134 VALUATION OF THE GROWING STOCK. 



Thinning in the vear p . . ^,^p X I'Op'-^ 



Expenses : 



(1.) Annual expenses to be incurred from the year m to the 

 year r; their present value amounts to — 



l-0/*"^T(V "^ • • • + i^->" = (ncfording to Formula YD 



e 

 ^ a-Gp^-"'-l) ^Op (l'Oi''^"-l) _ E (1-0//-'"- 1) 

 V02f-"'X 'Op ~ ' I'Op'-'" ~ I'Op'"' 



(2.) "Rent of soil to he paid from the year di to the year r; its 

 annual amount may he denoted hy ,S' X •O;^ ; the total present 

 value of the rent of the soil during r — vi years amounts to — 



.S' X -O;) S X -O p S X -Op S X -Op (l-OjV-"'-!) 



1-Op + VOp^ + • • •+ 1-0^/— - i-Op'-'" X -O;) 

 _ ,s' (l-o x-"'-l ) 

 l-Oj/-'" 

 The formula for the expectation value of a wood stands, 

 therefore, as follows: — 



Y,+ T„XlOp'""+ ••■ + T^Xl-Op'^-'>-(S + E) (lOp*-"-!) 

 l-Op"-" 



Example. — A fully-stocked Scotch pine wood, worked under 

 a rotation of 80 years, is feloniously burned when 45 years old; 

 what compensation per acre should be paid to the owner, if the 

 expected retuins are those indicated in the table at page 120? 

 Rate of interest = 2i per cent. 

 Value of soil = 404 shillings. 

 Annual expenses = 3 shillings, to 1 e incurred at the 

 end of each year : — 



3,004 + 87 X 1-025=" + 118 X l-025~" + 134 X l-025i" 

 - (404 + 120) (1-025=^^— 1) 



'(i. = 



1-0253S 

 '^(i,, = l,liJ8 shilhnos = £59 13.s. 0,1. 



