The Economic Aspect of Geology

by C. K. Leith

The Ad Valorem Method of Valuation

The ordinary commercial method of valuing mineral deposits recognizes the two main elements of value above discussed. This method is sometimes called the rational or ad valorem method. The profit per ton (or per other unit) of the product is established, on the basis either of past performance of the property or of experience with other similar properties. This profit is multiplied by the total tonnage estimated in the deposit, the estimate including known reserves, probable reserves, and in some cases possible and prospective reserves. The product of the profit per ton and the total tonnage gives the total net amount which will be received; it does not, however, give the present value, because the commodity cannot all be taken out and sold at once, but must be mined and absorbed by the market through a considerable period of years. The returns receivable some years in the future have obviously a lower proportionate present worth than amounts to be received at once. The interest rate comes into play, making it necessary to discount each annual 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 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.

In estimating the total reserves in a mine, geological considerations nearly always play a large part. An ore body may in some few cases be completely blocked out by underground work or drilling, eliminating the necessity for inferring conditions beyond those actually seen; but in the huge majority of mineral deposits the reserves are not so definitely known, and it becomes necessary for the geologist, through knowledge of similar occurrences, through study of the structural features of the deposit, its origin, and its history, to arrive at some sort of an estimate of reserves.

In estimating the life of a mineral deposit it is necessary to start with the figure of total reserves, and from a study of conditions of mining and of markets to estimate the number of years necessary to exhaust the deposit. This is a more nearly commercial phase of the problem, in which the geologist takes only part of the responsibility. Perhaps more estimates of value have gone wrong because of misjudgment of this factor than for any other cause. If the physical conditions are satisfactory, it is easy to assume a rate of extraction and life based on hope, which experience will not substantiate.

The choice of the interest rate to be used in discounting future receipts to present worth likewise is a financial and not a geologic matter. Again, however, the geologist must give consideration to this factor, in view of the fact that the interest rate must be varied to cover the different degrees of hazard and doubt in the geologic factors. For instance, to the extent to which the estimate of ore reserves is doubtful, it is necessary to use a high rate of interest to allow for this hazard. In a large, well-developed mineral deposit, with the geological factors all well known and the demand and market well established, it is reasonable to use a lower rate of interest. In general, the mineral industry is regarded in financial circles as being more hazardous than many other industrial lines; and money is put into the industry with the expectation of a high rate of interest, no matter how safe the investment may be. In actual practice interest rates used in making valuations vary from 6 to 15 or 20 per cent.

It is clear that, where a property has long life, the interest will very materially reduce the present value of the ores to be mined far in the future. Reserves to be mined more than thirty years hence have relatively little or no present value. Beyond a certain point, therefore, the acquirement and holding of reserves for future use by private companies has little commercial justification. This is a matter which is too often not sufficiently well considered. Man's natural acquisitiveness often leads him into investments which, because of the time and interest factor, have little chance of successful outcome. Of course a large corporation, anticipating an indefinitely long life, or perhaps aiming at monopoly, may afford to hold reserves as a matter of general insurance longer than a small company,—even though, because of the interest rate, these reserves have no present value on their books. It is likewise true that governments, looking forward to the future of the nation, and without the necessity of paying so much attention to interest and taxes, are not so limited by this consideration.

An illustration of the limiting effect of the interest rate on the acquirement of long-lived coal deposits by private interests is discussed in Chapter XVII on Conservation. Investments made many years ago have so augmented, even at low interest rates, as to make it practically impossible to count on a return of capital and interest; or if the return were to be exacted from the public it would mean excessive charges, which are not possible in competition with other mines not so burdened.

In the commercial valuation of oil wells and pools, much the same method is used as has been described for mineral resources in the solid form, but the estimate of reserves or life is based on consideration of curves of production of the sort mentioned on pages 134-136.

The essence of the ad valorem method of valuation above described is income-producing capacity. This method recognizes the fact that the value of the mineral deposit depends, not only on its physical constitution, but also on what performance can be expected from it.

Stock quotations on mineral properties in the standard markets are based substantially on estimates of income capacity, more or less on the ad valorem basis. However, the quotations also reflect the hopes and fears of the public, often resulting in valuations quite different from those based on studies of the objective conditions.

The war introduced new considerations into the problems of ad valorem valuation. Under peace conditions there is a tendency toward the establishment of normal costs, selling prices, and markets, which can be taken more or less for granted by anyone attempting to value mineral deposits. Under war and post-war conditions, few of these elements can be taken for granted; it becomes necessary to consider the entire world situation in regard to a mineral commodity, the effects of the Peace Treaty (which greatly concerns minerals), future international relations, tariffs, and other matters of a similar sort. If a person were today valuing a manganese deposit according to the method above outlined, and were to confine himself solely to a narrow consideration of past markets and profits on individual properties, he would be very likely to go wrong,—for the world manganese situation has an immediate and practical bearing on each local problem (see pp. 173-176).