62 FOREST VALUATION 



2. Expenses incurred to produce the stand or grow it to th 

 age of 45 years : 



Cost of planting prolonged, c (i.op m ), 

 or 8 (I.02 45 ) ..................................... $ 19.40 



Current yearly expenses e with .interest. 



e(iop m i ^, e 



- K - :=E(iop ni i) where E = 

 i. op i .op 



and yearly rent of land with interest, 



i. op i 



simplifying (E+Sc) (i.op m i) or 



(25 + 5) (I.02 43 i) ...V ........................... $43-13 



Thinning at age of 20 years, cost with interest. 



Ta(i.op ln -')= 3(i.o2 K ) ............................. 4.92 



Total expenses per acre ....................... $ 67.45 



3. Income per acre obtained from the stand during the 45 

 years, 



Thinning at 30 (just -paid expense) ................. $ o 



Thinning at 40, $10 with interest for five years ....... 11.04 



Total income $11.04 



4. Net cost per acre: 



$67.45 $n. 04 = $56.41 



and cost value of the stand of 80 acres, $4,512. 



5. This calculation is usually expressed in a formula as fol- 

 lows: 



in Gc=zc(i.op' n )-f- (Sc + E) (i.op" 1 i) (Tati.op 111 a )-f-Tb etc.) 



when Ta is made at a loss or is a negative quantity, Ta, is de- 

 ducted from costs as ( Ta) as in the sample case above. 



In the formula "'Gc means : the cost value of one acre of the 

 growing stock, m years old. 



(). The above case fully illustrates the usual calculation. If 

 natural reproduction replaces plant in-, c may be zero. Similarly, 

 if there are expenses of clearing the land, as on a burn, of cultivat- 

 ing the plantation, of filling fail places, etc., these expenses are 

 charged and prolonged exactly as planting, c. 



