VALUATION OF DAMAGES TO IMMATURE TIMBER 185 



,u f .1- YX.OpX (I . Op'"— I) 



the sum of m years rental is ^ — ——^ — ^ „ r — - , or 



^ .OpX (i .Op°— i) 



Y(i.Op°^— i) ^^ 



—^ — pr-^- r— . He seems to neelect cost, too. 



(i .Op° — i) to ' 



Jacquot^^ gets a similar formula, but instead of .Op uses .Ox, the 

 actual interest rate earned by the forest, whose value he estimates some- 

 what arbitrarily. This will not give the same results except at the yenr 

 O and the year n. 



Chapman's^* formula for expectation value of the stand, if carried 

 out further, gives the formula for accumulated rentals. He says the 



Y I c I p 

 value is ^ (S,. + E) (a is the same as m in other for- 



I .Op"-^ V V I / V 



Y C 



mulse), and that S,. is — 7^—- CC -4- E). If this value be substi- 



^ 'I .Op'^ — I 



tuted for S, in the first formula, we get 



'•"'^ :V' -[ri^^-(C + E)+E] 



Y (i .Opa — n — c (i .Op^— I .Op°) 

 °' : 1 .Op- -I ~ 



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



0^ i.opn-i + ^- 



Cost value, with S^, gives the same result. Thus cost is C (i .Op^) + 

 (S, + E) (i .Opa— i) ; substituting for S,., 



= C(i.Opa)+ [-^^=j^-(C + E)+E] (i.Opa-i) 



_ (Y-C) (i.Opa-i) , 

 ~ I .Op° — I "^ ^ 



Perhaps a clearer way of deriving tiiis formula, since it avoids the use 

 of the expectation value of soil and shows the combination of interest 

 and profit which makes up the value, is the following: The profit at 

 the end of the rotation is P = Y — (S^ + C + E) ( i .Op° — i ) — C ; 

 that is, the yield, minus interest on investment, minus sum of annual 

 expenses, minus depreciation \n investment (C, where artificial repro- 

 duction is used or where seed-trees are sacrificed for reproduction). 



"Incendies en Forct-Fischer's translation, pp. 7oflF. 

 •* Forest Valuation, pp. 133-134. 



