60 FOREST VALUATION 



(III and IV), and if intermittent and terminating, such as a 

 succession of thinnings from a crop of timber previous to final 

 cutting, they are also apt to be of different values, requiring 

 separate valuation. If assumed to be equal in value, they may 

 usually be assumed to recur perpetually (IX). 



83. Present, Expectation, or Capital Value of Temporary Inter- 

 mittent Rentals, Due First at n Years, and t Times at Intervals 

 of n Years Thereafter. The present, expectation, or capital 

 value of intermittent rentals limited in number is found as 

 in the case of annual rentals. 



The series decreases. 



For rentals due first after n years and t times at intervals of 

 n years thereafter, this series is 



R=-^ + ^- + -^-+ - | r ' 



i.op n i.op 2n i.op 3n i.op tn 



Then (Q 2 ), 



Q= 1 -^- 



i.op n 



i 

 i.op n 



i.op nt ) 



I 

 I 



i.op n 

 Multiplying numerator and denominator by i.op n X i.op nt , 



R _ /d.O^-1) 



(i.op n - i) i.op nt 

 The same result is obtained by discounting the future value 



of the series (V) to the present (II) using the factor as 



i.op nt 



the substitute for 

 i.op n 



R = r' (i.op nt - i) x i = r' (i.op nt - i) 



i.op n - i i.op nt (i.op n - i) i.op nt ' 

 84. Future Value of Temporary Intermittent Rentals, Due 

 First in a Years, and t Times at Intervals of n Years There- 

 after. When the value of the sum of temporary rentals is 



