EXPECTATION VALUE. 123 



q. Each of 



these thmnings occurs durmg every rotation, that is to say, 

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

 again after a -\- r years, again after « + 2 X r years, and so 

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

 to formula IX: — 



_ T, X 1-0// -° T, X l-O;/" , , 1\ X VOp'-" 



\-0f - 1 "*" VOp' - 1 ^ ■ • • "*" i-Qp'- - 1 



= ^'g X VO}f -" + Tr> X VOf ' + > • • + T„ X 1-Oj/ "^ 

 l-Oi/-l 



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

 as thinnings, if they occur at regular intervals. Let il/„ Mt 

 . . . Ml be the values of minor produce occurring in the 

 years s, t . . . z, and again every /■ years, then their present 

 value is-^ 



_ M, X 1-0^'-^ + .V, X 1-Oy + ■ . . H- M, X l-Oy--' 

 l-Qf — 1 



If items of minor produce, M, 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 i^. 

 •0}) 



h. Prosenf Valve of E.rpen.^es. 

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

 (»ost 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 :— 



Total present value of cost of formation = /' X 1 Up 



l-O^/ - 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 -r- 



e+ ^1 . 



