66 MISC. PUBLICATION 218, U. S. DEPT. OF AGRICULTURE 
if no costs are incurred and if the value increment accrues in the ex- 
pected amounts, the plan reduces to a tax on the initial value. — If 
annual expenses other than taxes are incurred, however, the tax after 
the first year is something more than an initial value tax. In fact, 
it increases each year by the amount of taxes on that part of the 
preceding year’s increase in value which reflects annual expense 
uy the current yield becomes equal to the current increment in 
value. 
In all cases of a deferred-yield forest managed on a regular rota- 
tion, the tax burden under the adjusted property tax is exactly equal 
to that produced by a tax on the net income from the property at an 
equivalent tax rate. 
The tax sequence is rVo, r(Vo+e), r(Vo+2e), . . . 7[LVot(n—1)e.] 
The sum of these taxes, with interest, to the end of the income cycle is 
Vy SEB pe] CEP ep ali, ve +1]- 
P P 
py dite! brn =n | 
P P Pp ; 
Since 
Ve (ae a Daal 
(l+p)*—1 
x=1] y—o—x—eC 4 PY ty (Creat —ne | 
P Pp Pp 
Vo = 
b] 
Simplifying the right member X ce [Y—C—X—ne]. 
Cross multiplying and transposing terms (p-+7r)X=r(Y¥Y—C—ne), or 
a 
Formula 9, ee (Y—C—ne). 
This is the identical form of the equation for the income tax with 
a tax rate of one and hence will give the same tax ratio. The tax 
+r 
ratio when an intermediate thinning, 7,,,, is realized is still identical 
with that for the net income tax (formula 2). 
LAND-VALUE TAX, TIMBER EXEMPT 
The complete exemption of timber, leaving only the land value 
subject to the property tax, is a proposal which is discussed in part 
12. A mathematical analysis of this proposal is in order here. 
An annual land tax, rZ, in the case of an even-aged deferred-yield 
forest regenerated without expense, produces a tax ratio equivalent 
to that of an annual sustained-yield forest. The vatue as of the 
end of the rotation (or income cycle) of land-value-tax payments 
is 
rit dp) +d+p). . -C-bp)e 4, on Xn 
