142 VALT'ATION OF THE GROWIXCt STOCK. 



years ; at the same time, every year formation will cost 

 c shillings, while supervision will cost r X e shillings. It 

 is of interest to the forester to ascertain the value of the 

 growing stock in such a forest, the same being known as " the 

 growing stock of a normal series of age gradations." 



The annual net return of a normal series of age gradations, 

 or a working section, forms the rental of the soil and normal 

 growing stock of that working section. Like the interest 

 yielded by any ordinary capital, that rental is produced w^ithin 

 the year, so that the growing stock at the end of the year 

 represents the capital plus one year's rental. Hence, the 

 capital alone is present immediately after the year's rental 

 has been removed. At that moment the oldest age gradation 

 is (r— 1) years old, the next (r— 2), etc., and the youngest 

 (which has just been cleared), is years old. 



Where cuttings are made in winter, the normal growing 

 stock is present in spring, before the trees have commenced to 

 lay on the new annual increment. 



The simplest way of calculating the value of the normal 

 growing stock is to capitalise the annual net income and to 

 deduct from the amount the value of the soil. 



The annual net income is represented by the expression — 

 Yr + 2'„ + . . . + r,, - (c + r X e) ; 

 hence, the value of the growing stock is equal to — 



Y,. + T, + • • • + r. - (c + r X g) _ , X v 



or for the unit of area 



r. + 7; + . . . + r, - {<■ + r X r ) _ ^ 

 r X -Op 



Example.— Taking the same data as before and a rotation 

 of 80 years, the normal growing stock standing on 80 acres is — 



8O/7 _ 



^-^ normal 



3,004+5 + 44+87 + 118+134-(60+80x3) Qnx/ mi 

 ^25 -80X404 



^-G„<,™^; = 91,360 shillings, 



