70 MISC. PUBLICATION 218, U. 8. DEPT. OF AGRICULTURE 
Formula 16, 
X=Vo] A+ptey—atoy |+[ et o—ryz [PEt 
ie lice) iar 
Pp 
When these formulas are applied to uneven-aged forests, the land 
value, L, is the land value of a corresponding even-aged forest, as 
explained in connection with formulas 12 and 13. 
Formulas 15 and 16 are derived as follows: The tax the first year is (r—r’)L 
+r’Vo, the second year (r—r’)L-+r’ Vol a Pohie anes Aor the third year 
(r—r')L+r’VoAitpt+r’)?+r’[(r—r’)L+e]+p+r’)+r’[(r—r’)L+e], and the 
nth year ae ane Va oar BPA a ga Canzone [(r—r’)L+ 
CGS Date ee ta et) tel 
Assume that there are no intermediate yields, in which case 7,,=0. These taxes 
accumulated to the end of the income cycle at the p rate of interest, by methods 
for summing series as used in connection with preceding formulas, are 
a 
(r—r')L+e_-+p-+r')»—(+p)"_ (+p)*—17 
a al r p | 
Simplifying 
If p)*—1, (tp tr) — n 
X=VolQtptr')-— (+p) 1+ rr) L[ SEB Crp" 
Re eee. (tp+r)=—(ltp)" [ES], 
Pelt Daivte ptr’ 
or 
X=Vol+ptr’)*—(+p)"14+ Sapte) Nt eo tp tr) 
_,tp)e=1. 
Pp 
Collecting similar terms results in formula 16. 
K=Vol(t ptr’) (+p) 1+le+ 1) Z) PEEPS ESB), 
This equation is simpler than formula 15 and is preferable wherever Vp is 
known. 
Formula 15 is derived by solving formula 16 and the initial value formula, 
Y—C—X-—e 
Gap 1 
Cee ciel 
io P 
simultaneously for X and Vo ; 
X= Vol tptr')9— (+p) I+ Pat ptr) 
Cle) Pm ll 
Pp 
Cea 
Pp 
X=—Vo[(1+p)*—1]+ Y—C-—e 
