68 FOREST VALUATION 



,^^ ^ Yr^o-(Sc. + E)(i.op--i) 

 I. op'-' 



.Q^_ Yr + T^d.op'-')— (Sc+E) d.op'-^— I'l 

 i.op'-^ 



, or _ Yr + T,d.op'-') — (Sc + E) (i.op'-''-i)* 

 ^e- i.op'-» 



To get a common denominator for S Ta, treat in this manner : 



Ta(l.opa— i) Lopr-a _ TaCl-Opr-a) (i.opa— i) 



IOpa(l.Op — I ^ I.opr-a ^ I.Op''(l.op — I 



adding we have : 



°-('-''Cc:^ (Yr-j-E + Sc) (i.opr_i)4-Tad.Opr-a) (l.opa-i) 



(I.OP-) d.op-i) -r^bc-l-Ji) 



as the expectation vaUie of the growing stock on the ten-acre, or r 

 acre sample. Dividing this by r the average value of the growing 

 stock per acre is obtained and the formula reads : 



"-('-')'Ge average per acre = 



(Yr + E+Sc) d.opr— l)+Ta(l.Opr-a) (i.opa_i; _ 



rCi.opr) (i.op— i) (.i>c-|-t,; 



3. To illustrate : Assume an area 16,000 ; clear cut, and plant, 

 p, 2%. 



Rotation, 80 years. 



Premises per acre: final yield or Yr, stumpage value per acre, 

 $400. 



Thinning at 20 years, no income. 



Thinning at 40 years, $10 stumpage. 



Thinning at 60 years, $20 stumpage. 



I -SO 

 Current expenses $1.50, hence E= , or $75. 



.02 

 Cost value of land, So, $10. 



* For the class it is helpful to write these out as follows : 



,.p Yr , Ta (Lop'-') _ QSc 4- E) i.op'-" (Sc + E) 



I.Op'-'" "•" LOp'-"" LOp'-"" """ I.Op'-"' 



this makes addition of 2Yr, 2Ta, etc., muoh easier and clearer. 



