186 JOURNAL OF FORESTRY 



The annual profit which in n years will amount to P is — ^ — '- — ~ 



I .Op° — I 

 or substituting the value of P given above,. 



-[,.OpT^,-(S. + C + E)]x.Op 



P ( I Op™ I ) 



The sum of m years annual profits, with interest, = — ^^ — ':=-^ 



^ ^ I .Op° — I 



The actual cost of the stand at m years is the cost of establishment, 

 with interest, plus interest on cost of land, plus sum of annual expenses, 

 = (S, + C + E) (i .Op°^— i) +C. The sum of actual cost and 

 profit accrued to year m is then : 



(Y — C) (I .Op™— i) 



I .Op° — I 



C 



Y (i .Op™ — i) 



With natural reproduction this reduces to j^~ and the 



^ I .Op° — I 



same result is obtained with artificially established stands which will 



be reproduced naturally in succeeding rotations. 



All of these methods give the value of the product, but do not cover 



the value of the stand as part of the producing capital. If a stand is 



destroyed without impairing its capital value, the loss will be equal to 



the value of the stand or part of stand destroyed. But it is frequently 



the case that the capital is also more or less damaged. This capital 



value is made up of two elements — the actual capital invested and the 



capital value of the profit or loss involved in the business. The capital 



invested is S„ -|- C + E. The capital value of profit or loss is annual 



P . Y C 



profit divided by .Op, or — , which equals 



I .Op° — I ' ^ I .Op° — I 



Y C 



(S^ -j- C -j- E). Since — p;— — (C + E) is expectation value of 



soil, capital value of profit equals S^ — S,, and the total capital value 

 of the business is 



(S. + C4-E)+(S.-SJ = S. + C + E= ^ Q~^, 



Where both stock and land are destroyed the damage will be 

 (Y-C)(..Op^-.) 

 I .Op'^ — I 

 (since E is released for other purposes, not lost). Substituting for 



Se, the total loss is ^^ ~^^ ^ '^P"* + C — E. 

 I .Op" — I 



