52 MISC. PUBLICATION 218, U. S. DEPT. OF AGRICULTURE 
been no such income and all other factors had remained the same. 
If there is no annual expense, an income from thinnings has no effect 
on the tax ratio, which remains equal to the rate of the income tax. 
If in illustration of the foregoing formulas, an example is taken in 
which there is no expense, the tax ratio equals the income-tax rate, 
as previously noted, and depends entirely on the tax rate, 7, and the 
interest rate, p. Thus if r=1 percent and p=3 percent, the tax ratio 
is then 25 percent, regardless of the values of Y, C, Tn, n, or m. 
If, as in actual practice, there is an annual expense, e, it is neces- 
sary to make further assumptions to illustrate the use of the formula. 
Let r=1 percent, p=3 percent, n=50 years, Y-C=$100, T,,=0, 
and e=5 cents. The tax ratio is then 26 percent. If the annual 
expense, ¢, is increased from 5 to 20 cents, the tax ratio under the 
income tax will be 29 percent. In the latter case, if a thinning yields 
an income so that 7,,=$10 and m=25, without change in the other 
factors, the tax ratio will be 28 percent. 
It is evident, then, that there may be an increase in tax ratio for a 
deferred-yield investment over an annual sustained-yield investment 
even under an income tax, though it will be shown later that in the 
case of forest investments this increase is relatively moderate com- 
pared with the increase under the property tax. Furthermore, this 
Increase in tax ratio under the income tax is not because taxes are 
imposed in advance of income, as under the property tax, but because 
the nature of the enterprise requires that expenses be incurred in 
advance of income. If the taxes on that part of the income which 
represents interest on these additional investments in the form of 
annual expenses were remitted, the tax ratio would remain the same 
as for an annual sustained yield investment. However, such remis- 
sion would be contrary to generally accepted opinion as to justice in 
taxation, since it would fail to recognize that annual expenses in the 
case of a deferred-yield investment represent an increase in the 
amount of the investment and consequently in its tax-paying ability. 
Therefore, the income tax (tax on net yield) may be regarded as 
imposing a fair burden on deferred-yield forests, even though the tax 
ratio is not perfectly equalized with that of an annual sustained- 
yield forest. 
UNMODIFIED PROPERTY TAX 
SUSTAINED-YIELD AND DEFERRED-YIELD FORESTS 
Tue Tax-RATIO FoRMULA (SIMPLIFIED) 
In developing mathematically the relations between the unmodified 
property tax and the value of the forest, under sustained-yield or 
deferred-yield management, it will be convenient to start with a 
simplified case in which neither incidental income, as from thinnings, 
nor annual expenses are considered. These intermediate items of ‘n- 
come and cost will be introduced into the formulas at a later point. 
Assume an annual sustained yield forest with a net income before 
taxes (Y—C) of $800, the interest rate being 3 percent and the tax 
rate 1 percent. Obviously, in order to satisfy the interest-rate and 
tax-rate proportions three-fourths of the net income before taxes 
must go for interest and one-fourth for taxes. Thus, the interest is 
$600, and the taxes $200, and the value of the forest is $20,000, i. e., 
$600 Pee 3 200 
a The tax ratio is 25 percent, 1. e., 800. 
