54 



FOREST VALUATION 



The expression o.op is an arithmetical term, in which the letter 

 p is substituted for the numeral representing the rate of interest. 

 For a given rate, as 4 per cent, the expression reads 0.04; for 10 

 per cent, it reads o.io. 



o.op is the ratio between capital and interest for one year. 

 Therefore i + o.op, or i .op, is the ratio between the capital at 

 the beginning and end of the year, assuming that the interest is 

 added to the principal. 



7i:P ::i.o:i. 



Vi = V X i. op. 



At the end of the second year 



F 2 : Vi : : i.op : i. 

 F 2 =Vi X i. op 



= (Fo X i .op) i. op 



= Fo X i.of, 

 V z = (V X i. op 2 ) i. op 



= Fo X i. of 

 and V n = (Fo X i.op^ i.op 



= Fo X i. op". (I) 



This formula is used to determine the accumulation of cost on 

 an investment which does not produce income until the close of 

 a stated period. In such a cost account ( 25 and 36) all in- 

 vestments are charged with interest. Sums representing expend- 

 itures which occur only once and cannot be treated as rentals, 

 as, for instance, the cost of planting trees, are totalled for n 

 years by this means. 



All formulae dealing with future values of present sums show 

 also the present cost of past expenditures. They reckon forward 

 from beginning to end of an investment. 



77. Present, Expectation, or Capital Value of Future Sums. 

 In computing future sums, the value at a future period has no 

 special significance until it is discounted to the present. 



If V n = Fo X i.op n 



then V Q = n . (II) 



