64 MISC. PUBLICATION 218, U. S. DEPT. OF AGRICULTURE 
ah. by definition, the land 
having zero value at the end of the & year period. Simplifying (1+ p)V’i-+4 
Formula 8 may be derived as follows: V’,i= 
Us = 7! Rae) sah 
+rV’,-1=d, or J eS poe. 
dé V'y-1 , d—rV' 5-2 Wis tans AY Sie ie 
And V'z2=7 = ae eens Substituting for V’,-1 and simplifying. 
d “i di+d+p+r)] 
u 9+ - uf SS 1 T t =) aerate CE 
a DU ror marae pee | 2 OU) manganese 
Als 1) 2 
Similarly, it may be shown that V’ eee, 
and, in general, bree 
_ d{it+(+ptrn+. ..+0+ptr)m] 
Hors CGF) 
This expression may be simplified to 
_@(tptni-i, 
Me tpt pen) 
In particular 
y! Oa Date ®) Bel 
Tepes) 
On the other hand, 
ed pe ete tea 1 
Meceegt epee = eee 
sty USED) Eel aes Chie) coat 
to Op pm pas D) 
pte) Rett tape Usa Pxtal) eal 
Worn Vo 0) Esa ie Diao asia 
Therefore, 
Wo Gap eaa! 
p(1+p)* 
or (formula 8)— 
Worl tei MGnro in) te asap oe 
Wo (1+ p+r)*(p+7)[(+p)*—1] 
If, now, p and r be 3 percent and 1 percent, respectively, as in the 
example under formula 3, and k& be 50 years, the tax ratio is 17 per- 
cent. This compares with 25 percent for the sustained-yield forests 
and 45 percent for the deferred-yield forests under formula 3, and 
38.3 percent for the financially immature timber under formula 7. 
If the virgin forest had been entirely cut over in only 20 years, the 
tax ratio would have been but 9 percent, still further emphasizing 
the tax advantage of cutting a financially mature forest rather than 
of holding it for speculation. The tax ratios for different tax rates 
are shown for three kinds of forests, annual sustained yield, deferred 
yield, and depletion yield, in figure 2. 
CERTAIN MODIFICATIONS OF THE PROPERTY TAX FOR DEFERRED- 
AND SUSTAINED-YIELD FORESTS 
ADJUSTED PROPERTY TAX 
As one remedy for the inherent disability of the property tax when 
applied to deferred-yield forests, it will be proposed in part 12 that 
the required tax payments under the property tax be so adjusted as 
to compensate for the lack of conformity between the sequence of 
q 
ty 
