142 THE MANAGEMENT OF WOODLANDS. 



in a normal condition, capable of yielding a regular annual fall 

 of equal amount, then there will be a regular gradation of age- 

 classes normally distributed throughout the woodlands and 

 varying from 1 to n years (just before the annual fall) or from 

 to n 1 years of age (just after the fall), n being the rotation 

 with which the woods are worked. It is therefore of advantage 

 to estimate the money value of the normal capital in wood so 

 as to know the rate of interest actually yielded by the working- 

 circle. 



For example, say the normal annual returns from a working-circle of 800 

 acres in normal condition, worked with a rotation of 80 years, consist of 

 2400 for the mature fall of timber, and 300 from thinnings in woods of 

 different ages, that each year the cost of planting the area cleared is 40, 

 and that the gross general charges amount annually to 160 ; what is the 

 present value of the Normal Capital in Wood, if the annual rental value 

 of the land is 10s. an acre, and the rate of interest be 3 per cent ? Here 

 the net receipts are 2700 -200 = 2500, and their capitalised value is 



^jj|j = 83,333 . The rental value of the land being 400 a-year, its 



capital value is ^-^ = 13,333^. Hence the capital value of the Normal 



Capital in Wood is 83,333J- 13,333 = 70,000. 



The " normal condition " being always a mere ideal, when a valuation of 

 woodlands is made it must necessarily be that of the actual growing-stock 

 or capital in wood. It is only by making such a valuation that the actual 

 rate of interest obtained on the capital invested in the woodlands can be 

 ascertained. 



The Net Income obtained from Woodlands may be calculated 



. . . . . . Tq-(c+fv) 



by the formula - - - - -, where 



F=the value of the yield of timber obtained at the final clearance. 



T(a, &,...<?) = the value of thinnings carried out in the years a, b, 

 . . . q, calculated at compound interest up to the date of the final 

 clearance. 



c = the outlay for cultural costs, calculated at compound interest. 



v=the various annual outlays, e.g., protection, rates, &c., calculated 

 at compound interest. 



/=the number of years included in the fall or period of rotation of 

 the crop. 



