DETERMINATION OF THE PROFIT. 155 



In this formnlapart (11.) represents the expectation valne of the 

 soil discounted for r — m years, and the bracketed part of expres- 

 sion (III.) represents the cost value of the m 3'ears old growing; 

 stock ; hence, the above formula can be written as follows : — 



p_ r,.+r,,xi-Oj/-"+...+r,xi-o;/-^^+^s;-j^(i-Ojf-'"-i) 



-(.S.+'^G,). 



Here again, the positive part represents the expectation value 

 of the forest (see page 144), and the negative part the cost 

 value of the forest ; hence — 



Profit P = "T^ — "F^ = (S3 — SJ X l-Op*". 



It will be seen, that this formula agrees with tliat given for 

 a blank, because for the year the expectation value of the 

 forest is equal to the expectation value of the soil, and the 

 same holds good for the cost values. 



The conclusions drawn on page 153, headings (1.) to (4.), 

 with regard to the formula P = S^ - »SV, also hold good with 

 regard to the formula P = '"F, — '"F,. 



h. C'ahmlaUon for the Annual Worlnni]. 

 In this case the returns and costs occur regularly every 

 year. If the}' are of annually equal amounts, the returns are 



= Yr+T„+ + T„ 



The costs consist every 3'ear of — 



(1.) Interest on the value of the soil . = r x S, x "O^) ,- 



(2.) Interest on the value of the normal 



growing stock . . . . = /• x "Or X "0/) .- 

 (3.) The annually recurring cost of ad- 

 ministration, protection, taxes, etc. = r x c ; 

 (4.) The cost of formation . . . =^ ^ ; 

 hence, the annual profit — 



P = Y..+ T.. + .. . + T- c- r X f - [r X *S',.+ r X "G,] X '0]) ; 

 or. 



Annual P ^ i;+r„+. • . + T-c-rXr ^^.^^^ ^ ^ ^.^„^^^ 

 •Op "Op 



