FOREST TAXATION IN THE UNITED STATES 615 
where s, the yield tax rate, is assumed for the purposes of illustration to be 10 
times the property tax rate, or 10r. 
With Y constant for each forest, substitutions are made in the above tax 
formulas and the initial value formulas, and the resulting equations are solved 
simultaneously for Vj and X 
xX 
For any tax system the tax ratio is, by definition, ————_______., 
iy Gi a 1 
W==G 
The essential features of the various plans suggested are sufficiently 
illustrated by a few hypothetical forests constructed on the basis of 
assumptions limited to a small number of combinations. Low rota- 
tions and but a few of the possible income cycles have been chosen. 
The rotation is the predetermined, approximate felling age of 
stands or trees. For an even-aged forest, it is the period between two 
successive final yields; for an uneven-aged forest it is a similar period 
from the standpoint of a single age class. The income cycle is the 
planned interval between the final yields of the successive age classes of 
an uneven-aged forest; in an even-aged forest it is the same length 
as the rotation. In all cases it is the interval between major yields. 
It is assumed that each final yield is the same as the prior final yield. 
Forests A and B (tables 159 and 161) have 30-year rotations; forests 
C and D, 45-year; forests E and F, 60-year. Each of these forests is 
even-aged. ‘The forests represented in tables 160 and 162 have a 
rotation of 60 years, but each is composed of 12, 6, or 4 age classes. 
Accordingly, their income cycles are 5, 10, and 15 years, respectively. 
An uneven-aged forest in these examples may be regarded as a selec- 
tion forest, in which case the series of age classes is represented by 
regular gradation of ages among individual trees, or it may be regarded 
as composed of a regular series of even-aged stands. 
Each forest in tables 159 and 160 has a land value of $7,500 under 
an income (net yield) tax and annual expenses of $300. In table 159 
the regeneration cost 1s $2,500 while in table 160 it is 
$2,500 
k 
k being the number of income cycles in a complete rotation. The 
yield in all cases is calculated to equal the exact amount necessary to 
return all costs, including taxes, and interest on the capital at a rate 
of 3 percent. The property tax rates (based on full value) are 1 and 
2 percent; the corresponding income tax rates are 25 and 40 percent; 
and the yield- tax rates (10 times the corresponding property tax rates) 
are 10 and 20 percent. The legal interest rate under the adjusted 
property tax plan is taken to be 3 percent. The reduction factor for 
use under the differential timber-tax plan is 50 percent in tables 159 
and 161, where the shortest income cycle is 30 years. In tables 160 
and 162, this plan is illustrated by three different examples for each 
forest, assuming in turn uniform reduction factors of 10, 20, and 30 
percent. These factors correspond to standard income cycles of 5, 
10, and 15 years, respectively. 
Certain assumptions are necessary with reference to the various 
tax plans in order to apply them to the conditions of these hypothet- 
ical forests. ‘Taxes under the property tax and its modifications are 
levied each year on the value at the beginning of the year and payable 
