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"Logically the prospective value can be simply a factor of how far the ore in the individual mine may be expected to extend

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"Extension of half length of ore shoot in depth used as minimum in vein mines or shear zones but not in replacement mines.

"All mines become completely exhausted at some point in depth. The really superficial character of ore deposits even outside of the region of secondary enrichment is becoming every year better recognized.

"Conclusion: The prices asked for vein mines are in excess of the profits to be won from the standing ore. Whether or not the price should be paid depends on the engineer's estimate of the possibility of finding sufficient additional ore, based on (1) the origin and structural character of the ore deposit; (2) the position of the opening in relation to secondary alteration; (3) the size of the deposit; (4) the depth to which the mine is already exhausted; and (5) comparison with the depth and continuity in adjacent mines."

H. D. Hoskold (Engineers Valuing Assistant (2d edition, Longmans Green & Co., 1905)):

Mr. Hoskold cites 19 prominent mining engineers, actuaries, and mathematicians of Great Britain in the preface of the first edition, published in 1877, as having reviewed and approved the principles and formulas of valuation presented in his book. (See pp. IX-X of preface of 2d edition.)

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'Every beneficial interest or sum of money accruing, or to accrue, and to be paid at the end of a year, or portion of a year, may be considered as an annuity, and may be either terminable with the life of an individual or perpetual. Any sum of money left unpaid for a certain number of years is called an annuity in arrear, and when not payable until after a fixed number of years it is said to be a reversionary or deferred annuity.

"On either case the annuity is transferable and may be purchased on certain agreed terms; each class of annuities must, however, receive a particular mode of treatment, adapted to, and peculiar to, the nature of the circumstances connected with each particular case.

If money could not be employed, and a marketable rate of interest obtained for its use, the value of any sum of money or annuity would be equal to that to be paid at the end of one year, multiplied by the whole period or number of years the annuity has to run; but as compound interest is involved in all these cases, it is clear that if A desires to sell an annuity to B, and which has to last a certain number of years, a certain agreed interest or discount must be allowed to B upon the whole sum to be purchased and received by him for the fixed period.

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Tables of the value of leases on annuities have frequently been published. That of Mr. Ward was written as far back as 1710; but Mr. Smart's celebrated five tables of compound interest, which appeared in 1726, far excelled all that had been done previously to that time; indeed, his tables have been incorporated more or less into the works of many writers to the present time. "The tables specially referred to are: 1. The amount of £1 in any number of years. 2. The present value of £1 due at the end of any number of years. 3. The amount of £1 per annum for any number of years. 4. The present value of £1 per annum for any number of years. 5. The annuity which £1 will purchase for any number of years.

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None of the tables of this class that I have seen (and I have examined a large number of works upon the subject) are computed to rates of interest higher than 10 per cent, and many of them extend only to 5 per cent.

"The rate of interest allowed to a purchaser of mineral property, such as collieries, iron mines, and others, frequently ranges between 10 and 25 per cent, but more generally between 14 and 20 per cent, depending, of course, upon the character of the property. It is evident, therefore, that tables calculated for rates of interest no higher than 8 or 10 per cent and to two or three places of decimals could not be employed for ascertaining the true value of annuities derived, or to be derived, from high rates.

"It is stated on page 2 of all the editions of Inwood's Tables of Annuities that I have seen--that is to say, those published from 1837 to 1866-that 'A lease or annuity for 14 years, to make 3 per cent and get back the principal, is worth 11.296 years' purchase of the clear annual rent,' and this rule is repeated as a footnote as far as page 9 as being true for all the rates of interest up to 10 per cent. The table goes no higher than 10 per cent, but it is identical with Mr. Smart's table--and that of all subsequent writers of the present value of £1 per annum for any number of years. This table, and others of its kind to be found in most works on annuities, is constructed correctly according to the

mode laid down, but as that mode is based on incorrect principles its application to the valuation of annuities, where interest is allowed at higher rates per cent than can possibly be found for reproducing capital, is entirely fallacious, for the principle upon which it is based assumes that we can reproduce capital which may have been invested at the same rate of interest as that allowed and expected to be realized on the purchase money invested.

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The practice, therefore, of valuing upon tables constructed on the assumption of reproducing capital at the same high rate of interest as that which may be realized on it is opposed to the truth and calculated to mislead and injure a purchaser to a very large extent.

"Thoman's definition is that the present value of a deferred annuity is equal to the difference between two immediate annuities of the same yearly income, one for the whole term, the other to continue until the time of entering on the deferred annuity.

"This rule, however, embraces but one rate of interest in the present value of £1 per annum, but it has, I believe, been followed by all writers on annuities and by many valuers since Thoman's time.

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"It will be observed that throughout the problems where the condition was introduced that a certain sum was necessary to be expended upon open or unopened mines with a view to obtain an estimated yield of minerals and constant profit extending over a definite future period the ordinary or customary mode of allowing 5 per cent upon any such sum has been followed. It was considered advisable that this mode of solution should be fully exhibited, as it is believed to be good practice by some of the profession."

Speaking of deferred annuities, Hoskold says:

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Generally, therefore, in cases of deferred annuities of this kind-that is, when two rates of interest are involved-a certain sum, Pt+n, has to be paid down immediately; but as no annuity is or can be payable under the circumstances during the deferred period the purchase money, Pt+n, accumulates at the rate allowed to the purchaser on his capital, or r' per £, to a certain sum= Pt+n(1+r')t=Pn; but at the expiration of t years the deferred period closes, and the annuity commences or is then entered upon, and its payments have to yield interest at the rate agreed upon between the parties to the business, or r' per £ on the accumulated purchase money, P=Pt+n(1+r')t, and also a sum sufficient to reinstate the sum Pa, to which the purchase money has accumulated at the end of the assigned term of t+n years, at another rate per £, or r." Ruckard Hurd, 'Iron Ore Manual, Lake Superior District" (Syndicate Printing Co., Minneapolis, Minn., 1911):

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"Rule for determination of present value of royalties: "

Gross receipts equal tonnage not paid for in advance times royalty rate per ton.

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Life of the mine equals gross receipts divided by minimum royalty payment per year; or the unexpired term of the existing lease, if this is a shorter period. Multiply the annual payment, payable quarterly, by the present value of $1 per annum, payable quarterly, at the assured rate of interest and for number of years determined as the life of the mine. The result is the present royalty value of the lease.

"Determining interest rate and factors. While under the conditions named the security of the investment is unquestioned, for calculating present value the determining interest rate depends upon a number of factors, such as"1. Average worth of money at the given time and interest rate expected for a long-time investment.

"2. Fluctuating yearly income as the property passes back and forth from shipping and nonshipping stages, from large royalty income on shipments one year to minimum annual payments when not operating.

"3. Quality of the ore and availability for furnace demands.

"4. Amount of the tonnage and the time required under normal mining conditions to exhaust the ore.

"5. Character and standing of the lessee and his ability to meet the terms of the lease.

"6. Possibility of a surrender of the lease, depending upon whether the ore is good or lean, monetary situation, and the financial condition of the lessee. "Under all these conditions such an investment demands and is entitled to a high rate of interest even greater than a highest-grade preferred stock or bond security would yield. Capitalists would not entertain the purchase of such a proposition at ordinary rates of 5, 6, or even 7 per cent. While 10

per cent seems to be the customary prevailing interest rate, it would appear that 8 to 10 per cent should be now used in calculating the present value of iron-ore royalties; that is, the investment required to purchase the royalty rights of a mineral lease containing known developed tonnage of merchantable iron ore.

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'Royalty only basis of value.-It will be observed that the assessed or full value or market price of the tonnage is not and should not be considered. That concerns only the operating company and the tax officials. That value has gone beyond the control of the fee owner with the lease; his value is in the royalty alone."

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Hurd uses the Inwood tables of the present value of $1 per annum, payable quarterly or annually, as the case may be, for valuation purposes. William Young Westervelt, "Mine examinations, valuations, and reports (sec. 25, p. 1515, Peele's Mining Engineers' Handbook; John Wiley & Sons, 1918):

"Since the value of a mine is its resources for producing future profits, that value is no more susceptible of accurate determination than any other future value, even in the ideal case of an absolutely developed mine. Fluctuation in market value of all products (except gold) may change a profit into a loss or the reverse; and it is seldom, if ever, determinable whether or not further discoveries, laterally or in depth, will resuscitate an apparently exhausted deposit, or whether improvements in treatment, transport facilities, or labor conditions will render profitable a seemingly valueless mine. The engineer must bear in mind these uncertainties, use his best judgment to determine their probable combined effect, and the uncertainties in the basis of clusions should be so expressed in the report as will indicate degree of importance they occupied in the engineer's judgment. Proper margins of safety are essential, but a serious underestimate of value is as great an error as an overestimate; * though it usually involves less conspicuous censure, as close an approach as possible to the properties' true value must be made, * * * without concealing either favorable or unfavorable aspects.

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Sampling is the process of securing a more or less representative part or sample for the purpose of gaining information as to the composition of the whole.

"The process is essentially one of approximation

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"The greatest difficulty in securing an accurate sample is due to the inaccessibility of most of the interior of the mass.

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Owing in part to the more finable nature of the valuable minerals, and particularly to the inevitable inclusion, when mining, of some of the adjacent lowgrade or barren material the yield per ton of a carefully sampled deposit is generally lower than the calculated average, and the tonnage higher. An allowance (say, 10 per cent) should therefore be made for this in reporting values.

"In general deposits not definitely limited are likely to contain at least 25 to 100 per cent more ore than can be actually assured.

"In estimating total costs, ample allowance must be made for general overhead charges, selling, and sampling costs, freight to market, and contingencies, the last usually being put at 10 per cent (sec. 21; sec. 28; art. 36; sec. 32).

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Fluctuations in market price of all other mineral products (except gold) form one of the most uncertain elements of mine valuation. In case of the metals or coals having a standard market, it is questionable whether an engineer should recommend purchase of a property which he estimates is incapable of making a small profit, when mining its choicest reserves and selling its product at the minimum price of, say, 25 years past. The value of a property which would fail to make an attractive profit under normal operation, at the average price for a like period, is even more doubtful."

Price table (pp. 1543–1544) gives highest and lowest prices with quantities sold, and the average 25-year price and quantity sold for all common metals and nonmetals.

Scale of operation limited by minimum rate of profitable working on the one hand; and by assured and probable ultimate mineral resources, available capital, available market, etc. "The profit per unit multiplied by the proposed annual production (on the usual basis of 300 days' actual operation) gives the estimated annual profit."

66 * * * there should be assured mineral reserve at least sufficient to produce profits that will more than return the capital required to put the property into successful operation."

The cost of securing capital under favorable conditions "often does not exceed 10 per cent and may not be more than 5 per cent."

66 * * * the engineer must make allowance for amortization in drawing conclusions as to the value of the property. Amortization of capital is its return, with interest at or before the time of exhaustion property."

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Table of Hoskold formula rates with 4 per cent sinking fund interest is given for 5 to 10 per cent risk rates, and 6 to 30 per cent dividend rates (p. 1546).

"In the absence of assured mineral reserves, the whole question of value is one of inference, and amortization tables have little application."

(Whereupon, at 12.55 o'clock p. m., the committee adjourned until to-morrow, Wednesday, January 21, 1925, at 10.30 o'clock a. m.)

INVESTIGATION OF THE BUREAU OF INTERNAL REVENUE

WEDNESDAY, JANUARY 21, 1925

UNITED STATES SENATE,

SELECT COMMITTEE TO INVESTIGATE THE

BUREAU OF INTERNAL REVENUE,

Washington, D. C. ·

The committee met at 10:30 o'clock a. m., pursuant to adjournment of yesterday.

Present: Senator Couzens (presiding).

Present also: L. C. Manson, Esq., of counsel for the committee; Mr. L. H. Parker, chief engineer for the committee; Mr. Raleigh C. Thomas, investigating engineer for the committee; and Mr. James M. Robbins, assistant engineer for the committee.

Present on behalf of the Bureau of Internal Revenue: Mr. C. R. Nash, Assistant to the Commissioner of Internal Revenue; Mr. Nelson T. Hartson, Solicitor Bureau of Internal Revenue; Mr. James M. Williamson, office of solicitor Bureau of Internal Revenue; Mr. S. M. Greenidge, head, engineering division, Bureau of Internal Revenue; and Mr. John A. Grimes, chief, metals valuation section, Bureau of Internal Revenue.

The CHAIRMAN. Mr. Hartson, you had something more to present to-day?

Mr. HARTSON. No; Mr. Manson announced yesterday that he wanted to question Mr. Grimes.

The CHAIRMAN. Oh, yes.

Mr. MANSON. Before questioning Mr. Grimes I wish to make a short statement.

Mr. Grimes's statement is a general explanation and defense of the analytic system of appraisal. It is confined almost entirely to the application of that system to the appraisal of mines. It is perhaps unnecessary, but well for me to say, that so far we have considered no cases in which this method of appraisal has been applied to mines. When we reach that point, as we will when we take up the matter of the revaluation of copper mines, I expect to discuss this method of appraisal more at length.

I do desire to say at this time, however, that the instances in which its use has been condemned by the committee counsel, as well as by Senator Jones, who was quoted to some extent in the statement of Mr. Grimes, are all cases where this system of appraisal has been applied to nonmetal resources, where the element of profit constituted a large part of the selling price, and in which cases it was possible to show the market value by either the sale of the property itself or by sales of similar properties.

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