48 MISC. PUBLICATION 218, U. S. DEPT. OF AGRICULTURE 
tangible income with a definite money value. To the extent that the 
value of an annual sustained-vield forest refiects intangible income in 
addition to money and other tangible income, a situation found in 
certain countries of Europe, the property tax would be in excess of the 
ordinary income tax. 
In all of the above discussion no account has been taken of irregu- 
larities in the administration of the property tax, the present assump- 
tion being a property tax theoretically correct and perfectly ad- 
ministered. In particular nothing here should be taken as denial of 
the possibility of just complaint against the property tax on the part 
of the sustained yield forest, as well as of other types of property, 
on account of illegal discriminatory administration of the property 
tax. 
The remainder of this part is devoted to a rigid mathematical 
demonstration of the foregoing general propositions together with 
the formulation and demonstration of certain other propositions 
dealing with the relation of different kinds of taxes to the value of 
forest investments under various conditions. 
GENERAL DEFINITIONS 
For the purpose of the following mathematical analysis, it will be 
convenient to set forth at this point formal definitions of certain 
terms and the corresponding symbecls which will be used in the 
' equations and formulas. 
In the absence of complete data as to the complex considerations 
of various sorts that enter into the consummation of sales and the 
making of value, a simplified approximation to value is employed, 
namely, the sum of all expected future returns discounted to some 
point in time at a given interest rate, minus all expected future 
expenses, including taxes, discounted to the.same point in time and 
at the same interest rate. This balancing of income and cost, both 
discounted to the present, is the identical procedure which buyers 
and sellers must use in arriving at a price, although buyers and sellers 
usually use “judgment” rather than a mathematical analysis. The 
future is so uncertain that judgment, for most practical purposes, is 
quite as satisfactory as the more seemingly exact mathematics, but 
the principle of both is the same—the discounting of expected f uture 
net returns. A value so found is herein assigned the symbol V, and 
if the chosen point in time is at the beginning of an income cycle, 
the symbol V is given a subscript 0. The income cycle is the 
period between successive major yields. The subscript 1 is given to 
V for the value at the end of the first year, and so on to n, when the 
first major yield is to be received. The income cycle, therefore, 
comprises a total of m years. When the forest is composed of a 
single age class the income cycle is equal to the rotation (the pre- 
determined, approximate felling age), and V, becomes equal to the 
land value or soil expectation value, L, plus the cost of regeneration, C. 
An uneven-aged forest, for the purposes of this discussion, may be 
regarded as a selection forest, in which case the series of age classes is 
represented by regular gradation of ages among individual trees, or 
it may equally well be regarded as composed of a regular series of 
even-aged stands, 
