The nature of capital and income

Bibliographic data

Monograph

Identifikator:: 100669000X

URN:: urn:nbn:de:zbw-retromon-18753

Document type:: Monograph

Title:: Die freiwilligen sozialen Fürsorge- u. Wohlfahrtseinrichtungen in Gewerbe, Handel u. Industrie im Deutschen Reiche

Place of publication:: Halle a.S.

Publisher:: Carl Marhold Verlagsbuchhandlung

Year of publication:: 1913

Scope:: 1 Online-Ressource (X, 70, 441 Seiten)

Digitisation:: 2017

Collection:: Economics Books

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

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: III. Allgemeines und Spezielles über Entwicklung und Stand der Wohlfahrtspflege

Collection:: Economics Books

282 NATURE OF CAPITAL AND INCOME [Car XV) . would have if it were certain to yield the (arbitrarily assumed) 5 per cent forever — never more and never less. The riskless value is therefore simply the capitalized value of a perpetual annuity of $5 per share of $100 face value. If the rate of interest is 4 per cent, the result is $5 divided by 4 per cent, or $125. To obtain the “mathematical” value we simply add to the riskless value the value of the chance of getting more, and subtract that of the chance of getting less. The chance of getting an additional $1 a year is found by expe- rience, as set forth above, to be two in twelve, or } each year. The present value of the right to this chance has therefore a mathematical value } as great as though the $1 increment were a certainty. But the certainty of $1 a year would be worth $25. Hence a chance of 1 in 6 of getting $1 a year would be worth mathematically & of $25, or $4.16}. In like manner the chance of a second addi- tional dollar is one in twelve and is worth (mathematically) 1 of $25, or $2.08%. These two terms, $4.163 and $2.08%, are the additive terms sought. The subtractive terms are the mathematical value of the chance of getting $1 less than the $5, and of getting still another $1 less. These chances, being 3 in 12 and 1 in 12 respectively, are worth 25 of $25 and 4 of $25 respectively, or $6.25 and $2.08}. The whole mathematical value is therefore $1254 (84.163 + $2.081) — ($6.25 + $2.083), or $122.913. Applying to this the factor of caution, which, let us say, is 1%, we find the commercial value to be $110.63. The three values are thus, approximately: — Wriekloga 7 VAIUE . ss ev ese sie Wow a ls ow $125 Cathemiatical "valle vo evi ve wie wie a $123 “oommereial Tt VANE Llc ve a Ee Del a aR le $111 In this manner we may compute the three values in any other case. Usually, however, the chances involved are so indefinite that the reckoning is made only by rule of thumb.

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