STUMPAGE VALUES 175 



elation expense is heaviest in the earlier years, and steadily 

 diminishes. 



Let z = per cent of depreciation, and 



o.oz = per cent expressed decimally. 



Then A(i - o.oz) n = W, 



O.OZ = I - t, 



A 



This method is seldom employed as it is inconvenient to write 

 off large sums for depreciation in the earlier stages of the business, 

 especially in lumbering. 



Method D. This method proposes to increase the amount 

 charged to depreciation annually, and combine it with an annual 

 interest return on the diminished or residual capital, in such 

 amounts that the sum of interest and depreciation will require 

 equal annual payments. Depreciation, by reducing the invested 

 capital, correspondingly lowers the interest returns required 

 by a given rate of interest. This reduction in interest may be 

 added annually to depreciation. It only remains to determine 

 what annual sum in excess of interest on the original investment 

 is required for the first payment, to secure this balance between 

 the two elements of interest and depreciation, so that the 

 sum of the increasing payments on account of depreciation will 

 at the close of the period just equal the total amount to be 

 written off. 



In this case, either of two solutions is possible to determine the 

 annual payment. 



Let Z = annual payment for interest and depreciation. 



Let d = ^^- - - , when p = rate of interest to be earned on 

 o.op 



capital A. 



