FOREST TAXATION IN THE UNITED STATES 45 
TAX CAPITALIZATION AND DEFERRED INCOMES 
It has been shown that, under a permanently fixed property-tax 
rate, complete capitalization would so affect the present value of 
different types of income streams that discrimination could not © 
justly be attributed to the present workings of the property tax so 
far as concerns owners who acquired their property after existing 
tax conditions had been established. But the tax rate does not 
usually stay permanently fixed for any great length of time. Suppose 
that the tax rate unexpectedly rises from 1 to 2 percent shortly after 
the three brothers have made their investments. The first brother’s 
net income after tax is then so reduced that it, plus the 2 percent 
tax on its capital value, equals $400. In mathematical terms, 
(0.03 +0.02) V»>=$400, where V, is the capital value. The solution 
of this equation gives V)»=$8,000, and the annual tax on this value 
is $160. The tax ratio is oa 
brother, therefore, the sudden doubling of tax rate increases the tax 
ratio from 25 to 40 percent, or, in other terms, lowers the initial 
value from $10,000 to $8,000, a loss of 20 percent. 
In the case of the second brother, the capital value at the end of 
17% years and thereafter is reduced from $20,000 to $16,000, while 
the annual tax is increased from $200 to $320. The income is, as 
before, $267 the eighteenth year and $800 thereafter. The present 
value of these incomes before tax is also, as before, $15,820, but the 
present value after tax is not $10,000, but considerably less than that. 
In fact, it is that value which, with 3 percent interest and 2 percent 
taxes, will equal $16,000 at the end of 17% years. The discount of 
$16, 000 for 173 % years at 5 percent yields $6,759. The tax ratio is 
15, 820— 6,759 
15,820 
therefore, the sudden doubling of tax rate increases the tax ratio 
from 36. 8 to 57.3 percent, or in other terms, lowers the initial value 
from $10,000 to $6,759, a loss of 32 percent. 
It is not necessary in this connection to consider the depletion 
annuity of the third brother. The loss in his case is very small. 
Doubling the tax rate causes a 20 percent loss in capital to the 
first brother and a 32 percent loss to the second. Here is clearly 
distinguishable the magnified effect of tax capitalization where 
deferred yields are involved. An unexpected decrease in the tax 
rate would, of course, have the opposite effect—that is, the owner of 
a deferred-yield investment would benefit more than the annual- 
yield owner. One of the indictments against the property tax, 
even when perfectly administered in accordance with the law, is, 
thus, that it makes the net returns from deferred-yield properties 
more uncertain than those from the ordinary run of property. In 
other words, its tendency is to intensify the risk element in a deferred- 
yield investment. 
The tax ratio is an index for the determination of what areas are 
or are not supermarginal for a deferred-yield use. Consider a certain 
property, close to a bare-land condition, whose value before taxes is 
$5 per acre for a deferred-yield use (like forestry) and $4 for some 
use (like grazing) which would yield an annual return. If there is 
no tax obligation in either case, the former use will be chosen in 
»or 40 percent. In the case of the first 
» or 57.3 percent. In the case of the second brother, 
