112 FOREST VALUATION 



In this formula, E = , and as p is determined, this term 

 o.op 



has a definite value (but see Formula N 2 ). 



Capital invested by owner = S e , 

 Rate earned = x per cent, 



Period of time = n years. 



By use of Formula XIV ( 89), 



S c (I.Q*) = Y + S v + E - (C + ) i.o/>, 



or 



v - . ,. 



i.ox n = -*~z (N) 



Oc 



This division of capital is purely arbitrary. An equally 

 justifiable assumption is that the owner also invests the capital 

 needed for silvicultural operations and all initial expenses (Group 

 B, 104). In this case, the borrowed capital E is first repaid 

 with p per cent interest from the gross income and x per cent 

 determined for the remainder. 



Net earnings = Y + S v E (i.op n i), 



Capital invested by owner = S c + C. 



Then (S e + C) i.ox* = Y + S v + E-E (i.o/>), 



O c T 



-E(i.op") 

 - 



Both of these solutions (N and Ni) give a value for x, 

 greater or less than that actually earned by the entire capital 

 investment. The difference is greatest when only the investment 

 in soil is used as a basis. Method NI has been advocated for use 

 in this country.* 



The true "economic" per cent (121) earned by an investment 

 is the rate paid on all capital invested for periods of one year or 



* Forest Management of Loblolly Pine, Bulletin n, U. S. Department of Agri- 

 culture, W. D. Sterrett, Jan. 23, 1914, p. 21. 



