110 FOREST VALUATION 



In the same way, it can be shown that for definite costs and 

 income, the profit determined for any year may be converted 

 into that for any other year by the use of Formulae I and II. 



Substituting S, for S c in Formula LI, thus reducing profit 

 to zero, this formula becomes 



r + s.+E_ 



i.op 

 Then 



Y+S+E_ 

 i.op n 



Resuming the value of S e as cost of land, the profit is 



P = Y + S * + E _ ( C + ) - s c 



I. Op* 



= S V - S c . (See L 3 .) 



Since Formulae LI and L 3 are thus derived from Formula L 

 by discount (II), the reverse is true, and for any year a 



P-(-Sjinp- CU) 



128. Profits Expressed as a Ratio of Income to Capital. 



The economic forecast shows profits as a net sum or balance 

 between assets and cost, which sum cannot be realized in money 

 without a sale of ownership. But the net future income which 

 is accountable for this balance of profit shown may be also 

 expressed in terms of interest earned on the cost instead of as 

 capitalized value (121). The rate or ratio of income to capital 

 depends directly upon the period of time elapsing between ex- 

 penditure and income ( 23), a fact often lost sight of. In quick 

 profits, earned largely by the sale of property at an advance in 

 capitalized value rather than by awaiting the slow realization 

 of income, the element of time is lost sight of; yet every profit 

 should be standardized by reducing it to the rate of interest 

 which it represents on the investment for the period of waiting. 

 Should a property be sold at double its cost, the profit is 

 100 per cent on cost. But with the element of time intro- 

 duced, the rate earned would be as follows (Formula XIV) : 



