TABLE III.
| Annual Rate of Dividend. | Number of years of life required to yield—% interest, and in addition to furnish annual instalments which, if reinvested at 4% will return the original investment at the end of the period. | |||||
|---|---|---|---|---|---|---|
| % | 5% | 6% | 7% | 8% | 9% | 10% |
| 6 | 41.0 | |||||
| 7 | 28.0 | 41.0 | ||||
| 8 | 21.6 | 28.0 | 41.0 | |||
| 9 | 17.7 | 21.6 | 28.0 | 41.0 | ||
| 10 | 15.0 | 17.7 | 21.6 | 28.0 | 41.0 | |
| 11 | 13.0 | 15.0 | 17.7 | 21.6 | 28.0 | 41.0 |
| 12 | 11.5 | 13.0 | 15.0 | 17.7 | 21.6 | 28.0 |
| 13 | 10.3 | 11.5 | 13.0 | 15.0 | 17.7 | 21.6 |
| 14 | 9.4 | 10.3 | 11.5 | 13.0 | 15.0 | 17.7 |
| 15 | 8.6 | 9.4 | 10.3 | 11.5 | 13.0 | 15.0 |
| 16 | 7.9 | 8.6 | 9.4 | 10.3 | 11.5 | 13.0 |
| 17 | 7.3 | 7.9 | 8.6 | 9.4 | 10.3 | 11.5 |
| 18 | 6.8 | 7.3 | 7.9 | 8.6 | 9.4 | 10.3 |
| 19 | 6.4 | 6.8 | 7.3 | 7.9 | 8.6 | 9.4 |
| 20 | 6.0 | 6.4 | 6.8 | 7.3 | 7.9 | 8.6 |
| 21 | 5.7 | 6.0 | 6.4 | 6.8 | 7.3 | 7.9 |
| 22 | 5.4 | 5.7 | 6.0 | 6.4 | 6.8 | 7.3 |
| 23 | 5.1 | 5.4 | 5.7 | 6.0 | 6.4 | 6.8 |
| 24 | 4.9 | 5.1 | 5.4 | 5.7 | 6.0 | 6.4 |
| 25 | 4.7 | 4.9 | 5.1 | 5.4 | 5.7 | 6.0 |
| 26 | 4.5 | 4.7 | 4.9 | 5.1 | 5.4 | 5.7 |
| 27 | 4.3 | 4.5 | 4.7 | 4.9 | 5.1 | 5.4 |
| 28 | 4.1 | 4.3 | 4.5 | 4.7 | 4.9 | 5.1 |
| 29 | 3.9 | 4.1 | 4.3 | 4.5 | 4.7 | 4.9 |
| 30 | 3.8 | 3.9 | 4.1 | 4.3 | 4.5 | 4.7 |
Table III. This table is calculated by inversion of the factors in Table I, and is the most useful of all such tables, as it is a direct calculation of the number of years that a given rate of income on the investment must continue in order to amortize the capital (the annual sinking fund being placed at compound interest at 4%) and to repay various rates of interest on the investment. The application of this method in testing the value of dividend-paying shares is very helpful, especially in weighing the risks involved in the portion of the purchase or investment unsecured by the profit in sight. Given the annual percentage income on the investment from the dividends of the mine (or on a non-producing mine assuming a given rate of production and profit from the factors exposed), by reference to the table the number of years can be seen in which this percentage must continue in order to amortize the investment and pay various rates of interest on it. As said before, the ore in sight at a given rate of exhaustion can be reduced to terms of life in sight. This certain period deducted from the total term of years required gives the life which must be provided by further discovery of ore, and this can be reduced to tons or feet of extension of given ore-bodies and a tangible position arrived at. The test can be applied in this manner to the various prices which must be realized from the base metal in sight to warrant the price.
Taking the last example and assuming that the mine is equipped, and that the price is $2,000,000, the yearly return on the price is 10%. If it is desired besides amortizing or redeeming the capital to secure a return of 7% on the investment, it will be seen by reference to the table that there will be required a life of 21.6 years. As the life visible in the ore in sight is ten years, then the extensions in depth must produce ore for 11.6 years longer—1,160,000 tons. If the ore-body is 1,000 feet long and 13 feet wide, it will furnish of gold ore 1,000 tons per foot of depth; hence the ore-body must extend 1,160 feet deeper to justify the price. Mines are seldom so simple a proposition as this example. There are usually probabilities of other ore; and in the case of base metal, then variability of price and other elements must be counted. However, once the extension in depth which is necessary is determined for various assumptions of metal value, there is something tangible to consider and to weigh with the five geological weights set out in Chapter III.
The example given can be expanded to indicate not only the importance of interest and redemption in the long extension in depth required, but a matter discussed from another point of view under "Ratio of Output." If the plant on this mine were doubled and the earnings increased to 20% ($400,000 per annum) (disregarding the reduction in working expenses that must follow expansion of equipment), it will be found that the life required to repay the purchase money,—$2,000,000,—and 7% interest upon it, is about 6.8 years.
As at this increased rate of production there is in the ore in sight a life of five years, the extension in depth must be depended upon for 1.8 years, or only 360,000 tons,—that is, 360 feet of extension. Similarly, the present value of the ore in sight is $268,000 greater if the mine be given double the equipment, for thus the idle money locked in the ore is brought into the interest market at an earlier date. Against this increased profit must be weighed the increased cost of equipment. The value of low grade mines, especially, is very much a factor of the volume of output contemplated.
CHAPTER VI.
Mine Valuation (Concluded).
| VALUATION OF MINES WITH LITTLE OR NO ORE IN SIGHT; VALUATIONS ON SECOND-HAND DATA; GENERAL CONDUCT OF EXAMINATIONS; REPORTS. |
A large number of examinations arise upon prospecting ventures or partially developed mines where the value is almost wholly prospective. The risks in such enterprises amount to the possible loss of the whole investment, and the possible returns must consequently be commensurate. Such business is therefore necessarily highly speculative, but not unjustifiable, as the whole history of the industry attests; but this makes the matter no easier for the mine valuer. Many devices of financial procedure assist in the limitation of the sum risked, and offer a middle course to the investor between purchase of a wholly prospective value and the loss of a possible opportunity to profit by it. The usual form is an option to buy the property after a period which permits a certain amount of development work by the purchaser before final decision as to purchase.
Aside from young mines such enterprises often arise from the possibility of lateral extension of the ore-deposit outside the boundaries of the property of original discovery (Fig. 3), in which cases there is often no visible ore within the property under consideration upon which to found opinion. In regions where vertical side lines obtain, there is always the possibility of a "deep level" in inclined deposits. Therefore the ground surrounding known deposits has a certain speculative value, upon which engineers are often called to pass judgment. Except in such unusual occurrences as South African bankets, or Lake Superior coppers, prospecting for deep level of extension is also a highly speculative phase of mining.
The whole basis of opinion in both classes of ventures must be the few geological weights,—the geology of the property and the district, the development of surrounding mines, etc. In any event, there is a very great percentage of risk, and the profit to be gained by success must be, proportionally to the expenditure involved, very large. It is no case for calculating amortization and other refinements. It is one where several hundreds or thousands of per cent hoped for on the investment is the only justification.