THE SIMPtE FORMULA 69 



The average value per acre of the growing stock on this forest 

 is: 



(400 + 75 + 10) (1.02"— I'j+Tod.oa") (i.02'°—i) + 20(1.02'") (l.02°°— I) 



80(1.02") (1.02— I) 



— (75+10) 

 =: 253 — 85 = $168 per acre, or about $2,688,000 for the property. 



This case closely resembles a fair case in spruce in Germany, 

 site II, except that the cost value of the land is taken rather low. 

 The calculation indicates that the growth produced by this growing 

 stock will pay two per cent on the capital invested in the property 

 and composed of $160,000 for land and $2,688,000 in growing stock. 



4. Simplifying the above formula by substituting Se, or its 

 value for Sc, results as follows and gives a very useful form : 



sinceSe = Yrf Ta(i.opr-a)— c(i.opr)— Ed.op-"— i) 

 (i.op'— i) 



Se (i.op^ — i) may replace Sc (i.op'' — i) in the above for- 

 mula as follows : 



°-('-')Ge per acre = 

 Yr(i.opr— i)+E(i.op'-— i)+Yr + Ta(i.opi--a)— c(i.opr)— Ed.opr— 1) + 

 r(i.op') (i.op— I) 

 Ta(i.opr-a)(x.op^i) _ 3^^ 



T(i.opr) (i.op — i) 



which simplifies into : 



Yr + Ta— c ,_ ,, ^ Yr + Ta — c — re _ 



— , C" — (E-j- Se) = -. ; — — Se 



r(i.op — l) ■ r(i.op — I) 



In this last form the formula clearly shows the work, expense 

 and income of the r acre sample, of the regulated forest. The yearly 

 income is Yr and Ta ; the yearly expenses are c and re, the differ- 

 ence is the net income from the r acres. This net income divided by 

 r is -the net income per acre, and this capitalized gives the income 

 value of the forest, i. e., land and timber together, so that the value 

 of the growing stock is this income value of property minus the 

 value of the land. 



Using the premises set before and putting c = $10 and replac- 

 ing Sc with Se at $28 we have : 



,, , r . , 400 -I- 10 + 2 — 10 — 120 o ^ 

 Value of growing stock per acre ' — SoT'o?) — 2«==$iS9. 



In this particular case the result, $159, compares closely enough 

 with $168 as obtained by the ordinary formula. In any case it is 



