VALUATION O'P DAMAGES TO IMMATURK TIMBER 183 



X=(Ss+^£!:!l=.l)=C(..Op») + (Sc + E)(:.Op^-0 



or reducing, Y = C (i .Op°) + (Sc + E) (i .Op°— i). 



In other words, the final yield is worth just what it cost to produce 

 it, and there is neither profit nor loss. This means that .Op is the rate 

 actually earned by the forest, or .Ox, not an arbitrary rate chosen be- 

 forehand. If an arbitrary rate .Op is used, it will be necessary to use 

 the expectation value of soil rather than cost value. Without using 

 S^ the expectation value formula can give negative values for stands, 

 which is absurd. The capital value of soil for forest production may 

 well be negative, meaning that at present prices the cost of production 

 exceeds returns from the product ; but to say that a product which has 

 a positive sale value at maturity can be worth less than nothing some 

 time before maturity does not sound reasonable. The objection to use 

 of expectation value of very young stands on the ground that it gives 

 very low values^^ has no weight as long as such values are positive, as 

 they will be if based on S^. The product value of such stands, which 

 expectation value represents, really is very small, and their value as 

 part of the forest capital, which is the most important part of their 

 value, is not included in the expectation value. The cost value formula, 

 using Sc, can also give negative results for stands from which inter- 

 mediate returns have been received. Especially is this true of stands, 

 such as those on the National Forests, where cost of land and planting 

 was zero and administration cost has been very low. 



Most writers agree in recommending the use of sale value for stands 

 of merchantable size, even though not necessarily at the age of rota- 

 tion.^^ Glaser-* attempts to get around the use of either cost or ex- 

 pectation value, even for young stands, by using actual sale value as 

 soon as the stand has a sale value greater than its cost (not considering 

 interest), and for younger stands a value determined by the formula 



(Y^ — C) 2 -h C, where \\ is sale value at x years, when first mer- 

 chantable without a loss ; a is the actual age of the stand and C the cost 

 of the stand. Actual sale value is the correct one for stands which 

 have reached maturity, assuming that the rotation is fixed at the age of 



" See Standard Instructions for the Determination of Fire Damages, 1916, 

 p. 7. 



"See Standard Instructions for the Determination of Fire Damages, 1916; 

 Forstwissenschaftliche Zentralblatt, Aug., 1910, article by Keiper, reviewed by 

 Gaertner in Allg. F. & J. /.., 1910, pp. 224ff. ; Chapman. Forest Valuation, p. 128. 



"Zur Praxis dcr Waldwcrtsbercchnung-Ccntralblatt fiir das gcsamte F"orst- 

 wescn, January, 1913. 



