FOREST TAXATION IN THE UNITED STATES 41 
to be invested in a perpetual. annuity of $674 a year. (The reason 
for the choice of 17% years is for convenience in calculation, as will 
appear at a later point. Any other period of years, however, would 
have served.) The third brother, desiring immediate enjoyment of 
a larger income, purchases an annuity of $3,333 a year terminating 
in a little under 5 years, after which his capital is used up and he 
receives no further income. 
Assume now that immediately subsequent to the making of these 
several investments a tax, not heretofore anticipated, of 1 percent 
on property value or of 25 percent on income is imposed. The cap- 
ital of each of the three brothers will be diminished. In other words, 
while each paid $13,333 for his annuity, he would not be able to dis- 
pose of it at that price, if immediately after purchase the above- 
mentioned tax were announced. Anyone purchasing one of these an- 
nuities would then discount the effect of the tax in each case and pay 
only so much as the tax-free income (1. e., the net income each year 
after payment of the tax) showed it to be worth. And, of course, 
if the annuities could not be sold for $13,333, which they cost, they 
could not be taxed on that amount under the property tax, since 
that would no longer be the value and value is the legal base of the 
property tax. The effect of this tax innovation on the value of these 
three types of investment and the resultant tax situation of the 
several brothers will each be considered separately. 
The situation of the first brother represents the ordinary case. 
Taxes—both property and income—are usually assessed and levied 
once a year. Usually they are also collected once a year. And if 
they are in some cases payable in two or more installments during 
the year, that does not materially affect the situation. The 25- | 
percent income tax decreases successively the net annual incomes 
from $400 to $300 and consequently the value of the capital from 
$13,333 to $10,000, a drop of 25 percent in each case. The 1-percent 
property tax on the value must, for its part, leave sufficient net in- 
come after taxes to capitalize to this value at 3 percent. In other 
words, $400 minus the tax must equal 3 percent of the value. In 
equation form, 400—0.01X=0.03.X, where X stands for the value of 
the capital. The solution of this equation gives a value of $10,000. 
On this value the tax is $100 and the net income after tax $300, 
exactly as in the case of the 25-percent income tax. A 1-percent 
property tax is, thus, equivalent to a 25-percent income tax in the 
case of the first brother, when interest is 3 percent. The present 
worth (discounted value) of each tax in perpetuity is $3,333, or 25 
percent of the capital before taxes. 
In the case of the second brother the capital is so invested that 
it will yield no net income for a period of 17% years, after which it 
will yield a perpetual annual income of $674. The present worth of 
such a deferred income, discounted at 3 percent, is $13,333, the same 
as the value of the annual income of $400 beginning now. An in- 
come tax, subsequently imposed at the rate of 25 percent, would 
exact nothing for the first 17% years, after which it would take 
$168.50 a year. The present worth of these future tax payments is 
$3,333, or 25 percent of the value of the capital before tax, exactly 
as in the case of the annual income of $400 beginning at once. 
It is now in order to inquire how the annual property tax affects 
this second type of investment. After the period of deferment, 17% 
