184 JOURNAI, OF FORESTRY 



maximum returns. It is not correct for stands younger than the age 

 of rotation, even though the timber has a sale value, since if not dam- 

 aged the owner would receive a greater sum at maturity, which would 

 include not only his profits or loss up to the year of injury, but also 

 such profit or loss for the additional period up to maturity. If the 

 rotation has been fixed correctly, the rate of interest earned by the 

 forest at that age will be greater than that earned at an earlier age. It 

 has also been suggested that to be really correct the valuation of mature 

 stands which cannot or will not be cut for a number of years should 

 be based on a discounted sale value rather than an actual present sale 

 value. ^'^ This could perhaps be done if the date of cutting could be 

 even approximately foretold ; but as long as such dates are almost en- 

 tirely dependent on chance, and until definite working plans have been 

 prepared, such a valuation would have little value. It may also be con- 

 sidered that with rising prices, particularly for the upper grades of 

 lumber, the values of such mature stands will probably increase fast 

 enough to compensate for the delay in their utilization. 



Cost and expectation value formulae, if S^ is used, give the same re- 

 sult, which is the value of accumulated earnings on the capital invested, 

 and can be expressed in a somewhat simpler formula, which does not 

 require the computation of S^ or E. 



Albert^^ worked this formula out for naturally reproduced stands. 

 He says the cost of production at any age, m, is the accumulated inter- 

 est on the soil expectation value, together with the sum of expenses 



Y 



and interest. If S,= ■ — 7^— r E, then cost=S (i .Op™ — i) 



I .Op° I e V t- ! 



Y ( I Op™ I ) 



-j- E (i .Op™ — i) = — ' p -. The expectation value of the 



^ Y(i.Op°-™— i ) 

 stand is ^-(^.^^)(^^V--^^ ^ I '-Op--' -,_ 



Y (i.Op ™ — i) 



I .Op° — I ■ 



RiebeP^ gets the same formula in a dififerent way. He says that the 



Y X Op 

 annual rental which amounts to Y in n years is — -pr-^ — — , and that 



I .Op° — I 



°°Roth: Forest Valuation, p. 91. 



Chapman : Forest Valuation, p. 132. 

 " Lehrbuch der Waldwerthberechnung, Wien, 1862, p. 35. 



'^ Centralblatt fiir das gesamte Forstwesen, Jan.-Feb., 1915, pp. 1-15; abstracted 

 in Forestry Quarterly, March, 1916. 



