62 FORKST VALUATION 



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

 age of 45 years: 



Cost of planting prolonged, e (i.op'"), 



or 8 (1.02") $ 19.40 



Current yearly expenses e with interest. 



e(iop"' — I T-^ ni N I T- e 



— ^^ — = E(lop'"— l) where E= — 



I.op— I ' ' , .op 



and yearly rent of land with interest, 



rent ^'°P"'-') ■= Sc(i.op--l). 

 I.op — I 



simplifying (E+Sc) (i.op'" — i) or 



(25 + 5) (1.02"— I) $43.13 



Thinning at age of 20 years, co.st with interest. 



Ta(i.op'"-°)= 3(1.02=") 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, $ic with interest for live years 11 .04 



Total income $11.04 



4. Net cost per acre : 



$67.45 — $11.04 = $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: 



'"Gc = c(i.op"') + (Sc + E) (I.op'"— i)— (Tad.op'" °)+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 "Go means : the cost value of one acre of the 

 growing stock, m years old. 



6. The above case fully illustrates the usual calculation. If 

 natural reproduction replaces planting, 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. 



