The nature of capital and income

Bibliographic data

Monograph

Identifikator:: 102659555X

URN:: urn:nbn:de:zbw-retromon-82920

Document type:: Monograph

Author:: Fisher, Irving http://d-nb.info/gnd/118533541

Title:: The nature of capital and income

Place of publication:: New York

Publisher:: The Macmillan Company

Year of publication:: 1923

Scope:: XXI, 427 Seiten

Digitisation:: 2019

Collection:: Economics Books

Usage license:: Get license information via the feedback formular.

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Capital and income

Collection:: Economics Books

206 NATURE OF CAPITAL AND INCOME [Cuar. XIII have already seen, in the last chapter, that if a person owns the right to $1 a year payable at annual intervals forever, its present value, reckoned at four per cent, is &, or $25. If his annuity is $2 per year, its present value is evidently double this, or $50; and if it is any other sum, its present value is found by multiplying in the same way. Thus, an annuity of $17 is worth i. In other words, the value of a perpetual annuity 1s found by dividing the annual income by the rate of interest," or, what amounts to the same thing, by multiplying the income by the rate of capitalization, also called the number of years’ purchase. This proposi- tion, however, serves to determine only that capital-value which an annuity possesses at its inception (i.e. one year before the first installment) or at any other point taken one year in advance of the first of the installments to be included in ‘he calculation. The value of the annuity, taken immediately before any installment of income falls due, is evidently greater than the above, by the amount of that installment. Thus, if the rate of interest is four per cent, a perpetual annuity of $4 a year, of which the first payment falls due one year hence, is worth $100 to- day, and is also worth this same sum at any instant immediately following the payment of an installment. But next year, immediately before the first payment becomes due, it will be worth $104. At any intermediate point between the present when it is worth $100 and a year hence when it is worth $104, it will be worth an intermediate amount, determined by the discount curve; for its value will always be the discounted value of the $104, which could be realized on it at the time of the next imterest payment. As soon as this payment has passed by, the value will drop to $100 again, after which it will gradu- ally ascend as before, and so on, following a series of curves like the teeth of a saw, as shown in Figure 2. In this diagram, the value of the annuity is represented by suec- 1 For a mathematical statement, see Appendix to Chap. XIII, § 3.

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