78 FOREST VALUATION 



Then = R = E. capitalized annual expense. 



o.op 



The sum of these expenses, provided they remain at a constant 

 annual amount, is 



E (i.o/> B ) - E = E (i.op n - i). 



The analogy of this calculation to that used in Group A is 

 evident. The difference is that in A, S e represents existing 

 capital which remains as an asset, while in C, E represents 

 a fictitious capital which may have no existence and is never 

 expended. It represents the capital which would be tied up, 

 in order to produce an income to just balance the expense e. 

 This capital might, if the owner desired, be actually deposited 

 at interest, when the expense e would be permanently taken 

 care of and the capital remain intact at the end as in Group A. 

 But the proprietor usually meets this expense out of income 

 from other sources. The capital represented by E is, therefore, 



merely a mathematical device, and the expression better 



o.op 



expresses the status of the item, as it emphasizes the annual 

 expense. 

 Should expenses increase, the modified Formula Ilia is used, 



by substituting E' for -^- ( 79) . 

 o.op 



The total actual cost of production for timber grown under 

 management covers the period from its origin to its removal. 

 Adding the summaries for the three groups, we have 



G c = C (i.op n ) + S c (i.op n - i) + E (i.op n - i) 



= (C + S c + E) i.op n - (S c + E). (A) 



This formula suffices when all initial crop expenses occur in 

 the first year. 



Income during this period serves to cancel an equal value of 

 accumulated costs in the year in which it is received. Annual 

 income usually serves merely to reduce the net annual cost, and, 

 therefore, does not appear in the formula. But income received 

 from the sale of produc.ts obtained from advance cutting, or 

 thinnings, bears no constant relation to the total expenses for 



