232 NATURE OF CAPITAL AND INCOME [Cmar. XIV 
re 
that no product can be obtained until the end of ten years. 
We may suppose that then the yield is worth $1000 a year 
during the ensuing (second) decade, after which it will be 
worth $2000 a year forever. It may be shown that the 
present value of the forest, reckoned on a five per cent basis, 
is about $20,000. This would be the discounted value of an 
annuity of $1000 a year, whose commencement is deferred 
ten years from the date of investment, and which then 
runs ten years, plus the discounted value of a perpetual 
annuity of $2000 a year beginning twenty years in the 
future. On the five per cent basis, the forest will, 
in ten years from the present, be worth about $32,000 
(this being the discounted value of an immediate ten-year 
annuity of $1000 followed by a perpetuity of $2000). 
Twenty years from the present, the forest will be worth 
$40,000 (this being the discounted value of $2000 a year 
forever). The forest land therefore rises gradually in value 
from $20,000 to $32,000 in the first decade, during which no 
income is realized, and continues to rise, though less rapidly, 
to $40,000 in the second decade, during. which there is 
realized the comparatively small income of $1000 a year. 
The rate of return, therefore, at the beginning, being the quo- 
tient of the income realized divided by the capital, is 55, 
or zero. The rate of return evidently remains zero through- 
out the first decade. At the beginning of the second decade 
the rate is evidently 2% or 3.1 per cent; at the beginning 
of the third decade it is Af, or 5 per cent. We see, 
therefore, that in this case the rate of value-return gradually 
rises from zero to a height equal to the rate of interest. 
There may even be a negative rate of return. A colt, for 
instance, may occasion more trouble than it is worth for the 
first year, and produce a net expense or disservice of $20. 
Thereafter it may render a net income of $10 during the 
second year, $20 during each year from the third to the 
tenth inclusive, and $10 a year the next five years, after 
which it dies. Supposing, as our preliminary hypothesis