Obviously it is not sufficient for the mine investor that his capital shall have been restored, but there is required an excess earning over and above the necessities of this annual funding of capital. What rate of excess return the mine must yield is a matter of the risks in the venture and the demands of the investor. Mining business is one where 7% above provision for capital return is an absolute minimum demanded by the risks inherent in mines, even where the profit in sight gives warranty to the return of capital. Where the profit in sight (which is the only real guarantee in mine investment) is below the price of the investment, the annual return should increase in proportion. There are thus two distinct directions in which interest must be computed,—first, the internal influence of interest in the amortization of the capital, and second, the percentage return upon the whole investment after providing for capital return.
There are many limitations to the introduction of such refinements as interest calculations in mine valuation. It is a subject not easy to discuss with finality, for not only is the term of years unknown, but, of more importance, there are many factors of a highly speculative order to be considered in valuing. It may be said that a certain life is known in any case from the profit in sight, and that in calculating this profit a deduction should be made from the gross profit for loss of interest on it pending recovery. This is true, but as mines are seldom dealt with on the basis of profit in sight alone, and as the purchase price includes usually some proportion for extension in depth, an unknown factor is introduced which outweighs the known quantities. Therefore the application of the culminative effect of interest accumulations is much dependent upon the sort of mine under consideration. In most cases of uncertain continuity in depth it introduces a mathematical refinement not warranted by the speculative elements. For instance, in a mine where the whole value is dependent upon extension of the deposit beyond openings, and where an expected return of at least 50% per annum is required to warrant the risk, such refinement would be absurd. On the other hand, in a Witwatersrand gold mine, in gold and tin gravels, or in massive copper mines such as Bingham and Lake Superior, where at least some sort of life can be approximated, it becomes a most vital element in valuation.
In general it may be said that the lower the total annual return expected upon the capital invested, the greater does the amount demanded for amortization become in proportion to this total income, and therefore the greater need of its introduction in calculations. Especially is this so where the cost of equipment is large proportionately to the annual return. Further, it may be said that such calculations are of decreasing use with increasing proportion of speculative elements in the price of the mine. The risk of extension in depth, of the price of metal, etc., may so outweigh the comparatively minor factors here introduced as to render them useless of attention.
In the practical conduct of mines or mining companies, sinking funds for amortization of capital are never established. In the vast majority of mines of the class under discussion, the ultimate duration of life is unknown, and therefore there is no basis upon which to formulate such a definite financial policy even were it desired. Were it possible to arrive at the annual sum to be set aside, the stockholders of the mining type would prefer to do their own reinvestment. The purpose of these calculations does not lie in the application of amortization to administrative finance. It is nevertheless one of the touchstones in the valuation of certain mines or mining investments. That is, by a sort of inversion such calculations can be 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% |
|---|---|---|---|---|---|---|
| 1 | .95 | .94 | .93 | .92 | .92 | .91 |
| 2 | 1.85 | 1.82 | 1.78 | 1.75 | 1.72 | 1.69 |
| 3 | 2.70 | 2.63 | 2.56 | 2.50 | 2.44 | 2.38 |
| 4 | 3.50 | 3.38 | 3.27 | 3.17 | 3.07 | 2.98 |
| 5 | 4.26 | 4.09 | 3.93 | 3.78 | 3.64 | 3.51 |
| 6 | 4.98 | 4.74 | 4.53 | 4.33 | 4.15 | 3.99 |
| 7 | 5.66 | 5.36 | 5.09 | 4.84 | 4.62 | 4.41 |
| 8 | 6.31 | 5.93 | 5.60 | 5.30 | 5.04 | 4.79 |
| 9 | 6.92 | 6.47 | 6.08 | 5.73 | 5.42 | 5.14 |
| 10 | 7.50 | 6.98 | 6.52 | 6.12 | 5.77 | 5.45 |
| 11 | 8.05 | 7.45 | 6.94 | 6.49 | 6.09 | 5.74 |
| 12 | 8.58 | 7.90 | 7.32 | 6.82 | 6.39 | 6.00 |
| 13 | 9.08 | 8.32 | 7.68 | 7.13 | 6.66 | 6.24 |
| 14 | 9.55 | 8.72 | 8.02 | 7.42 | 6.91 | 6.46 |
| 15 | 10.00 | 9.09 | 8.34 | 7.79 | 7.14 | 6.67 |
| 16 | 10.43 | 9.45 | 8.63 | 7.95 | 7.36 | 6.86 |
| 17 | 10.85 | 9.78 | 8.91 | 8.18 | 7.56 | 7.03 |
| 18 | 11.24 | 10.10 | 9.17 | 8.40 | 7.75 | 7.19 |
| 19 | 11.61 | 10.40 | 9.42 | 8.61 | 7.93 | 7.34 |
| 20 | 11.96 | 10.68 | 9.65 | 8.80 | 8.09 | 7.49 |
| 21 | 12.30 | 10.95 | 9.87 | 8.99 | 8.24 | 7.62 |
| 22 | 12.62 | 11.21 | 10.08 | 9.16 | 8.39 | 7.74 |
| 23 | 12.93 | 11.45 | 10.28 | 9.32 | 8.52 | 7.85 |
| 24 | 13.23 | 11.68 | 10.46 | 9.47 | 8.65 | 7.96 |
| 25 | 13.51 | 11.90 | 10.64 | 9.61 | 8.77 | 8.06 |
| 26 | 13.78 | 12.11 | 10.80 | 9.75 | 8.88 | 8.16 |
| 27 | 14.04 | 12.31 | 10.96 | 9.88 | 8.99 | 8.25 |
| 28 | 14.28 | 12.50 | 11.11 | 10.00 | 9.09 | 8.33 |
| 29 | 14.52 | 12.68 | 11.25 | 10.11 | 9.18 | 8.41 |
| 30 | 14.74 | 12.85 | 11.38 | 10.22 | 9.27 | 8.49 |
| 31 | 14.96 | 13.01 | 11.51 | 10.32 | 9.36 | 8.56 |
| 32 | 15.16 | 13.17 | 11.63 | 10.42 | 9.44 | 8.62 |
| 33 | 15.36 | 13.31 | 11.75 | 10.51 | 9.51 | 8.69 |
| 34 | 15.55 | 13.46 | 11.86 | 10.60 | 9.59 | 8.75 |
| 35 | 15.73 | 13.59 | 11.96 | 10.67 | 9.65 | 8.80 |
| 36 | 15.90 | 13.72 | 12.06 | 10.76 | 9.72 | 8.86 |
| 37 | 16.07 | 13.84 | 12.16 | 10.84 | 9.78 | 8.91 |
| 38 | 16.22 | 13.96 | 12.25 | 10.91 | 9.84 | 8.96 |
| 39 | 16.38 | 14.07 | 12.34 | 10.98 | 9.89 | 9.00 |
| 40 | 16.52 | 14.18 | 12.42 | 11.05 | 9.95 | 9.05 |
| Condensed from Inwood's Tables. | ||||||