114 FOREST VALUATION 



investment that profits must be computed whether or not the 

 capital invested in future expenses is also entitled to share in the 

 profit. The rate of interest earned offers an intelligible standard 

 of comparison with the common forms of business enterprise. 



The profit ( 39) or enterpriser's gain is then found as a ratio 

 instead of a lump sum, by subtracting p per cent from x per cent. 



European methods of computing the rate x earned by capital 

 invested in forestry differ from those advocated above. The 

 capital investment is regarded as the cost of the forest soil, 

 in accord with Method N. But instead of computing the rate 

 of compound interest which is earned on S c , the first step is to 

 calculate the annual "rent" earned on S v , which is equivalent 

 to S v X o.op. This, divided by S c , gives o.ox, and x is termed 

 the mean annual forest per cent. As expressed by Schlich, 



x = | X p. (N,) 



The per cent x in this formula is more sensitive than in 

 Formula N. When x > p, a higher rate is shown for x than that 

 given by method N. This is due to the effect of using different 

 rates of interest, x versus p, in discounting by the two methods. 



Formulae N to N 3 express profits only for the beginning of 

 the enterprise, as forecasts or as summaries. When the poten- 

 tial annual or current rate of interest is desired, termed the cur- 

 rent annual forest per cent, this may be found, after the timber 

 becomes of merchantable value, by first determining the annual 

 increase in this stumpage value (Chapter XII, 182). 



Let Y n = stumpage value in year n. 



Y n+ i = stumpage value in year n + i. 



From the increase thus shown must be deducted the annual 

 expenses e. The investment consists of the cost of the forest 

 for the year n, consisting of soil and timber, and represented 

 (Formula A 2 ) by a F c . 



The formula for current forest per cent is 



