60 MISC. PUBLICATION 218, U. S. DEPT. OF AGRICULTURE 
Substituting the value for X as given in formula 6 and combining 
like terms, 
n—m Cy Rare: ; GG gm (1 + p)"*— 1 
y+ Toate tL pet 
GED) 
Dividing numerator and denominator by [(1+p)"—1] and simpl- 
fying, | 
Vo ane 
Th n—m __ Cnpamelen 2 
i eg ee e ace 
ae Ce 
This last formula for Vp is the same as the original except that X is 
omitted and r is added to the rate of discount, p. Thus the effect of 
the property tax is to increase the rate of discount applicable to the 
expected income by the amount of the tax rate. As the property-tax 
rate increases, the initial forest value will be reduced, other factors 
remaining the same. This is tax capitalization. 
The effect of the property tax at any given rate on the rotation that 
is most profitable from the financial viewpoint, commonly called the 
financial rotation, may be predicted in the case of any managed forest 
for which a money yield table is available. 
The financial rotation is the same whether the forest in question is 
composed of one or of many age classes, since the aggregating of a 
number of age classes in one forest property so as to shorten the inter- 
val between realization of income in no way changes the relation be* 
tween income and investment so long as the investment is assumed to 
equal the cost of growing the existing timber together with interest 
and other carrying charges. Therefore, it is sufficient for theoreticai 
purposes to consider only even-aged forests in which the income cycle 
and rotation are equal. 
An even-aged forest, as it grows older, is expected to increase from 
year to year in realization value, that is, in the sum which could be 
realized by cutting the timber and selling the land. The current 
increase in realization value, less the expense during the period when 
it accrues, constitutes the current net value increment. The ratio of 
this current net increment to the current realization value, expressed 
as a percent, is known as the ‘‘indicating percent.’”’ From the time 
that the timber has a substantial merchantable value, the indicating 
percent drops sharply. The point at which this percent reaches 
equality with the interest or discount rate marks the most profitable 
rotation, since beyond that age any increase in net increment from 
lengthening the rotation would yield less than this interest rate. For 
the same reason a rotation stopping at that point gives maximum 
figures, computed at the accepted interest rate, for the initial forest 
value and the soil expectation value. 
It was shown above that the effect of the property tax is to increase 
the rate of discount applicable to the expected income by the amount 
of the tax rate. Therefore, the sum of interest and tax rate may be 
treated as the interest or discount rate in estimating the financial 
rotation by the use of the indicating percent, provided that in calcu- 
lating the indicating percent the property tax be excluded from the 
annual expense in order to avoid double allowance for this tax. 
