586 MISC. PUBLICATION 218, U. S. DEPT. OF AGRICULTURE 
The concrete illustration given above may be expressed in general 
terms, where 7’ is the taxes, V the assessed value, Y the gross yield, 
L the ‘loss, r the tax rate, p the interest rate, and D the total accumu- 
lated adjusted value increment to date or the difference between the 
assessed value and the adjusted tax base. The subscripts indicate the 
year to which the above symbols refer; for example, 0 is the year prior 
to the adoption of the plan (corresponding to 1932 in the illustration) ; 
1 is the first year (corresponding to 1933 in the illustration); 2 the 
second year (corresponding to 1934); and 3 the third year (corre- 
sponding to 1935). 
Formula (1) hola 
Formula (2) T,=7,[Vi-— (pVo + To— Yo)]. 
(pV o+ T>— Yo) is the adjusted value increment before the first year or 
the deduction from the assessed value of the first year. It is always a 
positive amount, and is designated at D,. 
Formula (3) T,=r[V2—(D,+pVi+7,—Y¥)]. 
(D,+pV,+ 7;— Y,) is the adjusted value increment before the second 
year and is designated as D, 
Formula (4) Ty=r Vim (D.+pV2+ T,— Y2) a5] 
2 
V.—L, 
We 
is the adjusted value increment before the third year, or D;. This 
adjusted value increment is computed in the same way as in formula 
(3) and then reduced by the ratio of the loss, Z,, occurring in the 
second year, to the value of the second year, V3. 
A general formula, where n is any year and n—1 is the year preced- 
ing the nth year, may now be written: 
Formula (5) T.=r] Va Dnt PV rit 7,9, oye 
where (Dy +P Vn-1+ Ln-1— Yn_-1) 1s never less than 0, and eee 
L,-; can never be greater than V,_. 
To guard against evasion on the part of a taxpayer through the 
concentration of cutting on one parcel and the consequent retention 
of cumulative adjusted value increments on other parcels, all property 
in one ownership should be considered as a unit for the computation 
of the gross income, regardless of the manner in which the property 
is subdivided into parcels for purposes of assessment and levy. The 
total income from all forest property of one ownership for the pre- 
ceding year should be divided among the different parcels of that 
ownership in proportion to the adjusted value increment which in 
absence of this income would have accumulated to the credit of each. 
Logically, the income from all forest property in one ownership in the 
entire State should be treated as a whole. It would have to be re- 
ported to the State tax commission and be used to cause a proportional 
reduction of the adjusted value increment for each parcel of forest 
property in that ownership. However, the administrative readjust- 
ments required would, in most States, probably be too cumbersome to 
Of the above, (D.+ pV2+ T2— Yo) 
— Ln |) 
