614 MISC. PUBLICATION 218, U. 8S. DEPT. OF AGRICULTURE 
The formulas used in tables 159 and 160 were proved and dis- 
cussed at length in part 3. They will be briefly reviewed at this point. 
The formula for the initial forest value (value at the beginning of the income 
cycle), Vo, is as follows: 
Ne Ge eel ania eed 
Vo= (1+ p)*—1 
» where 
Y=vield, C=cost of regeneration, X=cost of taxes, e=annual expense, p= 
interest rate, and n=length of incomecycle. (Seep. 59.) 
For an even-aged forest (table 159) the land value, JL, is the initial forest value 
less the regeneration cost, L=V y—C. For an uneven-aged forest (table 160), L, 
the land value, is the land value of the corresponding even-aged forest as given in 
table 159. 
The formula for X under either the income (net yield) tax or the adjusted 
property tax (pp. 51 and 66) is: 
r 
AT ae 
(Y—C—ne), 
where — 
- is the income tax rate, r being the property tax rate. According to 
P 
the assumptions made, this formula and the one stated above for Vy will con- 
tain two unknowns, Y and X, for each forest indicated in table 159 (all are 
even-aged) and hence are solved simultaneously for these unknowns. In table 
160 the yield for the uneven-aged forest is a times the yield for the corresponding 
even-aged forest in table 159 where k is the number of income cycles in a complete 
rotation. 
The yields as computed in the preceding paragraph for the income tax and the 
adjusted property tax will be the same for each forest under the other tax plans 
enumerated. This means that not only will X be different for each plan, but 
Land Vo, the land value and initial forest value, will also be different. 
The other formulas for X are as follows: 
i Ea ee Chee Tale res Usp a)e—ell 
Property tax, x=(Y-O)|1 Caan=E eal al 5 | 
(See p. 58, formula 6.) 
Deferred timber tax (formula 13), 
GoD) ta Vin (Ua 2) Aral 
xary, GER hs (et (pty) [ S42) n | 
Differential timber tax (formula 16), 
Vi aids Ji Uae) arle@arlee uh) a SS 
where r’=tax rate on timber. This rate is determined by the following relation: 
r’=r(1—w), w being the reduction factor applicable to timber. 
Immature-timber exemption (p. 66), 
x=rp SR, 
Yield tax, (p. 72) 
pater) 
= VY. 
x str 53 
