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 such cases it is desirable in calculating averages to use a period covering one or more of these cycles, rather than some shorter or longer period. For many minerals, however, these cycles have been too irregular to afford a sound basis for future estimates. If the experience of the property itself is too short to afford a sufficient foundation for forecasting profits, or if there has been no previous work on the property, then it is necessary to use averages based on other properties or other districts; or if there are none strictly comparable, to build up a hypothetical figure from various estimated costs of labor, supplies, and transportation, selling prices, etc. In the estimate of the profit factor, the geologist is not primarily concerned.