1216 59 11.3443 5.5069 04.1626 12.8784 6.2215 03.3431 ; 60 5.8374 5.8374 100.0000 6.6569 6.6569 100.0000 : 75 YEAR LIFE 75 YEAR LIFE 4 per cent. 5 per cent. 1 |$100.0000 $o.2229 | $o0.2229 |$100.0000 $o0.1322 | $o.1322 ! 75 2 00.7771" 0.23130 0. 4547 09.8678 | 0.1387 | 0.2709 74 3 99.5453 0.2411 0.6958 99.7201 0.1457 0.4166 73 4 99.3042 0.2507 0.9465 || 99.5834 | o.1530 | 0.5696 72 b 99.0535 0.2608 1.2073 | 99.4304 0.1607 0.7303 71 5 93.7027 0.27120 1.4733 99.2697 0.1686 ' 0.8989 70 ‘ 08.5215 0.2820 1.7605 09.IOII Oo. 1772 1.0761 69 08.2395 | 0.2934 2.0539 08.9239 0.1859 1.2620 68 97.9461 | 0.3050 2.3589 98.7380 0.1953 1.4573 , 07 du 97.6411 0.3172 2.6761 08.5427 0.2050 ' 1.6623 66 P t Current P t Current | Expect- ares, | Seprecation vas, eprciation To TABLES TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Ri ini : Total R ini : Total , Domaining amortise. Tol, RANE | Amortise-) armors. "beginning oar fl tion end beginning a g| tion end of year. | year. of year. of year. | Year of year. 75 YEAR LIFE 75 YEAR LIFE 4 per cent. 5 per cent. a ¢ 11 | $97.3239 $0.3299 $3.0060 $98.3377 $o.2153 $1.8776 6b 12 96.9940 0.3432 3.3492 98.1224 0.2260 2.1036 64 13 96.6508 0.3568 3.7060 97.8964 0.2374 2.3410 63 14 96.2940 0.3712 4.0772 97.6590 0.2492 2.5902 62 15 95.9228 0.3860 4.4632 97.4098 0.2616 2.8518 61 16 95.5368 0.4014 4.8646 97.1482 0.2749 3.1267 60 17 | 95.1354 0.4175 5.2821 96.8733 0.2884 3.4151 59 18 94.7179 0.4342 5.7163 96.5849 0.3029 3.7180 58 19 94.2837 0.4515 6.1678 96.2820 0.3181 4.0361 57 20 | 93.8322 0.4696 6.6374 95.9639 0.3339 4.3700 56 21 93.3626 0.4884 7.1258 95.6300 0.3507 4.7207 Bb 22 92.8742 0.5080 7.6338 95.2793 0.3682 5.0889 54 2: 92.3662 0.5282 8.1620 94.9I1I 0.3866 8.475% 53 24 91.8380 0.5494 8.7114 94.5245 0.4059 5.8814 52 2b 91.2886 0.5714 9.2828 94.1186 0.4262 6.3076 51 26 go.7172 0.5942 9.8770 03.6924 0.4476 6.7552 60 27 90.1230 0.6180 10.4930 03.2448 0.4699 7.2251 49 28 89.5050 0.6427 11.1377 92.7749 0.4934 7.7185 48 29 88.8623 0.6684 11.8061 92.2815 0.5181 8.2366 47 30 88.1939 0.69352 12.5013 01.7634 0.5440 8.7806 46 31 87.4987 0.7229 13.2242 91.2194 ©O.5712 9.3518 4b 32 86.7758 0.7519 13.9761 90.6482 0.5997 9.9515 44 3 86.0239 0.7819 14.7580 go.0485 0.6298 10.5813 43 34 85.2420 0.8132 15.3712 89.4187 0.6612 11.2425 42 35 84.4288 0.8458 16.4170 88.7575 0.60943 11.9368 41 36 83.5830 0.8796 17.2966 88.0632 0.7200 12.6658 40 37 82.7034 0.9148 18.2114 87.3342 0.7654 13.4312 39 33 81.7886 0.9513 19.1627 86.5688 0.8037 14.2349 38 39 80.8373 0.9394 20.1521 85.7651 0.8440 15.0789 37 40 79.8479 1.0200 21.1811 84.9211 0.8861 15.9650 36 41 78.8189 1.0702 22.2513 84.0350 0.9304 16.8954 3b 42 77.7487 1.1129 23.3642 83.1046 0.9769 17.8723 34 "2 76.6358 1.1575 24.5217 82.1277 1.0258 18.8981 3, 75.4783 1.2038 25.7255 81.1019 1.0771 19.9752 3z 74.2745 1.2519 26.9774 80.0248 1.1329 21.1061 3T 7.0226 1.3020 | 28.2794 78.80:9 1.1875 22.2936 , 30 Current Current Expect- P: t Es P. t en) value. |Jibrecanen valve. (depreciate J 433 484 VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining | pop oue Total Remaining | Ap ortiza- Total Year. fystment (S| poy ipvetment | STE, amor of year. | Fear. of year. of year. | year. of year. v5 YEAR LIFE 75 YEAR LIFE 4 per cent. 5 per cent. aN 47 $71.7206 $1.3541 $29.6335 $77.7064 $1.2468 [$23.5404 29 48 70.3665 1.4082 31.0417 76.4596 1.3092 | 24.8496 28 49 68.9583 1.4646 32.5063 75.1504 1.3746 | 26.2242 27 60 67.4937 1.5232 34.0295 © 73.7758 1.4434 | 27.6676 26 51 65.9705 1.5840 35.6135 72.3324 1.5155 | 29.1831 2b 52 64.3865 1.6475 37.2610 70.8169 1.5913 | 30.7744 24 53 + 62.7390 1.7133 38.9743 69.2256 1.6709 32.4453 23 54 61.0257 1.7819 40.7562 67.5547 1.7545 | 34.1998 22 bb 59.2438 1.8532 42.6094 65.8002 1.8421 36.0419 21 56 | 57.3906 1.9272 44.5366 ~~ 63.9581 1.9343 1 37.9762 20 57 | 55.4634 2.0044 46.5410 | 62.0238 2.0309 | 40.0071 19 58 53.4590 2.0845 48.6255 | 59.9929 2 1326 ' 42.1397 18 59 : 51.3745 2.1680 50.7935 | 57.8603 2.2391 | 44.3788 7 60 49.2065 2.2546 53.0481 ' 55.0212 2.3511 | 46.7299 16 61 46.9519 2.3448 55.3929 53.2701 2.4687 49.1986 16 62 44.6071 2.4387 57.8316 50.8014 2.5921 5I.7907 14 63 42.1684 2 5361 60.3687 48.2003 2.7217 54.5124 a3 64 39.6323 2.6376 63.0053 45.4876 2.8577 57.3701 12 66 36.9947 2.7432 65.7485 + 42.6299 3.0007 60.3708 I 66 34.2515 2.8528 68.6013 | 39.6292 3.1507 63.5215 10 67 31.3987 2.9670 471.5683 36.4785 3.3082 66.8297 : 68 28.4317 3.0856 74.6539 . 33.1703 3.4737 70.3034 69 25.3461 3.2091 77.8630 29.6066 3.6473 73.9507 © | 70 22.1370 3.3374 81.2004 26.0493 3.8297 77.7804 i “71 18.7996 3.4709 84.6713 22.2196 | 4.0212 81.8016 J 72 15.3287 3.6097 88.2810 18.1984 4.2222 86.0238 73 II.7I190 3.7542 92.0352 13.9762 4.4334 90.4572 74 7.9648 3.9043 95.9395 | 9.5428 4.6550 95.1122 : 76 4.0605 4.0605 100.0000 4.8878 4.8878 100.0000 | 6 per cent. 7 per cent. . [100.0000 $0.0769 $o.0769 $100.0000 | $o.0441 | $o.0441 ' TB : 99.9231 0.0814 , 0.1583 99.9559 0.0471 0.0912 74 ; 99.8417 0.0864 0.2447 09.9088 | 0.0504 | 0.1416 ~3 q 99.7553 0.0916 | 0.3363 99.8584 + 0.0540 0.1956 72 3 99.6637 0.0970 © 0.4333 99.8044 0.0578 0.2534 71 Current Current . Expect- Pp: t ig P; t a |depeiaton le Tz 3 TABLE 33. AMORTIZATION AND DEPRECIATION (Continued) Remaining . 5 tiza. Total Remaining A tizas Total Year. pi emion tion during] JRertied fvesment (ion Gurlny mortiza of year. year. of year. of year. year. of year. 75 YEAR LIFE 75 YEAR LIFE 6 per cent. 7 per cent. : $99.5667 $o.1029 $0.5362 $99.7466 $0.0618 ' $0.3152 1 TO ; 99.4638 0.1000 0.6452 99.6848 0.0661 0.3813 69 } 99.3548 0.1156 0.7608 99.6187 0.0707 | 0.4520 68 J) | 99.2392 0.1225 0.8833 99.5480 o0.0757 0.5277 | 67 10 99.1167 | 0.1299 1.0132 99.4723 o0.0810 ! 0.6087 | 66 IT | 98.9868 | 0.1376 1.1508 99.3913 0.0867 0.6954 66 12 98.8492 | 0.1459 1.2967 99.3046 0.0927 0.7881 64 I 98.7033 0.1547 1.4514 99.2119 0.0992 0.8873 63 14 98.5486 0.1640 1.6154 99.1127 © 0.1062 0.9935 62 15 98.3846 0.1738 1.7892 99.0065 0.1136 1.1071 61 1% 98.2108 0.1842 1.9734 98.8929 0.1216 1.2287 60 1 98.0266 0.1932 2.1686 98.7713 0.1301 1.3588 39 IX 97.8314 0.2070 2.3756 98.6412 0.1392 1.4980 358 1y 97.6244 0.2104 2.5950 98.5020 0.1489 1.6469 57 20 97.4050 0.2326 2.8276 98.3531 0.1593 + 1.8062 56 21 97.1724 0.2465 3.0741 98.1938 o.1705 1.9767 BB 22 96.9259 0.2613 3.3354 98.0233 0.1824 2.1591 S54 2 96.6646 0.2770 3.6124 97.8409 0.1952 | 2.3543 53 24 96.3876 0.2936 3.9060 97.6457 0.2089 2.5632 52 25 96.0940 0.3113 4.2173 97.4368 0.2235 2.7867 SI 26 95.7827 0.3299 4.5472 97.2133 0.2391 3.0258 B60 27 95.4528 0.3497 4.8969 96.9742 0.2559 3.2817 49 28 95.1031 0.3707 5.2676 96.7183 0.2738 3.5555 48 24 94.7324 0.3929 5.6605 96.4445 0.2929 3.8484 47 30 94.3395 0.4165 6.0770 96.1516 0.3134 4.1618 46 31 93.9230 0.4414 6.5184 95.8382 0.3354 4.4972 4b 32 93.4816 0.4680 6.9864 95.5028 0.3589 4.8561 44 33 93.0136 0.4961 7-4825 | 95.1439 0.3840 5.2401 43 34 92.5175 0.5258 8.0083 94.7599 0.4109 5.6510 42 3b 91.9917 « ©.5574 8.5657 94.3490 0.4396 + 6.0906 41 2b 01.4343 0.5908 9.1565 93.9094 0.4704 6.5610 40 ) 90.8435 0.6262 9.7827 93.4390 0.5033 7.0643 39 2 90.2173 0.6638 10.4463 92.9357 0.5386 7.6029 38 89.5535 + 0.7037 1II.1502 92.3971 0.5763 8.1792 37 88.8498 | 0.7459 11.8961 91.8208 0.6166 8.7958 2. 88.1039 | 0.7906 | 12.6867 . 91.2042 | 0.6598 | 9.45.5 35 C t C Present or Present Gr Expect- value. tion during value. tion during ney. year. year. . ABLES 48% Lo) VALUATION, DEPRECIATION AND THE RATE-BASE TABLE 33. AMORTIZATION AND DEPRECIATION (Concluded) Remaining 5, isn Total Remaining | 5 oo. | Total Your | Umm ondune SIG Rm dondune SHOU of year. |. Year of year. I of year. | Ear. of year. 75 YEAR LIFE 75 YEAR LIFE 6 per cent. 7 per cent. 42 $87.3133 $0.8381 ,$13.5248 | $90.5444 | $o.7059 jf in 34 43 86.4752 0.8883 14.4131 89.8385 0.7554 | 10.9169 33 44 85.5869 0.9417 15.3548 89.0831 0.80820 ‘11.7251 32 45 84.6452 0.9982 16.3530 88.2749 0.8648 12.5899 ' 3I 46 83.6470 1.0580 17.4110 87.4101 0.9253 13.5152 30 47 82.5890 1.127518. 5325 86.4848 0.9901 14.5053 | 29 48 81.4675 1.1888 19.7213 85.4947 1.0594 15.5647 28 49 80.2787 1.2602 20.9813 84.4353 1.1336 16.6983 | 27 60 70.0135 1. 33570 22.3172 83.3017 RT . 2120017. 011 2 R26 5I 77.6828 T.41500 23-7531 82.0888 1.2979 19.209I 26 52 76.2669 1.5009 25.2340 80.7909 1.3887 20.5978 24 33 74.7660 1.5909 26.8249 79.4022 1.4859 22.0837 23 54 73.1751 1.6864 28.3113 77.9163 1.5899 23.6736 1 22 6b 71.4887 1.7875 30.2088 76.3264008 1 . 701200 25.3743 aT 56 69.7012 1.8048 32.1936 74.6252 1.8203 | 27.1951 20 57 67.8064 2.0085 34.2021 72.8049 1.94778, 29". 1423810 3 65.7979 2.1200 36.3311 70.8572 2.0841 31.2269 ' 18 59 63.6689 2.2567 38.5878 68.7731 2.2299 ' 33.4568 17 60 61l. 4122 2.3921 40.9799 66.5432 2.3860 35.8428 16 61 59.0201 2.535700 43.5156 64.1572 2.5531 38.3959 16 62 56.4844 2.6878 46.2034 !' 61.6041 2.73130 47.1 277 14 63 53.7966 2.8491 49.0525 58.8723 2.9230 | 44.0507 3 64 50.9475 3.0200 52.0725 55.9493 3.1276 47.1783 12 65 47.-927500 3. 20120 55. 2737 52.8217 3.3466 50.5249 oT 66 44.7263 3.3933 58.6670 49.4751 3.5808 54.1057 | 10 67 41.3330 3.5969 62.2639 45.8043 3.8315: 57.9372 1 68 37.7361 3.8127 66.0766 42.0628 4.0097 62.0369 3 69 33.9234 4.0415 70.1181 37.9631 4.3867 66.4236 7 70 29.8819 4.2839 74.4020 33.5764 4.6937 71.1173 6 71 | 25.5980 4.5410 78.9430 28.8827 5.0233 76.1406 6 72 21.0570 4.8135 83.7565 23.8504 5.3738 81.5144 ! 73 16.2435 5.1022 88.8587 18.4856 5.7500 . 87.2644 74 | II.1413 5.4084 04.2671 | 2.735606. 1525 | 93.4169 ; 76 5.7329 5.7329 .I00.0000 6.5831 6.5831 [100.0000 ! C t C t Present Tn. Present oro os value. tion during value. | tion during! Pears. year. year. 48¢€ INDEX (Reference is to Page.) " Amortization, distinct from deprecia- A tion, 11, 86. Abbreviations, vii. during life of franchise, 67. Academic discussion of methods of during probable life term, 175. procedure, 105. hypothetical case in illustration, 83. Accounting, construction account, In- incomplete, 87. terstate Commerce Commission, insufficient, an example of, g6. 229. of capital, rate, 34. depreciation and replacements, In- of reasonable cost, a fundamental terstate Commerce Commission, principle, 32. 230. owner controls amounts received, 35. engineering account, Interstate Com- period and rate of, 188. merce Commission, 232. use of fund, 89. interest-during-construction account, value of stock affected, 88. Interstate Commerce Commis- (see Depreciation). sion, 233. Amortization fund, accumulation not Interstate Commerce Commission, always essential, 8g, 127. various accounts, 229. accumulations become the property land retired from use, Interstate of owner, 170. Commerce Commission, 232. sometimes considered as measuring principles applied to Unlimited Life depreciation, 86. Method, 233. (see Replacement fund). principles applied to other methodsof Am. Soc. C. E. Committee, contingen- appraisal, 23s. cies, 49. purpose of the system, 229. engineering expenses, 43. Accrued depreciation, definition, 20. general expense, 48. value affected, 125. insurance and risk, so. (see Depreciation). interest and taxes, 52. Actual life (see Life). Annual depreciation (see Depreciation). Age, composite, definition of, 22. Annual replacement requirement (see Agency theory, owner as agent of rate- Replacement), 24. payer (see Owner), 5. Annuity, computations of, to meet re- Alvord’s method of determining going placements, 120. value, 653. methods of satisfying replacement Amortization, accrued, 170. requirements, 102. amount of, 180. Table 26, Amount of an Annuity of application of earnings, 95. $1, 366. complex plants, 89. Table 26, explanation, 364. definition, 23. Table 27, Annuity which will amount Depreciation and Amortization, to $1 in given time, 379. Table 33, 459. Table 27, explanation, 377. Depreciation and Amortization, Table 28, Present value of an Table 33, explanation, 453. Annuity of $1, 392. 487 488 INDEX Annuity, Table 28, explanation, 390. Business, volume in relation to rate- Table 29, Amount which $1 will pur- base, 160, 161. chase, 404. what the owner should know, 6. Table 29, explanation, 403. Antigo Water Company case (see Court cases). C Appraisal, as a basis for capitalization, California, public utilities act defines 130. “Public Utility,” 146. as a basis for fixing rates, 127. state constitution on regulation of as a basis for taxation, 138. rates, 143. extent of detail required, go. state constitution on public-utility tabulation of field results, 194. control, 146. various purposes, 123. utilities law prescribes depreciation (see Valuation). fund, 168. Appreciation, Consolidated Gas case, | water-right values in the state, 225. New York, 71. Capacity in excess of requirements, 8o, definition, 23. 82. excessive, 7I. Capital, invested, as rate-base, 30, 32, included in cost to reproduce, 76. 138, 158. Minnesota rate cases, 76. methods of amortization, 32. shall it be added to rate-base, 74. returned, owner’s rights to, 170. treatment of, 73. (see Amortization). Western Advanced-Rate case, as a Capitalization, appraisals for the pur- profit, 73. pose, 139. (see Unearned increment). of franchise value, 69. Appleton 2s. Appleton Water-works Co. (see Over-capitalization). (see Public-service commission Capitalized profitsin mine valuation, 240. decisions). Cast-iron pipe illustration of replace- ments, 98. Change of rates, frequent, 141. B Charles River Basin Commission, en- Base physical cost, 158. gineering expenses, 45. Basic price of metals, 245. “Com,” for commodity unit, 274. Basis of calculation in rate fixing, 155. Competition in public service, 149. Beggs on engineering expense, 55. Complex plants, amortization and re- Bluefield Water-works and Imp. Co. placements, go. Rate case, 316. Composite age and life, definitions, 22. Bonus, effect on rate-base, 156. Condition per cent, definition, 20. to induce investment, illustration, 14. Construction account, Interstate Com- Boston, Charles River Basin Commis- merce Commission, 229. sion, engineering expenses, 45. Contingencies, Am. Soc. of C. E. Com- subway, engineering expenses, 44. mittee quoted, 49. general expenses, 49. Control of public utilities, naturally Business, cost of establishing, 26, 63. followed privilege to operate, 142. prospective, must be considered, 36. of recent origin, 3. volume entitled to consideration, (see Public service control; see Public 33. utilities). x 2 429 Cooley, Prof. M. E., overhead expenses, | Court Cases Cited, Minn. St. Paul and 53, 35 Sault Ste. Marie Ry. Co. us. Cooperation between owner and public, Wisconsin R. R. Commission, 150. 148. Copper production in the United States, Minnesota Rate cases, 18, 76, 135, Table 15, 258, 250. 199, 205. Cost, base physical, discussed by Wis- Murray vs. Public Utilities, 137. consin Railroad Commission, 158. National Water-works Co. vs. Kansas determination of, 39. City, 60, 64. records used in rate-base, 193. New York & Queens County Gas Cost of article includes overhead ex- Co. Rate Case, 310. penses, 42. Reagan vs. Farmer Loan and Trust Cost of establishing the business, defini- Co., 73. tion, 26, 32. San Diego Land and Town Co. vs. treated as legitimate investment, 30. National City, 18. Cost of operation, determination of, San Diego Land and Town Co. vs. 125. Geo. Neale et al, 198. Cost of physical elements, determina- Shoemaker vs. United States, 198. tion of, 38. Smyth vs. Ames, 18. related to value, 309. Southwestern Bell Telephone Co. Cost of replacement, definition, 23. Rate case, 315. related to present worth, go. United States vs. Chandler Dunbar Cost of reproduction, appreciation in- Water Power Co., 108. cluded, 76. United States vs. Honolulu Planta- definition, 29. tion Co., 199. in relation to investment, 77. Willcox vs. Consolidated Gas Co. of is not value, 136. New York, 19, 71, 73. use in rate-base, 193. Young vs. Harrison, 198. Courts and the rate-base, 15. Croton dam, change in plans for, 51. Court cases cited, Boom Company vs. Curle,J. H.,on mining investments, 243. Patterson, 197. Current depreciation (see Depreciation). Atlanta Rate case, 316. Current replacement requirement, def- Bluefield Rate case, 316. inition (see Replacement), 24. Consolidated Gas case, New York (see Willcox, etc.), 19, 71, 73. . Galveston Rate case, 314. ! Georgia Ry. & P. Co. Rate case, 316. Days of the year, number of each day, Goodwin vs. Cincinnati & Whitewater 328. Canal Co., 198. Deferred maintenance, definition, 24. Interstate Commerce Commission vs. determination of, 125. B. & O. R. R. Co, 145. in an operating plant, 79. Kansas City Water-works case, 60, 64. Definitions subject to modification, 5. Kennebec Water District vs. City of Denny, G. A., rate of interest on mining Waterville et al, 17, 29, 63, 66, investments, 244. 72, 154, 160. Depreciation, account, explained by Knoxville vs. Knoxville Water Co., Interstate Commerce Commis- 134, 154. sion, 230. \NDEX a [3 Depreciation, accounts under the ! Depreciation account, Wisconsin Rail- various methods, 175. road Commission discusses -fund accrued, definition, 2o. and -reserve, go. amortization, depreciation and re- (see Lessening of Worth). placements, 84, 86. Depreciation fund, California law re- amortization not to be confounded strictions, 168. with, 11, 86. discussed by Wisconsin Railroad annual, definition, 23. Commission, go. assumptions for purpose of discus- Detail of the appraisal, required extent sion, 85. of, 40. complex plants, principles applied to, Development of business, cost of, 26. go. Discarded property, Wisconsin law on current, must be covered by earnings, (see Unused property), 84. 34. Donated extensions to water-works, 12. definition, 23, 84. Equal Annual Payment Methods, 165. - error in ordinary method of compu- + tation, 456. Early losses, 9, 32, 64. estimates of, are approximations, 104. Earnings, affected by ability to pay, failure to make allowance for, 159. 35 formula for estimating replacement, application to replacements and 10%. amortization, 95. hypothetical case in illustration, 8s. deficiency to be avoided, 42. Interstate Commerce Commission, deficient in early years, 153. rules for determining, 192. determination of, present and pros- not a withdrawal of capital, 4. pective, 125. Pocatello Water Co. case, not de- franchise value determined by, 10. ducted, 137. must cover current depreciation, private industrial establishments have 34. problems, 4. net, as an element of value, 150. rate-base, with and without, 129. net, and intangible values, 11. remaining value under law of proba- net, should exceed those of ordinary bilities, 117. investment, 36. restrictions on, under California law, owner requires that hazards be cov- 168. ered, 32. service value not reduced by, 33. procedure in estimating must be Sinking Fund Method, 164, 167. continuous, 36. Sinking Fund Method and Equal relation to rate-base and volume of Annual Payment Methods com- business, 150, 161. pared, 169. required, procedure for their com- Straight Line Method, 101, 165. putation, 34. Table 33, Amortization and Deprecia- should create value in excess of in- tion, 450. vestment, 35. Table 33, explanation, 453. Supreme Court of Maine, 17, 154. treatment of, with appreciation, 73. value affected by, 10, 70, 150. Unlimited Life Method, 166. water-right value determined by, Wisconsin Railroad Commission, 159. - an, 490 INDE : INDEX Empirical methods in valuing mining properties, 2309. Engineering account, Interstate Com- Failures, assumed hypothesis of, 106, merce Commission notes on, 117. 232. assumed hypothesis, diagram, 110, Engineering expenses, Am. Soc. C. E. IIT. committee quoted, 43. law of probabilities applied, 108, Equal Annual Payment Method for 117. rate-fixing, 1653. law of probabilities applied, Table 8, Equal Annual Payment Method and 118. Sinking Fund Method compared, merit of assumed law, 106. 169. Fair value, as a rate-base, 14, 18, 78. Establishing the business, cost of, 26. definition, 17. proper treatment of cost of, 32. Minnesota Rate cases, as basis for (see Business). rate fixing, 18. Estimation method in valuation of present value as a starting point, 12, mining properties, 240. 13. Eshleman, J. W., quoted on the rate- (see Value). base, 157. Field results, tabulation of, 104. Excess capacity of plant, 8o, 82. Filters, engineering expenses in con- Excessive profits of utilities, 142. struction of, 47. Expectancy, according to law of prob- Finlay, J. R,, quoted on interest on abilities, 117. mining investments, 243. definition, 21. Fisher, Irving, the standard dollar, 282. effect on present value, 105. Fixing of rates (see Rate-fixing), 140. illustration, high duty pump, 21. Fortuitous events, 291. illustration, irrigation canal, 22. Franchise, amortization during life, 67. of equivalent single articles, 116. capitalization of, 69. Table 31, Expectancy and Remain- Wisconsin Railroad Commission, ing Value, 432, 437. 69. tabular illustration for 10,000 articles, Public Service Commission law of 108. New York, 69. Expectancy of human life, 446. definition, 26, 66. (see Life). indeterminate term, 67. Expenses, engineering, Am. Soc. C. E. term of, 67. committee quoted, 43. value of, 10, 66. general, Am. Soc. C. E. committee value determined by earnings, 10. quoted, 48. value not included in rate-base, 67, overhead, Wisconsin Railroad Com- 162. mission cited, 53. Wisconsin Railroad Commission on overhead, definition, 28. value, 69. overhead, on railroad construction, Fundamental principles, applied to in- 52. dustrial establishments, 3. policing, Am. Soc. C. E. committee illustration, Panama Canal, 8. quoted, 49. rate-fixing appraisals, 32. promotion, definition of, 28. Future use, property held for, 79. promotion, reasonableness of, 57. (see Unused property). oT 491 rT INDEX Galveston Electric Co. Rate case, 314. Increment (see Unearned increment). General expenses, Am. Soc. C. E. com- Indeterminate franchise, 68. mittee quoted, 48. Industrial enterprises, basis for selling Georgia Railway case, right-of-way - - price, 6. value (see Court cases). fundamental principles applied to, 3. Georgia Ry. & P. Co. Rate case, 316. Insurance and risk, Am. Soc. C. E. Gillette, H. P., quoted on railroad over- committee quoted, so. head expenses, 52. Intangible value, as a protection to the Going concern, definition, 27. owner, 61. Kennebec Water District case, 63. created by earnings, 11, 57. unprofitable expenditures and early definition, 26, 57. losses, 0. Kansas City Water Works case, 60. value of, as distinct from going value, Kennebec Water District case, 61. 64. under a restricted franchise, 59. Going value, Alvord’s method of deter- (see Value). mining, 65. Interest and taxes, Am. Soc. C. E. com- as distinct from going concern value, mittee quoted, 52. 64. during construction, Interstate Com- decisions of Wisconsin Railroad Com- merce Commission quoted on mission, 64, 65. accounting, 233. definition, 27, 301-309. rate for mining investments, 241. Good-will, definition, 27. rate of return on public utility in- in San Francisco Water Rate case, vestments, 161. 301. Table 19, simple interest (360 days), relation to cost of establishing the 326. business, 304. Table 21, simple interest (365 and Gray, Prof. J. H., quoted on Public 366 days), 320. Utility control, 3. Table 22, Compound Interest, 331,333. Table 23, compounded every 6 H months, 345, 346. Table 24, compounded every 3 Hammond, John Hays, quoted as to months, 348, 349. rate of return on mining in- Interstate Commerce Commission, ap- vestments, 244. ; preciation, 73. Hazard, compensation for, 32, 160. construction account, 229. may affect rates, Kennebec Water depreciation account, 230. District case, 161. engineering account, 232. (see Risk). interest during construction, 233. Hoover, H. C., quoted on mining risks, purpose of Interstate Commerce Act, 242. 145. quoted on rate of return on mining retirement of land, 232. investments, 243. Invested capital, 25. Hudson River State Hospital, engineer- Invested capital as a basis for rate- ing expenses in construction of fixing (see Investment), iii, 30, sand filters, 47. 138, 155, 158. 492 il G 7 INDEX Investment, as a basis for rate-fixing, Wisconsin Railroad Commission, : 138, 158. Maine Supreme Court on hazard, 160. definition, 25. Maintenance, definition of deferred, 24. protection of, 127. Management, 293. (see Rate-base). Market value, affected by rate-fixing Irrigation canal as an aid in creating procedure, 195. land values, 5. defined in recent court decisions, 197. Irrigation water, value of, 208. definition, 16. Ithaca filters, engineering expenses, 47. not what the purchaser can afford to pay, 199, 202. K of real estate, 197. Kansas City Water-works case (see used ia he wluation of mines, 235. value multiple, 203. Court cases). aia Massachusetts Metropolitan Water- Kennebec Water District case (see Al : works, administration expense Court cases). at. 40, Knoxville Water Company case (see Massachusetts public service control, Court cases). rey Methods of procedure in fixing rates, 1. L may affect market value, 195. Land retired from use, Interstate Com- Metropolitan Water-works, Massachu- merce Commission quoted, 232. setts, engineering expenses, 44. Lead in the United States, production policing expense, 49. and price, Table 17, 262. Michigan Railroad valuation, overhead Life, actual and probable, assumptions allowance, 53. made, 83, 105. Mineral products, price of, 244. composite, definition, 22. Mines and oil properties, valuation of, departure of actual from probable, for owner’s information, 246. academic discussion justified, for purchase or sale, 24s. 105. for taxation, 247. effect of departure of actual from limitations upon accuracy, 237. probable, 172. methods, 238. hypothesis of failures, 107. purposes, 237. merit of assumed law of failures, 107. Mining risks, 242. of various articles, Table 30, 415, 418. Mining investments, proper rate of period of usefulness not usually as interest, 241. estimated, 107. Minnesota Rate cases (see Court cases). probable, its definition, 20. probable life, iii, 20. N probable life not always realized, 37. New York, control of public utilities, remaining, its definition, 21. 147. unlimited life, 35, 132. engineering expenses at water-works, Limited franchise (see Restricted fran- 44. chise). general expenses at water-works, 48. Louisville sewage works, Kentucky, police expense at water-works, 49. engineering expenses, 46. Public Service Commission law, 69. a 493 M Lr. ce. X New York and Queens County Gas Co. ' Overhead expenses, Metropolitan Rate case, 310. Water-works, Mass., 44. Non-agreement of actual with probable New York water-works, 44, 48. life, 104. Ogdensburg sand filters, 47. Normal price of metals, 244. Peekskill sand filters, 47. Notation, v. Pennsylvania Railroad tunnels, 46. railroad construction, 52. 0 Springfield Water-works, Mass., 47. Obligation to replace, definition, 24. Springfield, Mass., Ludlow filters, 47. general explanation, 188. Wachusetts Reservoir, Mass., 48. Obsolescence, 288. Watertown mechanical filters, 47. Ogdensburg sand filters, engineering Wisconsin Railroad Commission de- expenses, 47. cisions, 53. Oil properties, valuation of (see Mines Owner, agent of the taxpayer, 5. and oil properties), 237, 255. earnings required, 32. Operation, determination of the cost of, entitled to share in unearned incre- 125. ment, 33. Overbuilt plant, 8o. has right to returned capital, 35. discussed by Wisconsin Railroad intangible values, his protection, 61. Commission, 83. proper allowance to, 2. (see Unused property). public codperation desirable, 150. Over-capitalization, 6o. responsibility for replacements and Overhead expenses, Am. Soc. C. E. repair fund, 35. committee quoted, 43. what he is entitled to obtain, 131. Boston subways, 44, 45. Ownership of public utilities, 140. Charles River Basin, Boston, 45. contingencies, Am. Soc. C. E. com- z P mittee quoted, 49. definition, 28. Panama Canal, illustration of funda- engineering expenses, Am. Soc. C. E. mental principle, 8. committee, 43. Peekskill sand filters, engineering ex- general expenses, Am. Soc. C. E. penses, 47. committee, 48. Pence, W. D., engineering staff Wis- general expenses, Metropolitan Water- consin Railroad Commission, on works, Mass., 49. overhead expenses, 55. general expenses, New York Water- Pennsylvania Railroad tunnels, en- works, 49. gineering expenses at, 46. Hudson River State Hospital, 47. Physical cost, discussed by Wisconsin included in cost, 42. Railroad Commission, 158. insurance and risk, Am. Soc. C. E. Physical elements, cost of, 38. committee, 50. Pipe illustration of replacements, 98. interest and taxes, 52. . Pocatello Water Company case, no Ithaca filters, 47. depreciation deducted, 137. Kennebec Water District, Maine, Police expenses, Am. Soc. C. E. com- 46. mittee quoted, 49. Louisville Sewerage Works, Kentucky, Present value, as a starting point in : rate-fixing, 18, 19, 71. 494 INDF~ 46. Present value, effect of expectancy on, ! Public Service Commissions, attitude 105. of, 150. rental value an aid in determining, control the amount of detail required 181. in estimating the rate-base, 42. Table 25, Present value of $1.00 due Public Service Commission decisions, at a future date, 353. California Railroad Commission: Table 25, explanation, 351. J. A. Murray and Ed. Fletcher (see Value). water rates, 157. Present worth and the cost of replace- Nevada County Narrow Gauge ment (see Present value), 40. Railroad Company, 207. Price and production of metals in San Diego case, 211. United States (see Copper, Silver, Stockton Terminal and Eastern Lead, Zinc). Railroad, 207. Price “normal” and “basic,” of min- Idaho Public Service Commission: erals defined, 244, 245. Pocatello Water Company case, Price of the mineral product, 244, 257. 137. Principles, fundamental, 32. Interstate Commerce Commission: Probabilities, law of, applied to failing Western Advanced Rate case, 73. articles, 117. Wisconsin Railroad Commission: Probable life, iii. Antigo Water Company case (see based on experience, 104. Hill, etc.). definition, 20. Ashland Water Company case, 56. effect of departure therefrom of Cashton Light & Power Company actual life, 172. case, 04. not the actual life of an article, 37. City of Appleton case, 138, 162. Table 30, Probable life of various City of Beloit vs. Beloit Water, Gas articles, 415, 418. and Electric Company, 218. (see Life). City of Racine vs. Racine Gas Light Procedure, method of, in rate fixing Company, 54, 84. must be continuous, 36. City of Rhinelander vs. Rhinelander (see Rate-fixing). Lighting Company, 219. Production and price of minerals, Fig- City of Ripon vs. Ripon Light & ures 4-7, Tables 15-18, 257. Water Company, 54. Profits, capitalized, in the valuation of Dick et al »s. Madison Water mines, 240. Commission, 54. determination of, 126. Fennimore Mutual Water & Light excessive and fictitious, 142. Plant case, go. Profit-sharing with public, 150. Green Bay us. Green Bay Water Promotion expenses, definition, 28, 56. Company, 65. may increase cost of marketing bonds, Hill et al »s. Antigo Water Com- Wisconsin Railroad Commission, pany, 53, 64, 69, 158, 162. 57 La Crosse Gas and Electric Com- Property not in use, 4, 8o, 81, 84, 230. pany case, 54, 83, 84, 158. Prospective business must be considered, Manitowac Gas Company case, 56. 36. Milwaukee vs. Milwaukee Electric Public contribution to revenue of Public Railway, 54. Utility, 152. Oshkosh Water-works case, 56. INDEX 405 =. =X Public Service Commission decisions: : Wisconsin Railroad Commission: = Ross et al vs. Burkhardt Milling Railroad overhead expenses, 52. and Electric Power Company, Table 1, State of Michigan, 53. 210. Table 1, State of Washington, 53. State Journal Printing Company Rates, cost of service as a modifier of, vs. Madison Gas and Electric 153. Company, 54, 162. frequent changes undesirable, 141. Stevens Point Lighting Company regulation, provisions of California case, 150. State Constitution, 146. Superior Commercial Club ws. right to regulate, 143. Duluth Street Railway Com- San Francisco Charter on fixing of, pany, go. 144. Public Service Commission law of New various factors involved, 160. York on franchise capitalization, Rate-base, appreciation to be included 69. or not, 71, 74. Public Service concerns, competition definition, 30, 31, 155, 314. among, 149. depreciation deducted and not de- Public Service control, attitude of the ducted, 30, 129. Public Service Commissions, 150. determination of, 156, 196. California State Constitution, 143. effect of a bonus, 156. cooperation between commissions and factors to be considered in establish- owner, 150. ing, 157. Interstate Commerce Commission, franchise and water-rights not a part, J 148. 36. Massachusetts methods, 145. franchise value, 162. methods in other states, 147. general statement, 150. New York methods, 147. investment, must be determined, 30, Wisconsin methods, 147, 148. 35: (see Public utilities). J. W. Eshleman quoted, 157. Public service property, unlimited life Wisconsin Railroad Commission of (see Unlimited life), 35, 132. quoted, 138, 158. Public utilities, competition among, 149. without deduction of depreciation, control and regulation, 2, 142. 103. defined in California Public Utility natural, 31. Act, 146. ordinarily independent of market definition, 30. value, 197. excessive profits, 142. relation of earnings and volume of historical survey by Prof. J. H. Gray, business, 157, 161. 3 two procedures in determination, other property values affected, 151. 129. public contribution to revenue of, 152. various factors to be considered in quasi-public character, 140. determining, 160. regulation, 141, 142. with and without deduction of de- regulation essential, 143. preciation, 129, 169. unearned increment applied, 7o. Rate-fixing, book accounts under vari- what they are entitled to, 3. ous methods, 175. 496 INDE" % INDEX 4 7 Rate-fixing, comparison of various Replacement, fund, amount of money methods, 172, 174, 175, 182. in, 04, 97, 1609. conflicting views, 1. mathematical determinations of, effect of the departure of actual from 90, 96. probable life, 172. owner’s responsibility for, 35. Equal Annual Payment Method, 165. purpose of, 127. fairness the prime consideration, 163. Table No. 2, Replacement fund, 94. possible methods of procedure, 163. Interstate Commerce Commission on preferable method of procedure, 163. accounting, 230. procedure affects market value, 195. provisions for, distinct from amorti- Sinking Fund Method of deprecia- zation, 2. tion, 164, 167. requirements, according to law of Straight Line Method of deprecia- probabilities, 120. tion, 165. annual, definition, 24. Unlimited Life Method, 166. annual, computations of annuity Real Estate, admissibility of evidence for, 120. relating to value, 200. Comparison of methods of pro- market value and the rate-base, 197. cedure, Table 7, 115. property retired from use, Interstate current, definition, 24. Commerce Commission Act, 232. determination of, 36, gg. right-of-way value, 206, 207. hypothetical case in illustration, g8. value in eminent domain proceedings, illustration with cast-iron pipe, 199. 197. in the case of numerous articles, Reasonable value (see Value). III. Reasonable cost, amortization of, 32. provided for by alternate meth- Regulation, essential that it be fair to ods, 102. owner, 143. Table 4, Replacement Require- of rates, California Constitution, 144. ments, 5 yr. life, 112. of rates, the demand for, 2. Table 5, Replacement Require- of rates, the fairness of, 143. ments, 10 yr. life, 113. the result of monopolistic character, Table 6, Replacement Require- 142. ments, 20 yr. life, 114. Remaining life, definition (see Life), 21. Reservoir sites, effect of various factors Remaining service value, definition, 26. on value, 223. Remaining value, according to Law of general statement as to land value, Probabilities, Table g, 119. 221. definition, 20. value multiple applied to land, 220. Table 31, Expectancy and Remaining value in relation to water-right value, value, 432, 437. 220. (see Value). (see Watershed lands). Rental value, an aid in determining Residual value, definition, 20. present value, 72, 181. Restricted franchise, intangible value Replace, the obligation to, 24, 169, 188. under, 59. Replacement, cost defined, 25. Return, company entitled to fair depreciation and amortization, 86. return, Smyth vs. Ames, 18. earnings applied, 195. rate of, 160, 161. fund, accounting for, 35, 175. rate of, on donated extensions, 14. Nel: 4.5 Tax Revenue of public utilities contributed ! State Journal Printing Company us. to by public, 152. Madison Gas and Electric Com- Rickard, T. A., quoted on mining as a pany (see Public Service Com- speculation, 254. mission decisions). Right of way, use of the multiple, 203, Stevens Point Lighting Company case, 205, 207. service and rates (see Public value of, California Railroad Com- Service Commission decisions). mission, 207. Straight Line Method, 100, 101, 165. Minnesota Rate cases, 203. Strategic value, part of owner’s reward, Risk, and insurance, Am. Soc. C. E. 36. committee quoted, so. Strategic value of water-rights, 214. and mining investments, 241, 242. Superior Commercial Club vs. Duluth (see Hazard). Street Railway Company (see Royalty value in valuation of mines, Public Service Commission de- 230. cisions). Supply and demand controls value of property, 38. S Supreme Court of United States (see Sand filters, engineering expenses, 47. Court cases). San Diego Land & Town Co. »s. Na- tional City (see Court cases). San Francisco charter provisions re- L lating to rates, 144. Tables, reference to tables in this Selling price, basis in industrial enter- volume, 7, 325. prises, 6. Taxation, appraisals for this purpose, Service, value of the, 33. 138. Service value, definition, 25. of mines, conclusions relating thereto, remaining, definition, 25. 255. Sinking Fund Method of rate-fixing, in various states and territories, 248. compared with Equal Annual propriety of taxing mining property, Payment Method, 169. 253. explained, 164. valuation of mineral properties for, Silver in the United States, produc- 247. tion and price, Table 16, 260, Taxes, interest and, Am. Soc. C. IE. 261. committee, 52. Smyth vs. Ames, fair return upon value Term of the franchise, 67, 68. (see Court Cases). Southwestern Bell Telephone Co. Rate case, 315. u Springfield, Mass., engineering expenses ~~ Uglow, W. L., method of valuing a in construction of Ludlow filters, mine, 249. 47. Unearned increment, applied to Public engineering expenses in construction Utilities, 70, 293. of Water-works, 47. owner’s share in, 33. Standard of value, the, 270. Unlimited life, explanation of, 132. Starrett, M. G., quoted on overhead method of procedure, 75, 166, 192. expenses, 55. accounting principles applied, 233. al “NDE? IN: .X Unlimited life, method of procedure, | Value, definition of fair value, 17. advantages, 191. definition of going value, 27. always applicable, 122. definition of going concern value, 27. obligation to replace, 188. definition of intangible value, 26. of public service property, 35. definition of market value, 16. (see Life). definition of remaining value, 20. Unprofitable expenditures, 9. definition of remaining service value, Unused property (see Property retired 26. from use), 4, 8o, 81. definition of residual value, 20. United States Supreme Court (see Court definition of wearing or service value, cases). 2s, determination, for capitalization, 139. Vv determination, for taxation, 138. Valuation, details of, 40. discussed by Wisconsin Railroad Equal Annual Payment Method Commission, 159. applied, 165. earnings as basis of, 150. limitations on accuracy in case of elements, 124. mines, 237. essentials, 38. methods applied to mines, 238. fair value as rate-base, 14. method applied to oil property, 255. improper use of term, 134. of mines for owner’s information, 246. in relation to investment, 35. of mines for purchase or sale, 124, 245. investment should be less than value of mines for taxation purposes, 247. due to earnings, 35. of mines for taxation in various locali- intangible (see Intangible value), 26. ties, 248. irrigation water, 208. purchase or sale, 11, 124. Knoxville case, a basis for rate-fixing, purposes of, 123. 134. in the case of mineral properties, 237. lessening of worth, 79. Sinking Fund Method applied, 164. Minnesota Rate cases, definition, 135. Straight Line Method applied, 165. fair value as the starting point, 18. tabulation of field results, 194. the value multiple, 205. Unlimited Life Method, 166. multiple in the case of real estate for Value, admissible for special purpose as special uses, 203, 205, 207, 220. evidence, 200. net earnings as basis, 150. affected by earnings, 38. of real estate, 126. as basis for rates, 12. in eminent domain proceedings, as basis for rates, discussed in Willcox 197. vs. Consolidated Gas Company, present, affected by expectancy, 105. 19. as starting point according to cost of physical elements as related courts, 18, 10. to, 38, 39. as starting point in Willcox 2s. Con- company entitled to fair return, solidated Gas Company of New Smyth vs. Ames, 18. York, 10. deductions, 79. not desirable as starting point in definition, 16. fixing rates, 12. definition, in Minnesota Rate cases, remaining service, definition, 26. T strategic, a part of owner’s reward, 36. “DEX 499 .35. - INDEX Value, supply and demand affects, 38. ' Water-right value, determination of, of stock affected by amortization, 202, 88. San Joaquin and Kings River Canal reasonable, San Diego Land & case, 200. Town Co. vs. National City, 18. value of reservoir sites in relation to, taxation, 138. 200. ‘water-rights, 208. water power value discussed by Wis- wearing or service, 25. consin Railroad Commission, 218. (see Market value). Watershed land, value of, 224. Volume of business should be considered, = Watertown mechanical filters, engineer- 33, 205,208. ing expenses, 47. profit in relation thereto, 299. Wear and tear (see Depreciation), 24. Wearing or service value, definition, 23. Willcox vs. Consolidated Gas Company Ww of New York, present value as a Washington State Railroads, overhead basis for rate-fixing (see Court cost items, 53. cases). Water power value, discussed by Wis- Wisconsin law relating to discarded consin Railroad Commission, 218. property, 84. Water-rights, free grants in Western Wisconsin Railroad Commission (see states, 212. Public Service Commission de- notes on California values, 225. cisions). payment for, 208. rate-base should not always include, vi 36. Yonkers sand filters, engineering ex- relation of value to cost of works, 213. penses, 47. strategic value, 214, 216. time element in valuing, 217. 7 Water-right value, 10, 208, 209. California Railroad Commission de- Zinc in the United States, production cision, 211. and price, Table 18, 264, 265. zila Entsauerung 28 Okt. 2010 500 | “i } ] } ll P0030 / 5 Pa E TABLES 3 ceases to be useful, and the time when the article will go out of use. But this value is dependent too upon the probable life of a new article of the same kind. The remaining value of several articles with the same expectancy of which one is in the 10-year life class, another in the 20-year class and another in the go-year class will not be the same, because the proportional serv- ice yet to be expected when compared with that of new articles will, in these cases, vary inversely as 1o to 20 to 40, and the remaining values will depart widely from each other. If the expectancy, for example, of each of three such articles is 5 years, and 6 per cent interest be made the basis of the calculation, the remaining values will be 57.23 per cent, 36.73 per cent and 28.00 per cent of the cost of replacement. The article with the prob- able life new of 10 years has the highest value for the reason that its remaining service years are a larger proportion of its probable life new than in the case of the other two articles with longer probable life new. Illustration of the Use of Table 27 What amount at the end of the 26th year will be in a sinking fund for the retirement of a bond issue of $100,000 running 40 years, if the money accumulating in the sinking fund earns 6 per cent per annum? On page 361 in the 40-year life section of Table 27 at year 27 (beginning of year 27 is the end of year 26) in the left-hand column, the accrued amortization in the 6 per cent column | for each $100 will be found to be $41.1637. Consequently, the amount in the sinking fund to retire $100,000 will be $41,163.70. The amount which will be added to the sinking fund in the 27th year will be $2939.60. Let it be assumed that by any means, such as inspection by experts, the probable remaining term of usefulness of an electric generator 13 years old has been found to be 11 years and that the type of generator to which it belongs has a probable life new of 20 years. What at 6 per cent interest is the accrued deprecia- tion if the cost of the generator was $3000 and what is its re- =r hee