al payment for the number of years which will elapse before it is
received. It is evident, therefore, that an estimate of the _life_ of
the property is necessary, involving not only knowledge of the reserves,
but also a forecast of the annual extraction or _rate of depletion_.

As a simple case of _ad valorem_ valuation for illustrative purposes, a
deposit containing 1,000,000 tons in reserve has an estimated output of
100,000 tons a year for ten years, on which the profit per ton has in
the past averaged $1 and is expected to average $1 in the future. Ten
annual instalments or dividends of $100,000 are to be received. The
present value of the total of these instalments is figured by an annuity
method. It is the value upon which the series of dividends will pay
interest at a predetermined rate, in addition to paying to a sinking
fund annual instalments which, safely invested each year at a low rate
of interest (usually 4%), will repay the present value at the end of the
ten years. In our hypothetical case, if an interest rate of 8% be taken,
the present value of $1,000,000, to be received through ten years in ten
equal instalments, is $612,000. In other words, the sum of $612,000 will
be replaced by the sinking fund at the end of ten years, and will pay 8%
interest during this period,--this requiring total receipts of
$1,000,000 in ten equal annual instalments. If the deposit here cited as
an illustration were to be worked out in three years, thus yielding
three annual instalments of $333,000, its value would be $833,000.

Each of the factors entering into this method of valuation covers a wide
range of variables, any one of which may be difficult to determine.

The profit per ton for a given deposit may have been extremely variable
in the past, making it difficult to determine whether the highest or
lowest figure should be projected into the future or whether some
average should be taken; and if an average, whether the time covered by
the average should be long or short. For a small, short-lived deposit
obviously the most recent conditions would be taken into account in
estimating future profits. For a long-lived property there would be more
tendency to consider the long-time average vicissitudes, as reflected in
the average profits of the past. For some mineral commodities there are
cycles of prices, costs, and profits, of more or less definite length,
established during the long past history of the industry; and in s