FOREST TAXATION IN THE UNITED STATES 51 
Therefore, the income tax on each such item would be determined 
by applying the income-tax rate, Since this same part of all 
income before taxes would be taken by taxes, the tax ratio would 
always equal the income-tax rate and could be determined from the 
interest rate and the rate under the property tax for which the income 
tax would be substituted. 
For practical purposes it is necessary to take into account the nec- 
essary expenses connected with managing a deferred-yield forest, which 
may be considered to be the cost of regeneration, C, incurred at the 
beginning of each income cycle of n years after the first, and the 
annual expense, e. The cost of regeneration at the beginning of the 
first income cycle is considered part of the permanent investment, as 
previously explained. As a first approximation, consider a forest 
having only one major yield, at the end of the income cycle, and no 
intermediate yields from thinnings or otherwise. Both cost of regen- 
eration and annual expense are chargeable to the yield, Y, which is 
received at the end of the cycle. Under an income tax, the taxable 
income for the entire cycle es equal (Y—C—ne). Applying to 
this sum the income-tax rate Sap , the total tax, X oe. 
The total net income before bans with compound interest to the date 
of final yield, S, is obtained by subtracting from Y—C the amount of 
the annual expense with compound interest, or ée a. Thus, 
S=Y—C— ene The tax ratio is then 
i a C—ne) 
Honmulanitice ain ami aa 
S~y_¢_ dtd 
If n=1, that is, if an income is received every veoh, (Y—C—ne)= 
Y— caves *) and the tax ratio becomes 5 a ——» which is also 
the rate of the income tax. 
If n is greater than 1, and if there is an intermediate income from 
thinnings, 7,,, received in the mth year from the beginning of the 
cycle, the income at the end of the cycle will be increased by this 
amount with compound interest from the year of the thinning, or by 
al +)"-™, Introducing this term as an addition to Y in formula 1 
gives the formula for the tax ratio under the income tax where inter- 
mediate income from a thinning js involved, 
x i tare Uk Tn(l+p)"-"—C—ne) 
Formula 2, Ss Se LA CN PR RNR in ery OO 
Y+ Py tae Oe. Mee Rhee 
Thus an income from a thinning has the same effect on the tax ratio 
as an increase in yield. If there is an annual expense, an income from 
thinnings reduces the tax ratio below what it would have been had there 
