62 MISC. PUBLICATION 218, U. S. DEPT. OF AGRICULTURE 
shire. The data used in constructing this curve are those used in 
calculating table 93, part 7. It is evident that if the interest rate 
is 3 percent and the tax rate 2 percent, the financial rotation, indicated 
by the point on the curve where the indicating percent becomes 5 
percent, is 48 years. A reduction in the tax rate to 1 percent will 
increase the financial rotation in this case to 51 years. 
Some general deductions as to the influences affecting the financial 
rotation may be drawn from inspection of the above formula for the 
indicating percent. It is evident that in normal cases the effect of 
both the annual expense, e, and of the land value, L, is greatly over- 
shadowed by the effect of the money yields Y, ‘and Yaoi». Conse- 
quently changes in the amount of annual expense and land value 
would in general have only a small effect on the financial rotation 
regardless of the tax rate. It may also be seen that the curve of the 
indicating percent is likely to decline very steeply, since the term Y, 
is negative in the numerator and positive in the denominator. There- 
fore, changes in the sum of interest and tax rate because of increases 
or decreases in the tax rate are likely to have only a moderate effect 
on the financial rotation. 
FINANCIALLY IMMATURE OLD-GROWTH FORESTS 
An old-growth forest is not, in general, so heavily burdened under 
the property tax as is a cut-over forest. If, however, it must be held 
for a large number of years before the timber can be cut (because of 
inaccessibility, competition with better timber, possibility of flooding 
the market, “and the like), the tax ratio may mount rather high, 
although not so high as frequently happens in the case of a cut-over 
forest. The only difference between an old-growth forest and the 
deferred-yield forest analyzed in the preceding portion of this section 
is that the latter type of forest has a cyclic Income (every n years) 
while the former type has not. Slight changes in the deferred-yield 
tax formulas will make these formulas applicable to the old-growth 
type. 
To start with the simplest case, assume an old-growth forest which 
must be held for & years, at the end of which period the timber is 
entirely removed and the land is abandoned. No income and no 
expense, other than taxes, occur in any year except the last. The 
reasoning involved in the proof of formula 3 applies without change 
except that the initial value (called V’, in this analysis to distinguish 
it from the initial forest value at the beginning of an income cycle, V,) 
equals al ory rather than aa ee This change is, of course, 
due to the noncyclic character of the old-growth forest income, and 
with this change the tax ratio is 
Tak Gs ro GED et 
Formula 7, van 1 (arene 
en Coe ae 
SS) eos oe eo 
