FOREST TAXATION IN THE UNITED STATES | 261 
Then, if V;1 is just equal to $105, the owner is a marginal holder of 
timber, ‘and it is immaterial to him whether he holds it or cuts it. 
But, if Vii is more than $105 (say, $108), it will pay the owner to with- 
hold his timber from cutting. On the other hand, if V, is less than 
$105 (for example, $102), it will pay the owner to cut his timber. 
Thus if the owner has reason to believe that the increase in value of 
stumpage will not keep pace with the carrying charges, he will natur- 
ally be influenced to cut the timber and get what he can out of it. In 
this example, interest constitutes 60 percent of the total carrying 
charges, taxes 30 percent, and other carrying charges 10 percent. 
The effect of a change in taxes may now be examined. Let it be 
assumed, first, that the tax rate is increased from 1.5 to 2.0 percent, 
the other factors remaining the same. Then, the marginal owner 
with V, equal to $105 will become an operator, because now 
Vo i1+p+r)+e=$105.50. The status of each of the other owners 
remains the same, since $108 is greater than $105.50 and $102 is less 
than $105.50, but ‘the timber holder is drawn closer to the margin, and 
the operator is still more strongly induced to cut his timber. In this 
example, interest constitutes 54.5 percent of the total carrying charges, 
taxes 36.4 percent, and other carrying charges 9.1 percent. 
On the other hand, assume that the tax rate is decreased to 1 per- - 
cent. The marginal owner now becomes definitely a holder, since 
VY, (l+p+r)+e=$104.50. The holder is now even more deter- 
mined to allow his timber to stand, and the operator continues to 
operate, though with less to gain thereby than before. In this 
example, interest constitutes 66.7 percent of the total carrying charges, 
taxes 22.2 percent, and other carrying charges 11.1 percent. 
The preceding theoretical analysis, in order to simplify the mathe- 
matics involved, covered a period of only 1 year. Under normal 
conditions, where large tracts of timber are involved, the period for 
comparison of present realizable value and future realizable value 
would be much longer than 1 year, and the removal of the timber 
in 1 year would be impracticable. In such cases the realizable value 
at any time would be the present worth based on an orderly removal 
of the timber beginning at that time and covering the shortest period 
of years consistent =a maximum operating returns. The principles 
developed are obviously the same, however, whether the period for 
comparison of present and future realizable value is a single year or 
any number of years. 
As a general proposition all carrying charges are alike in their effect 
upon the policy of the timber owner. It is the total of all carrying 
charges which, in relation to the present realizable value and the value 
to be realized at some future time, determines whether timber should 
be cut now or later. In this total the several items are of relative 
importance merely in proportion to their respective amounts. As 
thus rated, interest ordinarily stands first among the carrying charges. 
Taxation comes next. Other items, such as protection and adminis- 
tration, are generally of far less importance. It should be clearly 
understood that interest, as a carrying charge affecting cutting policy, 
is not merely the interest which must be paid on borrowed capital. 
Neither is it the interest on the investment which the owner has made 
on the property. It is the total interest which might be earned on 
the present realizable value. ° 
