THE VALUATION OF FORESTS 89 



114. Value of a Forest of Even Age Just Previous to Cutting. 

 A forest or stand of even age may be cut clear at one time and 

 replanted. During the period immediately following the cut- 

 ting, the soil is bare of trees, while at all other times it is occupied 

 by timber of constantly increasing size. 



Since every item of either income or expense must be assumed 

 to recur for each future timber crop, the total present or dis- 

 counted value for each item is found by Formulae IX to XII. 



For the year n, and just previous to receipt of income Y, the 

 value of income Y, being the sum of all future payments dis- 

 counted to the present year, is 



The cost of planting or reproduction, which in destructive 

 lumbering does not occur, falls here in the same year as F and 

 recurs every n years. 



Value of expense C, totalled in the same manner, is 



c + ^_ + c + ... + ^_ = c + _^. 



I. Op I. Op* I. Op I. Op I 



The annual expenses e recur at intervals of i year, by defini- 

 tion, and are computed from the end of each year. 

 Value of the sum of annual expenses e: 



e e e e e e _ 



i. op i.op z i. op 3 i.op x i. op i o.op 



Let F v = expectation or capital value of forest property for 

 continuous production. 

 Then 



which is the value of forest property just previous to removal 

 of the timber. 



In this formula, no account has been taken of other items of 



