made to serve as a means to expose the amount
of risk,--to furnish a yardstick for measuring the amount of risk
in the very speculations of extension in depth and price of metals
which attach to a mine. Given the annual income being received,
or expected, the problem can be formulated into the determination
of how many years it must be continued in order to amortize the
investment and pay a given rate of profit. A certain length of
life is evident from the ore in sight, which may be called the
life in sight. If the term of years required to redeem the capital
and pay an interest upon it is greater than the life in sight,
then this extended life must come from extension in depth, or ore
from other direction, or increased price of metals. If we then take
the volume and profit on the ore as disclosed we can calculate the
number of feet the deposit must extend in depth, or additional tonnage
that must be obtained of the same grade, or the different prices of
metal that must be secured, in order to satisfy the demanded term
of years. These demands in actual measure of ore or feet or higher
price can then be weighed against the geological and industrial
probabilities.

The following tables and examples may be of assistance in these
calculations.

Table 1. To apply this table, the amount of annual income or dividend
and the term of years it will last must be known or estimated factors.
It is then possible to determine the _present_ value of this annual
income after providing for amortization and interest on the investment
at various rates given, by multiplying the annual income by the
factor set out.

A simple illustration would be that of a mine earning a profit of
$200,000 annually, and having a total of 1,000,000 tons in sight,
yielding a profit of $2 a ton, or a total profit in sight of $2,000,000,
thus recoverable in ten years. On a basis of a 7% return on the
investment and amortization of capital (Table I), the factor is
6.52 x $200,000 = $1,304,000 as the present value of the gross
profits exposed. That is, this sum of $1,304,000, if paid for the
mine, would be repaid out of the profit in sight, together with
7% interest if the annual payments into sinking fund earn 4%.

TABLE I.

Present Value of an Annual Dividend Over -- Years at --% and Replacing
Capital by Reinvestment of an Annual Sum at 4%.

=======================================================
Years | 5% | 6% | 7% | 8% | 9% | 10%
--