VAIvUATlON OF DAMAGES TO IMMATURE TIMBER 187 



Since the amount of the capital originally invested, being an actual 

 cost, is not changed by the damage, the loss falls on the capital value 



of the profit, or Se - S,., and equals (S, — S^) - (S,' — S^), or 

 Se ~ Se^> the difference in expectation values of the soil before and 

 after the damage. The total loss is 



( Y-C) (i.Op-^-i ) Y-C(i.Qp") 



Top^^^ri + c + s, s,. , Se IS J opn_i ^' 



in case of total loss S/ (all future income minus all future cost) is 



— Tir — (C^ 4- EM, where Y^ and E^ are zero, and C^ = C. 



I .Op° — I ' ^ 



Y C 



Se — S,.' then equals — p^^E^ ^> ^"^ ^^^^^ ^^^^ i^ 



(Y — C) i.Op'" , r- t;^ ,u K 



^ ^r — *-— 4- C — E, the same as above. 



I .Op° — I ^ 



Ordinarily, however, the destruction will not be so complete, but in 

 addition to the loss of the stand further damage will consist of (a) an 

 increased cost of establishment, particularly where intended natural 

 reproduction must be given up for artificial reproduction, with or with- 

 out additional costs for preparing the ground; (b) increased expenses 

 for protection, due to the increased hazard on burned-over areas; (c) 

 decreased productivity of the soil, due to actual reduction in its fer- 

 tility, to erosion, or to invasion by brush or inferior species of trees, 

 such as lodgepole pine, in regions where it is of secondary importance 

 as a timber tree. Where the original forest calls for natural reproduc- 



Y 



tion. S is- — 7=: E. If planting is required to restore the 



I .Op° — I 



stand, and succeeding generations can be reproduced naturally, S/ will 



Y 



be — ^ (C^ + E), so that the loss in capital will be C^ If 



I .Op° — I ^ ' ^ 



the original forest calls for artificial reproduction for each crop, its 



Y C (i Op°) 



S is ?^ ^^ — '- — — E. and if the stand must be planted after the 



" I .Op" — I ^ 



damage and for all succeeding crops at the same cost. S,' will also be 



— — — '- — ^-—^ — E, and there will be no loss in capital. If the new 



I .Op" — I ^ 



stand and all future stands call for a cost different from C. S/ will be 



Y — 0(1 -Op") ^ , ,. ., , , .„ , (O — C) i.Op° 



-z, — -^^ ^— ^ E. and the capital loss will be rrr— 



I .r)p" — I ^ I .Op" — I 



