Principles of Mining: Valuation, Organization and Administration

Some minerals are more freely soluble and more readily precipitated than others. From this cause there is in complex metal deposits a rearrangement of horizontal sequence, in addition to enrichment at certain horizons and impoverishment at others. The whole subject is one of too great complexity for adequate consideration in this discussion. No engineer is properly equipped to give judgment on extension in depth without a thorough grasp of the great principles laid down by Van Hise, Emmons, Lindgren, Weed, and others. We may, however, briefly examine some of the theoretical effects of such alteration.

Zinc, iron, and lead sulphides are a common primary combination. These metals are rendered soluble from their usual primary forms by oxidizing agencies, in the order given. They reprecipitate as sulphides in the reverse sequence. The result is the leaching of zinc and iron readily in the oxidized zone, thus differentially enriching the lead which lags behind, and a further extension of the lead horizon is provided by the early precipitation of such lead as does migrate. Therefore, the lead often predominates in the second and the upper portion of the third zone, with the zinc and iron below. Although the action of all surface waters is toward oxidation and carbonation of these metals, the carbonate development of oxidized zones is more marked when the enclosing rocks are calcareous.

In copper-iron deposits, the comparatively easy decomposition and solubility and precipitation of the copper and some iron salts generally result in more extensive impoverishment of these metals near the surface, and more predominant enrichment at a lower horizon than is the case with any other metals. The barren "iron hat" at the first zone, the carbonates and oxides at the second, the enrichment with secondary copper sulphides at the top of the third, and the occurrence of secondary copper-iron sulphides below, are often most clearly defined. In the easy recognition of the secondary copper sulphides, chalcocite, bornite, etc., the engineer finds a finger-post on the road to extension in depth; and the directions upon this post are not to be disregarded. The number of copper deposits enriched from unpayability in the first zone to a profitable character in the next two, and unpayability again in the fourth, is legion.

Silver occurs most abundantly in combination with either lead, copper, iron, or gold. As it resists oxidation and solution more strenuously than copper and iron, its tendency when in combination with them is to lag behind in migration. There is thus a differential enrichment of silver in the upper two zones, due to the reduction in specific gravity of the ore by the removal of associated metals. Silver does migrate somewhat, however, and as it precipitates more readily than copper, lead, zinc, or iron, its tendency when in combination with them is towards enrichment above the horizons of enrichment of these metals. When it is in combination with lead and zinc, its very ready precipitation from solution by the galena leaves it in combination more predominantly with the lead. The secondary enrichment of silver deposits at the top of the sulphide zone is sometimes a most pronounced feature, and it seems to be the explanation of the origin of many "bonanzas."

In gold deposits, the greater resistance to solubility of this metal than most of the others, renders the phenomena of migration to depth less marked. Further than this, migration is often interfered with by the more impervious quartz matrix of many gold deposits. Where gold is associated with large quantities of base metals, however, the leaching of the latter in the oxidized zone leaves the ore differentially richer, and as gold is also slightly soluble, in such cases the migration of the base metals does carry some of the gold. In the instance especially of impregnation or replacement deposits, where the matrix is easily permeable, the upper sulphide zone is distinctly richer than lower down, and this enrichment is accompanied by a considerable increase in sulphides and tellurides. The predominant characteristic of alteration in gold deposits is, however, enrichment in the oxidized zone with the maximum values near the surface. The reasons for this appear to be that gold in its resistance to oxidation and wholesale migration gives opportunities to a sort of combined mechanical and chemical enrichment.

In dry climates, especially, the gentleness of erosion allows of more thorough decomposition of the outcroppings, and a mechanical separation of the gold from the detritus. It remains on or near the deposit, ready to be carried below, mechanically or otherwise. In wet climates this is less pronounced, for erosion bears away the croppings before such an extensive decomposition and freeing of the gold particles. The West Australian gold fields present an especially prominent example of this type of superficial enrichment. During the last fifteen years nearly eight hundred companies have been formed for working mines in this region. Although from four hundred of these high-grade ore has been produced, some thirty-three only have ever paid dividends. The great majority have been unpayable below oxidation,—a distance of one or two hundred feet. The writer's unvarying experience with gold is that it is richer in the oxidized zone than at any point below. While cases do occur of gold deposits richer in the upper sulphide zone than below, even the upper sulphides are usually poorer than the oxidized region. In quartz veins preëminently, evidence of enrichment in the third zone is likely to be practically absent.

Tin ores present an anomaly among the base metals under discussion, in that the primary form of this metal in most workable deposits is an oxide. Tin in this form is most difficult of solution from ground agencies, as witness the great alluvial deposits, often of considerable geologic age. In consequence the phenomena of migration and enrichment are almost wholly absent, except such as are due to mechanical penetration of tin from surface decomposition of the matrix akin to that described in gold deposits.

In general, three or four essential facts from secondary alteration must be kept in view when prognosticating extensions.

Oxidation usually alters treatment problems, and oxidized ore of the same grade as sulphides can often be treated more cheaply. This is not universal. Low-grade ores of lead, copper, and zinc may be treatable by concentration when in the form of sulphides, and may be valueless when oxidized, even though of the same grade.

Copper ores generally show violent enrichment at the base of the oxidized, and at the top of the sulphide zone.

Lead-zinc ores show lead enrichment and zinc impoverishment in the oxidized zone but have usually less pronounced enrichment below water level than copper. The rearrangement of the metals by the deeper migration of the zinc, also renders them metallurgically of less value with depth.

Silver deposits are often differentially enriched in the oxidized zone, and at times tend to concentrate in the upper sulphide zone.

Gold deposits usually decrease in value from the surface through the whole of the three alteration zones.

Size of Deposits.—The proverb of a relation between extension in depth and size of ore-bodies expresses one of the oldest of miners' beliefs. It has some basis in experience, especially in fissure veins, but has little foundation in theory and is applicable over but limited areas and under limited conditions.

From a structural view, the depth of fissuring is likely to be more or less in proportion to its length and breadth and therefore the volume of vein filling with depth is likely to be proportional to length and width of the fissure. As to the distribution of values, if we eliminate the influence of changing wall rocks, or other precipitating agencies which often cause the values to arrange themselves in "floors," and of secondary alteration, there may be some reason to assume distribution of values of an extent equal vertically to that displayed horizontally. There is, as said, more reason in experience for this assumption than in theory. A study of the shape of a great many ore-shoots in mines of fissure type indicates that when the ore-shoots or ore-bodies are approaching vertical exhaustion they do not end abruptly, but gradually shorten and decrease in value, their bottom boundaries being more often wedge-shaped than even lenticular. If this could be taken as the usual occurrence, it would be possible (eliminating the evident exceptions mentioned above) to state roughly that the minimum extension of an ore-body or ore-shoot in depth below any given horizon would be a distance represented by a radius equal to one-half its length. By length is not meant necessarily the length of a horizontal section, but of one at right angles to the downward axis.

On these grounds, which have been reënforced by much experience among miners, the probabilities of extension are somewhat in proportion to the length and width of each ore-body. For instance, in the A mine, with an ore-shoot 1000 feet long and 10 feet wide, on its bottom level, the minimum extension under this hypothesis would be a wedge-shaped ore-body with its deepest point 500 feet below the lowest level, or a minimum of say 200,000 tons. Similarly, the B mine with five ore-bodies, each 300 hundred feet long and 10 feet wide, exposed on its lowest level, would have a minimum of five wedges 100 feet deep at their deepest points, or say 50,000 tons. This is not proposed as a formula giving the total amount of extension in depth, but as a sort of yardstick which has experience behind it. This experience applies in a much less degree to deposits originating from impregnation along lines of fissuring and not at all to replacements.

Development in Neighboring Mines.—Mines of a district are usually found under the same geological conditions, and show somewhat the same habits as to extension in depth or laterally, and especially similar conduct of ore-bodies and ore-shoots. As a practical criterion, one of the most intimate guides is the actual development in adjoining mines. For instance, in Kalgoorlie, the Great Boulder mine is (March, 1908) working the extension of Ivanhoe lodes at points 500 feet below the lowest level in the Ivanhoe; likewise, the Block 10 lead mine at Broken Hill is working the Central ore-body on the Central boundary some 350 feet below the Central workings. Such facts as these must have a bearing on assessing the downward extension.

Depth of Exhaustion.—All mines become completely exhausted at some point in depth. Therefore the actual distance to which ore can be expected to extend below the lowest level grows less with every deeper working horizon. The really superficial character of ore-deposits, even outside of the region of secondary enrichment is becoming every year better recognized. The prospector's idea that "she gets richer deeper down," may have some basis near the surface in some metals, but it is not an idea which prevails in the minds of engineers who have to work in depth. The writer, with some others, prepared a list of several hundred dividend-paying metal mines of all sorts, extending over North and South America, Australasia, England, and Africa. Notes were made as far as possible of the depths at which values gave out, and also at which dividends ceased. Although by no means a complete census, the list indicated that not 6% of mines (outside banket) that have yielded profits, ever made them from ore won below 2000 feet. Of mines that paid dividends, 80% did not show profitable value below 1500 feet, and a sad majority died above 500. Failures at short depths may be blamed upon secondary enrichment, but the majority that reached below this influence also gave out. The geological reason for such general unseemly conduct is not so evident.

Conclusion.—As a practical problem, the assessment of prospective value is usually a case of "cut and try." The portion of the capital to be invested, which depends upon extension, will require so many tons of ore of the same value as that indicated by the standing ore, in order to justify the price. To produce this tonnage at the continued average size of the ore-bodies will require their extension in depth so many feet—or the discovery of new ore-bodies of a certain size. The five geological weights mentioned above may then be put into the scale and a basis of judgment reached.

CHAPTER IV.

Mine Valuation (Continued).

The method of treatment for the ore must be known before a mine can be valued, because a knowledge of the recoverable percentage is as important as that of the gross value of the ore itself. The recoverable percentage is usually a factor of working costs. Practically every ore can be treated and all the metal contents recovered, but the real problem is to know the method and percentage of recovery which will yield the most remunerative result, if any. This limit to profitable recovery regulates the amount of metal which should be lost, and the amount of metal which consequently must be deducted from the gross value before the real net value of the ore can be calculated. Here, as everywhere else in mining, a compromise has to be made with nature, and we take what we can get—profitably. For instance, a copper ore may be smelted and a 99% recovery obtained. Under certain conditions this might be done at a loss, while the same ore might be concentrated before smelting and yield a profit with a 70% recovery. An additional 20% might be obtained by roasting and leaching the residues from concentration, but this would probably result in an expenditure far greater than the value of the 20% recovered. If the ore is not already under treatment on the mine, or exactly similar ore is not under treatment elsewhere, with known results, the method must be determined experimentally, either by the examining engineer or by a special metallurgist.

Where partially treated products, such as concentrates, are to be sold, not only will there be further losses, but deductions will be made by the smelter for deleterious metals and other charges. All of these factors must be found out,—and a few sample smelting returns from a similar ore are useful.

To cover the whole field of metallurgy and discuss what might apply, and how it might apply, under a hundred supposititious conditions would be too great a digression from the subject in hand. It is enough to call attention here to the fact that the residues from every treatment carry some metal, and that this loss has to be deducted from the gross value of the ore in any calculations of net values.

PRICE OF METALS.

Unfortunately for the mining engineer, not only has he to weigh the amount of risk inherent in calculations involved in the mine itself, but also that due to fluctuations in the value of metals. If the ore is shipped to custom works, he has to contemplate also variations in freights and smelting charges. Gold from the mine valuer's point of view has no fluctuations. It alone among the earth's products gives no concern as to the market price. The price to be taken for all other metals has to be decided before the mine can be valued. This introduces a further speculation and, as in all calculations of probabilities, amounts to an estimate of the amount of risk. In a free market the law of supply and demand governs the value of metals as it does that of all other commodities. So far, except for tariff walls and smelting rings, there is a free market in the metals under discussion.

The demand for metals varies with the unequal fluctuations of the industrial tides. The sea of commercial activity is subject to heavy storms, and the mine valuer is compelled to serve as weather prophet on this ocean of trouble. High prices, which are the result of industrial booms, bring about overproduction, and the collapse of these begets a shrinkage of demand, wherein consequently the tide of price turns back. In mining for metals each pound is produced actually at a different cost. In case of an oversupply of base metals the price will fall until it has reached a point where a portion of the production is no longer profitable, and the equilibrium is established through decline in output. However, in the backward swing, due to lingering overproduction, prices usually fall lower than the cost of producing even a much-diminished supply. There is at this point what we may call the "basic" price, that at which production is insufficient and the price rises again. The basic price which is due to this undue backward swing is no more the real price of the metal to be contemplated over so long a term of years than is the highest price. At how much above the basic price of depressed times the product can be safely expected to find a market is the real question. Few mines can be bought or valued at this basic price. An indication of what this is can be gained from a study of fluctuations over a long term of years.

It is common to hear the average price over an extended period considered the "normal" price, but this basis for value is one which must be used with discretion, for it is not the whole question when mining. The "normal" price is the average price over a long term. The lives of mines, and especially ore in sight, may not necessarily enjoy the period of this "normal" price. The engineer must balance his judgments by the immediate outlook of the industrial weather. When lead was falling steadily in December, 1907, no engineer would accept the price of that date, although it was then below "normal"; his product might go to market even lower yet.

It is desirable to ascertain what the basic and normal prices are, for between them lies safety. Since 1884 there have been three cycles of commercial expansion and contraction. If the average prices are taken for these three cycles separately (1885-95), 1895-1902, 1902-08) it will be seen that there has been a steady advance in prices. For the succeeding cycles lead on the London Exchange,[*] the freest of the world's markets was £12 12s. 4d., £13 3s. 7d., and £17 7s. 0d. respectively; zinc, £17 14s. 10d., £19 3s. 8d., and £23 3s. 0d.; and standard copper, £48 16s. 0d., £59 10s. 0d., and £65 7s. 0d. It seems, therefore, that a higher standard of prices can be assumed as the basic and normal than would be indicated if the general average of, say, twenty years were taken. During this period, the world's gold output has nearly quadrupled, and, whether the quantitative theory of gold be accepted or not, it cannot be denied that there has been a steady increase in the price of commodities. In all base-metal mining it is well to remember that the production of these metals is liable to great stimulus at times from the discovery of new deposits or new processes of recovery from hitherto unprofitable ores. It is therefore for this reason hazardous in the extreme to prophesy what prices will be far in the future, even when the industrial weather is clear. But some basis must be arrived at, and from the available outlook it would seem that the following metal prices are justifiable for some time to come, provided the present tariff schedules are maintained in the United States:

[Footnote *: All London prices are based on the long ton of 2,240 lbs. Much confusion exists in the copper trade as to the classification of the metal. New York prices are quoted in electrolytic and "Lake"; London's in "Standard." "Standard" has now become practically an arbitrary term peculiar to London, for the great bulk of copper dealt in is "electrolytic" valued considerably over "Standard."]

In these figures the writer has not followed strict averages, but has taken the general outlook combined with the previous records. The likelihood of higher prices for lead is more encouraging than for any other metal, as no new deposits of importance have come forward for years, and the old mines are reaching considerable depths. Nor does the frenzied prospecting of the world's surface during the past ten years appear to forecast any very disturbing developments. The zinc future is not so bright, for metallurgy has done wonders in providing methods of saving the zinc formerly discarded from lead ores, and enormous supplies will come forward when required. The tin outlook is encouraging, for the supply from a mining point of view seems unlikely to more than keep pace with the world's needs. In copper the demand is growing prodigiously, but the supplies of copper ores and the number of copper mines that are ready to produce whenever normal prices recur was never so great as to-day. One very hopeful fact can be deduced for the comfort of the base metal mining industry as a whole. If the growth of demand continues through the next thirty years in the ratio of the past three decades, the annual demand for copper will be over 3,000,000 tons, of lead over 1,800,000 tons, of spelter 2,800,000 tons, of tin 250,000 tons. Where such stupendous amounts of these metals are to come from at the present range of prices, and even with reduced costs of production, is far beyond any apparent source of supply. The outlook for silver prices is in the long run not bright. As the major portion of the silver produced is a bye product from base metals, any increase in the latter will increase the silver production despite very much lower prices for the precious metal. In the meantime the gradual conversion of all nations to the gold standard seems a matter of certainty. Further, silver may yet be abandoned as a subsidiary coinage inasmuch as it has now but a token value in gold standard countries if denuded of sentiment.

COST OF PRODUCTION.

It is hardly necessary to argue the relative importance of the determination of the cost of production and the determination of the recoverable contents of the ore. Obviously, the aim of mine valuation is to know the profits to be won, and the profit is the value of the metal won, less the cost of production.

The cost of production embraces development, mining, treatment, management. Further than this, it is often contended that, as the capital expended in purchase and equipment must be redeemed within the life of the mine, this item should also be included in production costs. It is true that mills, smelters, shafts, and all the paraphernalia of a mine are of virtually negligible value when it is exhausted; and that all mines are exhausted sometime and every ton taken out contributes to that exhaustion; and that every ton of ore must bear its contribution to the return of the investment, as well as profit upon it. Therefore it may well be said that the redemption of the capital and its interest should be considered in costs per ton. The difficulty in dealing with the subject from the point of view of production cost arises from the fact that, except possibly in the case of banket gold and some conglomerate copper mines, the life of a metal mine is unknown beyond the time required to exhaust the ore reserves. The visible life at the time of purchase or equipment may be only three or four years, yet the average equipment has a longer life than this, and the anticipation for every mine is also for longer duration than the bare ore in sight. For clarity of conclusions in mine valuation the most advisable course is to determine the profit in sight irrespective of capital redemption in the first instance. The questions of capital redemption, purchase price, or equipment cost can then be weighed against the margin of profit. One phase of redemption will be further discussed under "Amortization of Capital" and "Ratio of Output to the Mine."

The cost of production depends upon many things, such as the cost of labor, supplies, the size of the ore-body, the treatment necessary, the volume of output, etc.; and to discuss them all would lead into a wilderness of supposititious cases. If the mine is a going concern, from which reliable data can be obtained, the problem is much simplified. If it is virgin, the experience of other mines in the same region is the next resource; where no such data can be had, the engineer must fall back upon the experience with mines still farther afield. Use is sometimes made of the "comparison ton" in calculating costs upon mines where data of actual experience are not available. As costs will depend in the main upon items mentioned above, if the known costs of a going mine elsewhere be taken as a basis, and subtractions and additions made for more unfavorable or favorable effect of the differences in the above items, a fairly close result can be approximated.

Mine examinations are very often inspired by the belief that extended operations or new metallurgical applications to the mine will expand the profits. In such cases the paramount questions are the reduction of costs by better plant, larger outputs, new processes, or alteration of metallurgical basis and better methods. If every item of previous expenditure be gone over and considered, together with the equipment, and method by which it was obtained, the possible savings can be fairly well deduced, and justification for any particular line of action determined. One view of this subject will be further discussed under "Ratio of Output to the Mine." The conditions which govern the working costs are on every mine so special to itself, that no amount of advice is very useful. Volumes of advice have been published on the subject, but in the main their burden is not to underestimate.

In considering the working costs of base-metal mines, much depends upon the opportunity for treatment in customs works, smelters, etc. Such treatment means a saving of a large portion of equipment cost, and therefore of the capital to be invested and subsequently recovered. The economics of home treatment must be weighed against the sum which would need to be set aside for redemption of the plant, and unless there is a very distinct advantage to be had by the former, no risks should be taken. More engineers go wrong by the erection of treatment works where other treatment facilities are available, than do so by continued shipping. There are many mines where the cost of equipment could never be returned, and which would be valueless unless the ore could be shipped. Another phase of foreign treatment arises from the necessity or advantage of a mixture of ores,—the opportunity of such mixtures often gives the public smelter an advantage in treatment with which treatment on the mine could never compete.

Fluctuation in the price of base metals is a factor so much to be taken into consideration, that it is desirable in estimating mine values to reduce the working costs to a basis of a "per unit" of finished metal. This method has the great advantage of indicating so simply the involved risks of changing prices that whoso runs may read. Where one metal predominates over the other to such an extent as to form the "backbone" of the value of the mine, the value of the subsidiary metals is often deducted from the cost of the principal metal, in order to indicate more plainly the varying value of the mine with the fluctuating prices of the predominant metal. For example, it is usual to state that the cost of copper production from a given ore will be so many cents per pound, or so many pounds sterling per ton. Knowing the total metal extractable from the ore in sight, the profits at given prices of metal can be readily deduced. The point at which such calculation departs from the "per-ton-of-ore" unto the per-unit-cost-of-metal basis, usually lies at the point in ore dressing where it is ready for the smelter. To take a simple case of a lead ore averaging 20%: this is to be first concentrated and the lead reduced to a concentrate averaging 70% and showing a recovery of 75% of the total metal content. The cost per ton of development, mining, concentration, management, is to this point say $4 per ton of original crude ore. The smelter buys the concentrate for 95% of the value of the metal, less the smelting charge of $15 per ton, or there is a working cost of a similar sum by home equipment. In this case 4.66 tons of ore are required to produce one ton of concentrates, and therefore each ton of concentrates costs $18.64. This amount, added to the smelting charge, gives a total of $33.64 for the creation of 70% of one ton of finished lead, or equal to 2.40 cents per pound which can be compared with the market price less 5%. If the ore were to contain 20 ounces of silver per ton, of which 15 ounces were recovered into the leady concentrates, and the smelter price for the silver were 50 cents per ounce, then the $7.50 thus recovered would be subtracted from $33.64, making the apparent cost of the lead 1.86 cents per pound.

CHAPTER V.

Mine Valuation (Continued).

It is desirable to state in some detail the theory of amortization before consideration of its application in mine valuation.

As every mine has a limited life, the capital invested in it must be redeemed during the life of the mine. It is not sufficient that there be a bare profit over working costs. In this particular, mines differ wholly from many other types of investment, such as railways. In the latter, if proper appropriation is made for maintenance, the total income to the investor can be considered as interest or profit; but in mines, a portion of the annual income must be considered as a return of capital. Therefore, before the yield on a mine investment can be determined, a portion of the annual earnings must be set aside in such a manner that when the mine is exhausted the original investment will have been restored. If we consider the date due for the return of the capital as the time when the mine is exhausted, we may consider the annual instalments as payments before the due date, and they can be put out at compound interest until the time for restoration arrives. If they be invested in safe securities at the usual rate of about 4%, the addition of this amount of compound interest will assist in the repayment of the capital at the due date, so that the annual contributions to a sinking fund need not themselves aggregate the total capital to be restored, but may be smaller by the deficiency which will be made up by their interest earnings. Such a system of redemption of capital is called "Amortization."

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%.

Table II is practically a compound discount table. That is, by it can be determined the present value of a fixed sum payable at the end of a given term of years, interest being discounted at various given rates. Its use may be illustrated by continuing the example preceding.

TABLE II.

Present Value of $1, or £1, payable in — Years, Interest taken at —%.

If such a mine is not equipped, and it is assumed that $200,000 are required to equip the mine, and that two years are required for this equipment, the value of the ore in sight is still less, because of the further loss of interest in delay and the cost of equipment. In this case the present value of $1,304,000 in two years, interest at 7%, the factor is .87 X 1,304,000 = $1,134,480. From this comes off the cost of equipment, or $200,000, leaving $934,480 as the present value of the profit in sight. A further refinement could be added by calculating the interest chargeable against the $200,000 equipment cost up to the time of production.

TABLE III.

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.