EXPECTATION VALUE. 125 



(2) Intermediate Cuttings, or Thinnings. Let T a , T b , T c 

 . . . T q , represent the value of thinnings, less cost of 

 harvesting, occurring in the years a, b, c, . . . q. Each 

 of these thinnings occurs during every rotation, that is to say, 

 every r years. Thus the first thinning occurs after a years, 

 again after a + r years, again after a + 2 x r years, and so 

 on ; hence the present value of all these thinnings, according 

 to formula. IX. : 



= T a xl'op r ~ a T b xl'ojf~ b 

 l-op r -l ' l'op r -l 



^T a x l'op r ~ a + T b x l'ojf- b 

 l'op r -l 



(3) Minor Produce. These are dealt with in the same way 

 as thinnings, if they occur at regular intervals. Let M s , M h 



. M st be the values of minor produce occurring in the 

 years s, t . . . z, and again every r years, then their 

 present value is 



M s xl'op r - 8 +M t xl'op r - t 



l'op r -l 



If items of minor produce occur regularly every year, as 

 grazing fees, rent from shooting, etc., and of equal value year 

 after year, their present value amounts, according to formula 



VII., to**. 



'op 



I. 'Present Value of Expenses. 



(1) Cost of Formation. Assuming that c represents the 

 cost of formation, whether artificial or natural, which has to 

 be incurred at the commencement of each rotation, then the 

 present value of all such expenses comes, according to formula 

 X., to : 



C ^ 1 V}71^* 



Total present value of cost of formation = - J . 



1'oj/ 1 



If the first cost differs from that on future occasions, and if 

 the latter is represented by c, then the total present value is 



