66 FOREST VALUATION 



The capital value of an intermittent rental is and 



i.op n i 



of an annual rental . Since the annual income for each is 

 o.op 



required to be equal, these expressions must have the same value. 



If 



i. op" i o.op 

 then r = ^ ' _- X o.op. (XIII) 



The annual rental equivalent to an intermittent rental falling 

 due first at an interval shorter or longer than n is found in 

 the same way by multiplying the capital values given in for- 

 mulae XI and XII respectively by o.op. The results show that 

 notwithstanding the fact that the intermittent rentals are 

 equal in amount and paid at equal intervals, the capital value, 

 and its equivalent in permanent annual income, constantly rises 

 until one of the intermittent payments is received, which at 

 once diminishes this capital value by the exact amount of the 

 payment. If exchanged for an annuity at this time, the per- 

 manent income thus secured is the lowest for any portion of 

 the period, while a similar exchange effected just previous to 

 receipt of intermittent income secures the maximum annual 

 revenue. 



89. The Ratio of Income or Earnings. The "rate of inter- 

 est," p per cent, is accepted as a fixed standard in computing 

 cost (I); or in discounting for value (II). But when both cost, 

 or investment, and income are known, the ratio of this income 

 to cost represents the earnings of the capital invested, or divi- 

 dends. A rate of interest can be found by which the discounted 

 value of income is made to exactly equal cost, or the accumu- 

 lated costs to just balance income. This rate is the per cent 

 earned by the investment. 



To distinguish this rate from the "rate of interest" p, the 

 term x will be used. 



x = per cent representing income earned. 



