78 FOREST VALUATION 



and volume known ; stumpage $10 per M. feet ; assume that the stand 

 now, 80 years old, contains 250 M. feet. Value of this 250 X 10 = 

 $2,500. 



From growth study it appears that the stand 10 years ago con- 

 tained 200 M. feet, valued at $2,000. Then the growth in value, be- 

 side increase in market price, is $500 in 10 years. Expressed as per 

 cent: 



This p x or 2.3% includes both the growth in volume and the 

 growth in quality as it finds expression in our present day practice 

 of scaling timber so that we may state: 2.3% =p x =:p v -j- p q , and 

 this requires merely the addition of p s or the growth in market price 

 to state the total growth in value. 



b. Rate of interest made by the growth of an even aged stand 

 during the entire rotation, i. e., from the time of planting to time 

 of cutting. 



Here again it is convenient to apply the fundamental form of 

 reasoning that 



r Cr Capital or values at end of rotation 



~~ Co ~ Capital or values at 'beginning 



The initial capital Co is made up of : land, Sc ; cost of planting, c, 

 or the value of young growth ; capital E, to take care of the stand, 

 pay taxes, protection, etc. 



While this capital, E, is not really on hand, the results are the 

 same, the owner must provide from some source, an amount equal 

 to the interest on E at p per cent. At the end, or time of cutting 

 the final capital, Cr, into which Co has grown, is made up of: land, 

 Sc; capital for expenses, E, stand of ripe timber, Yr, and the state- 

 ment becomes: 



r _ stand + land -\- expense capital _ _ Yr -f Sc -j- E 

 ~~ land -f~ expense capital -(- cost of planting c -J- Sc -j- E 



Concrete case: Land $15 per acre, p 2%, e = $i, hence E 



1. 00 



_ = $50 ; Yr, $400 ; c, $12 ; r, 80 years ; then : 

 .02 



40^ ^ 

 = T =6.04 



12 H- 15 + 50 77 

 and from tables : p f = 2.3%. 



