Engineering valuations of raining properties are made for a number of purposes, principally the following:

1. For purposes of purchase or sale on behalf of prospective buyers or vendors.
2. For purposes of financing by bond issues or sales of stock.
3. As a basis for taxation.
4. In connection with trespass or damage suits.

Theoretically the value of a mine should be the same, whatever the purpose of the valuation; as mining operations are conducted for profit, this value at any time is the present worth of the profits that will be earned after amortization of capital investment during the life of the mine.

It is apparent from a consideration of the discussions and data presented in the preceding sections of this bulletin that many variable factors impossible of exact determination affect the profits that may be realized from the exploitation of a given mineral deposit; hence, valuations derived from a considered weighing of all these factors cannot be precise.

Because of these inherent inaccuracies, a valuation is likely to be colored, to some extent at least, by the purpose for which it was made or by the viewpoint of the engineer, no matter how great his moral and intellectual honesty. Careful and conscientious valuations of the same mine made independently by different engineers may differ widely, depending upon the different interpretations of and the weights given to the various engineering and economic factors involved. It is only human for a prudent prospective purchaser to foresee and give more weight to possible contingencies that may arise to increase costs or to reduce income than would the seller who is trying to obtain the maximum possible price for his property.

In spite of the difficulty of accurately estimating future costs and revenues, valuations based on present worth of anticipated profits are most logical and long have been accepted for all the above purposes.

In transactions involving the sale of a mine the price actually paid usually will be decided by negotiation and may differ considerably from that derived, by engineering appraisal. In such instances, however, the engineering appraisal is indispensable as a basis for intelligent negotiation.

The subject of mine valuation and the mathematics involved have been discussed at length in a number of standard works, among the best known of which are the following:

Hoskold first prepared and published in 1877 full sets of tables required for computing present worth, and later writers on the subject have reproduced these tables in part. By their use, computations are greatly simplified. They cover a range of dividend and interest rates and terms of years especially suited to mine valuation in which, on account of the risks peculiar to mining, the investor demands a higher return on his money than he would require from other types of productive enterprise where the operation is not dependent on a wasting raw-material resource and the risks are smaller.

Of especial value are tables 6, 7, 8, and 9, in which the factors have been calculated so as to combine income rates of 3½ to 25 percent per annum with interest rates on invested sinking fund of 2½, 3, 3½ and 4 percent, respectively; and tables 10 and 11, in which similar combined factors are given for computing present worth where income is deferred for 1, 2, 3, and 4 years, respectively.

Hoskold and other writers stress the importance of allowing for amortization of capital investment in view of the limited life of a mining operation (determined by the total ore reserves and the rate of production).

The following discussion of mine valuation is confined to brief observations on the engineering principles and data presented in the preceding sections of this bulletin as they affect the use of accepted methods of mine appraisal.

A rational appraisal of the potentialities of a mine for earning profits over a period of years requires a broad understanding of the geology and of the operating and economic problems involved, together with sound judgment. Experienced mining engineers are assumed to be already conversant with most of the subjects previously discussed in this bulletin, but it is hoped that such may find some of the engineering and cost data useful. On the other hand, students and younger practicing engineers may find the discussions useful also in approaching mine-appraisal problems.

Metalliferous deposits may be divided roughly into two classes for valuation purposes:

1. Deposits with substantial tonnages of assured (proven) ore.
   (а) Extensive deposits of uniform tenor (usually low-grade).
   (b) Large ore bodies of erratic occurrence (erratic in grade or of complex mineral combination, or both).
2. Deposits with little or no proven ore.

A further distinction may be made, depending on whether the deposits are supporting established operating mines, that is, have an operating history, or have not yet entered the regular productive stage.

Properties with Large Assured Ore Reserves

The number of variable factors in valuations of deposits of type 1-a are a minimum. The “porphyry” copper deposits of the southwest, the lead mines of the Southeast Missouri district, and the iron mines of the Lake Superior and Birmingham districts are examples of this type of deposit. Here, substantial reserves will have been proved usually by drilling or underground development before production begins. Hence, the mining and milling operations may be highly systematized and approach in effect the operation of a manufacturing plant, the main difference being that the raw material of a mine—its ore reserve—is definitely limited and not replaceable and, with the exhaustion of the ore, production ceases.

For such deposits the ore-reserve tonnage and grade may be determined by procedures discussed in the sections on sampling and estimation of ore reserves, with a relatively high degree of accuracy and an average yearly rate of production and life can then be predicted with some confidence, although probable fluctuations in price and market demand must be considered. Production costs can be estimated closely, particularly if the mine under consideration has a production record from which accurate cost data can be derived.

The most uncertain elements in valuing deposits of this class are the price that will be received for the product and the rate of production that market demands will support.

Valuation engineers are accustomed to employ curves showing variations in and general trends of metal prices and consumption over a long period of years for projecting prices into the future. Studies of price trends should be supplemented by consideration of the possible effect of such factors as general exhaustion of other mines in the country and the prospects for important new domestic ore discoveries, possible tariff changes, foreign ore discoveries, and competition from secondary or scrap metals and from new synthetic substitutes for metals.

It is therefore apparent that long-range predictions of metal prices are precarious and that mineral economics and the world situation with regard to the reserves of metallic ores in the ground must be considered.

The difficulty in long-range price prediction may not be a serious matter, however, if the nearer range prices can be approximated closely, because, as pointed out by standard works on mine valuation, the present worth of profits that will not accrue for 20 years or more is small. Hotchkiss and Parks have shown that “present value of an annuity of one dollar, using interest rates of 8 percent for return on capital and 4 percent for accrual on redemption fund extended to infinite life at these rates, is $12.50, or 12½ times the yearly income; that of this ultimate maximum present value, 50 percent is attributable to income of the first 10 years, 80 percent to the income of the first 28 years, and 88 percent to the income of the first 40 years.” On these assumptions the present worth of income of the first 10 years would be 62.5 percent of that for the first 28 years, and that of the first 28 years about 91 percent of that of the first 40 years. Therefore, it may be concluded that small errors in estimating prices after 15 or 20 years will have little effect upon the present worth and larger errors will have small relative effect.

In general, application of the present-worth method to valuation of mines of type 1, and especially of type 1-a, may be made with considerable confidence in the resulting figure, which in most instances probably will be nearer the actual sale price of such mines than it would be for mines of the other types. Hence, a lower rate of return on capital may be used in calculating present worth of type 1 mines than when applying this method to mines where the risk is greater because a greater number of factors are variable and impossible of close determination.

In 1911 the Michigan State Tax Commission adopted the present worth method for valuing iron and copper mines, employing a 6- percent return on capital and a 6-percent sinking fund rate.

The uncertainties in valuations of properties of type 1-a apply equally to those where there is less certainty as to production costs and ore reserves, except that for short-life properties prices sometimes may be predicted more accurately. The importance of skilled management in the earning of profits from operation of mines of any class cannot be overemphasized, and therefore, wherever possible the type of management that is likely to be had should be considered.

Additional uncertainties arise in valuing properties in the other classes. With deposits of type 1-b, there is more question as to operating costs that will be realized and as to the grade of ore that will be mined, these factors often being complementary. These deposits are also typically irregular with respect to characteristics that determine the mining methods and practices that can be employed, and with increased depth the mineralogical character of the ore may change, requiring changes in ore-dressing treatment. The effect upon costs of natural mining conditions and the methods of mining employed has been discussed under Stoping.

The mining method adopted may depend to a considerable extent on the policy with respect to grade of ore that is to be mined.

Thus, if it is decided to mine selectively only the better-grade ore, leaving in the mine that upon which little profit can be expected, a relatively high-cost mining method may be required. Or, if the policy is to mine this ore by a method that will not preclude mining the lower-grade ores later when market prices are high and demand heavy, a still more expensive mining system may be necessary. Obviously, a policy of mining only the better-grade ore will result in smaller ore reserves and a shorter productive life. Normally this will result in a higher valuation for this class of deposit, because a high income rate is realized during early years when present-worth discounts are a minimum, unless the life were so shortened that high amortization charges would overbalance the greater profits.

It has been argued that since the primary object of mining is for profit, the operating policy that will result in the highest present worth of profits is the one that should be adopted. Even aside from the question of conservation of natural mineral resources, however, this is not invariably so. Thus, in the case of integrated companies that are engaged in the manufacture of metal products and own the mines upon which they depend for their raw material, a policy of rapidly depleting the higher-grade ores with the loss of lower-grade and marginal ores would shorten the life of the enterprise as a whole or force it to enter the market for ores from outside sources. The sacrifice of ore reserves to maximum profits from the mine would therefore be a detriment to the company and actually lower the value of its assets.

Since the question of conservation is assuming more importance and public attention is being focused upon it, the trend of legislation is likely to be toward measures that will prevent wasteful operation of mines for the sake of large immediate profits.

Properties with Little or no Assured Ore Reserves

In the case of properties having large assured ore reserves and long-life, the effect upon present worth of additional ore that may be found later is relatively small because the profit to be derived from it is remote.

In the case of a property with small proved reserves, however, the present value of profits to be derived from the known ore may be only a small fraction of the actual value. The value of the known ore may be computed readily by the regular methods, but evaluation of the potentialities of the property requires the exercise of judgment based upon a knowledge of the ore habits in the district and of structural and other geological, controls. The question of probable and possible ore has been discussed in the section on Estimation of Ore Reserves, where the uncertainties regarding conclusions as to tonnage and grade were pointed out. As a basis for valuing this unproved ore, the usual calculations may be employed, using, however, a high rate of return because of the uncertainties involved. It is apparent that widely different results may be derived by different engineers, depending upon their relative optimism or pessimism, which will be reflected both in the tonnages and grades of ore estimated and in the percentage of return judged to be commensurate with the risk to the investment. Likewise, the price that is paid for such a property will depend largely upon the confidence of the purchaser in its possibilities and the size of the risk his speculative instinct prompts him to take on the chance of large profits. Often the risk may be minimized by obtaining an option to purchase that permits a period of development before substantial payments on the purchase price must be made.

Undeveloped Properties

In the valuation of undeveloped, unequipped properties, whether having large or small ore reserves or none at all, consideration, must be given to time and expenditure required to equip, develop, and bring the mine into profitable production. The expenditures up to the time of profitable production (including the purchase price of the property), with interest thereon, must be amortized from profits. The tables referred to above include, as stated, factors for computing present worth on profits deferred for from 1 to 4 years.

Rates of progress and costs of the various phases of mine development are engineering matters that were discussed in preceding sections of this bulletin.