FOREST TAXATION IN THE UNITED STATES 59 
Cis Qs 
amount of that expense accumulated with compound interest through 
the income cycle, and to decrease the numerator, X, by the same 
the denominator of the tax-ratio fraction, S, by e 
amount times ee Thus the introduction of the expense item 
results in a smaller proportionate reduction in the numerator than 
in the denominator, and makes the tax ratio larger than it would 
have been without any expense. This conclusion, while true for 
deferred-yield forests, does not apply to annual sustained-yield 
forests. In the case of aneue sustained-yield forests n=1, the tax 
ratio becomes exactly a and the effect of introducing the expense 
item is to reduce the numerator and denominator of the tax-ratio 
fraction in exactly the same proportion, thus making no change in 
the tax ratio. 
Formula 6 may be derived as follows: Assume, for the moment, that e is an 
income rather than an outgo. By formula 3, then, the annual tax on the capita] 
represented by the annual income e is e =a The balance left to the owner is 
Pax 
Dah 
mathematically it makes no difference whether e is an income or an outgo, the 
obviously e—e f 7) or € This capitalized at p percent is te Since 
term or remains intact irrespective of the algebraic sign of e. If eis an expense, 
is the capitalized expense. The tax rate times this capitalized expense 
é 
per 
compounded to the end of the income cycle at the interest rate p is ate 
[(a+p)2714+ (1+p)7?+ ...+(1+p7)+1), the bracketed portion of enioh 
(Fp) tal , 5 : ‘ re eee), 
This entire quantity, i-e., aus 
must now be subtracted from the expression on the right of the equation given 
in formula 5 to obtain the next subformula for X, namely (formula 6), 
simplifies to 
= ws im — 2—m LS Dee rae ae 
ies ila lier Aint taihnd? | oe 
J; ore" |. 
7 1+ 1 
In this case S= Y—C+T,,(1+p)2-"—e feel and the tax ratio is the 
ratio of X to this quantity. 
EFrrect oF THE PROPERTY TAX ON THE INITIAL FOREST VALUE AND Most 
PROFITABLE ROTATION 
As previously indicated, the initial forest value is the expected future 
net income discounted to the beginning of the income cycle and in the 
case of an even-aged forest equals the soil expectation value plus the 
cost of regeneration. The general formula for this initial forest value 
is as follows: 
e jab GH Na ary sr allls olen Oae 
zi (i+p)*—1 
se 
