A critical examination of mineral valuation methods in current use - Hoskold and Morkill.pdf

7/27/2019 A critical examination of mineral valuation methods in current use - Hoskold and Morkill.pdf

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-4 summ ary of th e more populur mineral valu ation techniq ues bein gused b y the mining industry, wi th examples of their variousinterrelationships Some of the older methods may be in error wh encom par ed to mo dern me tho ds of finuncial analysis .

A Critical Examination of MineralValuation Methods in Current Use

John J. Dran, Jr.andHenry N. McCarlSchool of BusinessUniversity of Alabama

The academic community and the larger andmore sophisticated mining companies have largelyrejected the older mineral valuation methods suchas the Hoskold and Morkill concepts and replacedthem with "discounted cash flow" ( D C F ) tech-niques. The relevancy and usefulness of the oldermethods have been questioned primarily on thebasis of their underlying assumptions that miningcompanies do not have numerous alternative in-vestments and must use sinking funds deposited atmark et or "safe" rates of retur n to recover th e pur-chase price of mineral reserves. The ability to re-invest in numerous (often nonmining) alternativebusiness ventures, the changing purchasing powerof the dollar, corporate income and other taxes,depreciation and depletion allowances, and mod-ern financial management practice all militateagainst the continued use of the older valuationmethods, especially for the larger mining compa-nies. Small mining companies and individuals stilluse these meth ods largely out of hab it a nd famil-iarity.The Hoskold M ineral Reserve Valuation MethodThe Hoskold method was developed prior to theevolution of modern accounting practices and be-fore the days of the corporate income tax. At thetim e of its dev elop me nt, annu al earnings of th e firmwere represented by the difference between cashrevenues and cash expenses and were not subjectto taxation by the government. Thus, earnings atthat time were equivalent to what is today knownas cash flow.

In the Hoskold method, estimated future annualearnings (i.e., cash flows) are divided into twoparts for the determination of the present value ofthe mineral reserve. These parts are ( 1 ) an annualsinking fund designed to recover t he purchase price(discovery cost) of the reserve at the tim e of itsdepletion, and ( 2 ) the remaining cash availableannually to t he investor. Mathematically:

where A is the annual earnings or cash flows to theinvestor, S is the annual sinking fund necessary torecover th e purchase p rice of th e mine ral reserve,and R is the remaining net cash flows to the in-vestor.The amount that the investor must set aside an-nually to recover his purchase price is a function ofthe rate oE interest that the sinking fund will return.The Hoskold method assumes that this fund is in-vested in a "non-speculative" manner at a "safe"rate of return, 7 . This could mean short term U.S.government securities or any investment with anassured "risk-free" interest rate.It is possible to determine the annual amountnecessary to recover the purchase price in n yearsby the equation:S - s - = P

nl r ( 2 )where s - is the amount to which an annuity of $1

nlrwill accumulate at the end of n years at a rate ofinterest r ( r e a d s angle n a t r ) , and P is the pur-chase price of t he property to b e recovered at th een d of n years.MINING ENGINEERS MINING ENGINEERING 71


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It may be shown mathematically that:

By assuming that the present value of the property(V , ) not only represents t he maximum amount thatthe investor would be willing to pay but also thathe does, in fact, pay this a mou nt, then

and by substitution of Eq. 3 and 4 into Eq. 2 theannual amount of the sinking fund is determinedas :T 7

If the sinking fund is used for reinvestment inanother mineral reserve when the given mineralproperty is depleted then the remaining net cashflows ( R ) available to the investor become a per-petual annuity. Because mining is a speculativeventure the investor requires a "speculative" rateof return, r', on his investment. The equation forth e present value of a n annuity of R dollars at aninte res t rat e, r', is:

where a Z r , s the present value of an annuity of $1for n yeais a t the rat e of interes t r' (als o known asthe Inwood coefficient), which as n goes to per-petuity becomes :

Rvp=-r' ( 7 )Thus the required annual net cash flows necessaryto obtain a rate r' are determined to be:

R = V, . r'. ( 8 )Substituting Eq . 5 and 8 into Eq. 1 and solving forth e present value of t he mine ral reserve we findthat:

which is the familiar Hoskold equation based uponuniform annual income.The Morkill Method of ValuationAnother traditional method for valuation ofmineral reserves is the Morkill technique.' Thismethod has been found particularly applicable indetermining the value of the reserves to the landowner on the basis of estim ated royalty paym entsto be received by him n2

The Morkill method, like the Hoskold method, isbased upon a division of the estimated annua l earn-ings into sinking fund contributions and net cashflows to the investor. However, although the netcash flows to the investor are valued on the basisof a "speculative" interest rate r', the sinking fundpayments are non-interest earning contributions.In addition, the annual sinking fund contributionsin the Morkill approach are not fixed over timebut instead begin at an amount equal to A - Vpr'and increase over the life of the reserve at a rateequal to the speculative interest rate. Since theestimated annual earnings remain constant, eachincrease in the sinking fund must be accomplishedby a reduction of an equal dollar amount in theannua l net ca sh flows to the investor.Because the sinking fund contributions are grow-ing at a rate r', the fund will increase in size in thesame manner as if t he a i~ nu al ontributions wereconstant and the fund was earning an interest rateof r'. Thus at the end of n pears the sinking fundwill total:

Assuming ( 1 ) that th e sinking fund will be usedto recover th e purchase price of th e property at th e11

time of depletion of the reserve (i.e., 2 S = P ) ,i= land ( 2 ) that the investor purchases the reserve atits present v alue ( i.e., P = Vp ), then:

Solving Eq . 11 fo r V, gives us:

which is the standard Morkill formulation.Th e combination of a sinking fund which ear nsno interest yet grows a t a rate e qual to the specula-tive rate of return, w ith a ne t cash flow to the in-vestor which decreases by the amount of increasein the sinking fund contributions and is valued atthe speculative rate of return, obscures the underly-ing foundations of the Morkill formulation. Eq. 1 2may be better understood by dividing both thenumerator and denominator of the right side bythe quanti ty (1+ r')-". This gives us:The bracketed term in Eq. 13 is nothing more tha nthe mathema tical formulation for the present value

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of an annuity of $1 for n years at an interest ratef which may be expressed as a,,r, (and is alsoknown as the Inwood coefficient). ~ h u she Morkillformula reduces to:

the present value of an annuity of A dollars for nyears at an interest rate r'.The "True" Difference Between theHoskold and M orkill Equations

It is appropriate for us to examine the Hoskoldand Morkill methods in order to point out the"true" differences (as opposed to any superficialdifferences) between these approaches. In com-paring Eq. 9 and 12 the most obvious difference isthe lack of a "safe" rate in the Morkill formulation.

In the mining industry of the 19th and early 20thcentury the small mine or single-mine companywas dominant, and attitudes toward continual rein-vestment were quite different from those held bythe major mining and mineral companies of today.Most businessmen would agree that in this con-text, the assumption of two rates of return is quiteunrealistic for firms in today's economy. In generalcash flows which do not provide direct returns toinvestors are reinvested, not in a bank or other"safe" investment, but instead are put back intothe business and thus should be accorded the"speculative" rate r'. When this adjustment is madeto the Hoskold method, Eq. 9 becomes:

Multiplying both the numerator and denominatorof the right side of Eq. 15 by the term [ (1+ r')"- 11 gives:which reduces to:

Eq. 17 may be immediately recognized as theMorkill equation, thus indicating that the onlyreal difference between the Hoskold and Morkillformulations is the Hoskold assumption of a "safe"rate of return.

After accounting for the difference of the as-sumption of a safe rate, it is apparent that bothmethods simply discount the annual earnings overthe life of the mineral reserve. It may be notedagain that at the time of the formulation of thesemethods, in the days prior to corporate taxation,depreciation and depletion allowances, annual earn-ings represented cash flows to the investor. Afterthe proper adjustments to compensate for the

changes that have occurred in taxation and ac-counting practices since the time of their formula-tion, both methods may be reduced to:

where C is annual cash flow (assumed constantover the life of the mineral reserve).

Thus both methods represent discounted cashflow techniques with slightly different underlyingassumptions. Due to th,e changes in our accountingand taxation systems these assumptions have be-come obsolete. This has rendered the Hoskold andMorkill formulas, without compensating adjust-ments, inappropriate for current investment anal-ysis.The Discounted Cash Flow Technique ofColby and Brooks

Colby and Brooks (CB) have presented amethod for valuing mineral resources which theyspecify as a discounted cash flow me t h ~ d . ~n theirpaper, they give considerable attention to definingcash flows within the scope of current accountingand taxation procedures. Based on the assumptionsthat annual cash flows are constant over the lifeof the project, and that all capital improvementoccurs at the time of valuation of the reserve, theCB equation for the present value of a mineralreserve may be written as:

where K is the capital improvements occurring atthe time of valuation, and r' is the risk adjusteddiscount rate.

The equation simply states that the present valueof a mineral reserve is equal to the present valueof the cash flows which the reserve will generateover its life less any initial capital costs necessaryto exploit the reserve.

The discounted cash flow approach as used byCB is an accepted method of asset valuation andas such requires no further comments. Other as-pects of their paper as well as certain interpreta-tions of the CB approach found in recent literaturedeserve comment.

Focusing on the CB paper, it is important topoint out an unnecessary assumption stated by CBwhich may serve to restrict the application of theirmethod. They assume that funds for the exploita-tion of the mineral reserve are provided entirelyby equity financing4 This assumption appears tolimit the discounted cash flow technique to thosefirms which are not financially leveraged. Such anassumption is unnecessary. Manufacturing firmswith debt in their capital structure have for yearsused the discounted cash flow method for the valu-ation of industrial investment opportunities. Thereis no reason why financially leveraged mining firmscannot utilize the same method. The discounted

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cash flow equation remains the same whether usedby a firm financed entirely by equity capital (allequity) or by a firm with debt in its capital struc-ture. The only difference in the use of this equationbetween firms that are financially lever~gedandthose which are not is in the determination of therate at which cash flows are discounted to thepresent.

For the all-equity firm, the discount rate is simplythe required rate of return on equit) c'ipital. 111financial terminology this is known as the cost ofequity capital and is equivalent to what is know11as the speculative or risk rate in the literature re-garding mineral reserve valuation. On the otherhand, for the financially leveraged firm, the rateat which cash flows are to be discounted to thepresent is determined on the basis of a weightedcost of equity capital and debt capital. The pro-cedure for this determination of the weighted costof capital will not be discussed here. However,many references regarding this calculation may befound in the literature pertaining to corporationfinance and capital budgeting5

It has been stated that the CB nlethod "does notattempt to determine the 'in-place' value of themineral deposit as much as it does to determinetotal efficiency and value of an actual or hypo-thetical ~peration."~t should be pointed out thatthe value of a mineral reserve is inherently de-pendent upon the efficiency of the operation b!which that reserve is exploited. In other words,if one firm has an operation which is highly effi-cient and which enables it to evploit the reserveat a much lower cost than any other firm, thenthat firm will place a higher value on the reservethan will be placed on the reserve by other firms.Thus, this "limitation" of the Colby and Brooksmethod is not a restriction on the use of theirmethod but rather an economic fact of life.

Another "limitation" that has been attributed tothe CB method is that "when purchasing a possiblereserve, the producer himself, never . . . . . . . . usessuch a method of ~a lu a ti on ." ~f the fact that amethod has never been used before is construed asa limitation on that method and an argumentagainst its use, then any new method is handi-capped because of the simple fact tha t it is new.This criticism of the CB approach is entirely un-founded.

It has also been contended that the CB methodis "more applicable to operating properties thanto giving value to a piece of mineral land."8 In factthe discounted cash flow approach as put forthby Colby and Brooks is applicable to both valua-tion of operating properties and valuation of unex-ploited mineral resources. There exist only hvodifferences between the alternate applications ofthe CB method. When applying the discountedcash flow method to unexploited mineral reserves

it is necessary to (1 ) estimate the time at whichthe reserve will be put into use, and ( 2 ) to estimatethe capital equipment costs that will be requiredat this time. For valuation of operating propertiesthese estimates are unnecessary.

A final comment with respect to interpretationof the CB paper is tha t Colby and Brooks in thedevelopment of their valuation equat ion (Vp =C a,,,, - K) have assumed that all capital im-provkments K occur at the present time. Since useof the equation without recognizing the assump-tion can result in an incorrect valuation, it is sug-gested that whenever the valuation equation isreproduced this assumption be explicitly specified.If the assumption that all capital expenditures oc-cur at the present time does not hold true, a cor-rect valuation may be obtained by interpreting thevariable K in the equation to represent the presentvalue of all capital improvements.The Transportation Advantage DiscountedCash Flow Method

A recent development in the valuation of mineralresources has been termed the transportation ad-vantage DCF m e t h ~ d . ~his approach to discount-ing cash flows developed by Dunn, Hudec, andBrown emphasizes differences in transportationcosts among alternative mineral producing proper-ties. Placing the emphasis of property valuation ontransportation cost can be especially useful in thosesituations where the value of the mineral resourceper unit of volume is especially low. In these cases,transportation costs comprise a relatively high pro-portion of the producer's total costs and thereforedeserve particular attention.

The originators of the transportation advantageapproach assume that unit production costs andprices do not vary among different potential min-eral reserves, and therefore the only relevant factorin deciding which of several resource locations toexploit is the cost of transporting the output fromeach reserve to the market. Based upon this reason-ing the basic transportation advantage equationhas been formulated as : o

VP = Q a,,,.where t is the transportation advantage expressedas the differential cost per unit of output betweentwo alternate sites, and Q is the estimated annualproduction in units of output ( a constant).

The solution of this basic equation results in thecalculation of the difference in present values oftwo alternative reserves rather than the presentvalue of either, as the use of the term V, in theequation implies. Thus, the transportation ad-vantage method determines the relative valuationof two alternative sites rather than an absolutevaluation as determined by other discounted cashflow approaches.

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Strong reservations must be expressed regardingthe use of a relative value approach. First, althoughsuch an approach indicates whether the purchaseof one piece of property, would be favorable whencompared with another piece of property, it doesnot indicate whether purchase of either would beeconomically justifiable. In order to determinewh ethe r th e pur cha se of a ny asset is justifiable it isnecessary to determine an absolute value againstwhich the potential purchase price may be com-pared.Secondly, despite the fact that a relative valueapproach does not indicate economic justification,the transportation advantage method has been mis-interpreted to imply such justification or a lackthereof. For example, it has been stated that when"the transportation advantage of one deposit overanother is approximately zero . . . . it is difficult tojustify paying prices much higher than normal landprices in th e area."" Th e analysis preceding thisstatement in the original article compares two al-ternative deposits but m akes no comparison of thevalue of e ither depos it to are a land prices.Thirdly, not only may relative value analysis bemisinterpreted to imply absolute value analysis, butalso relative and absolute value calculations can beimproperly combined to give meaningless results.This occurs when such combinations result inomission of im portant cash inflows an d/ or outflows.It must be kept in m ind that in the transporta tionadvantage method, cash flows pertaining to pro-duction costs and revenues are assumed to be thesame for alternative mineral reserves and thus areomitted from the relative value calculations. Like-wise transportation costs common to alternate sitesare netted out in the calculation of the transporta -tion advantage. These cash flows must be addedback when absolute values are desired. In twoadaptations of t he transportation model purpo rtingto show absolute values, these essential cash flowshave be en om itted.12In addition to the general difficulties associatedwith the relative value approach as stated above,there are two additional specific criticisms of thefinal form of th e transportation advanta ge model.13First, the model includes the annual interest pay-ment made as part of the annual cash flows. Thepurpose of a present value analysis is to determineif the annual cash flows from the investment itselfjustify the use of funds which are not free but forwhich some rate of return is required. Since therequired rate of re turn is included in th e discount-ing procedures it is therefore inappropriate to in-clude them again as part of the cash flows. Thiswou ld be "double counting."14The second objection relates to the use of theland pr ice as one of th e cash flows in th e transporta-tion advantage model. The objective of a presentvalue equation is to determine the maximum price

that you would be willing to pay for the land . Th einclusion of the land price as a cash flow on theright side of the transportation advantage equa-tion simply inflates the present value by thatamount. Thus, the equation indicates that thehigher th e land price, the higher th e present valueand the higher the maximum price a potential pur-chaser would be justified in paying. This is in-correct. Th e price of th e land should be excludedas a cash flow in the transportation advantageequation.Conclusions1) In both theory and practice, a discountedcash flow approach to mineral reserve valuationshould be used.2 ) Th e development an d application of presentvalue equations for mineral reserve valuation mustbe based upon economic and financial theory. Val-uation of mineral reserves like valuation of anyasset is more than simply plugging numbers intoan equation. There are many pitfalls for the un-wary.3 ) It is important that land valuation be carriedout on an absolute basis rather than attempted ona relative basis. If the final objective is to deter-mine th e relative values of tw o potential sites thiscan always be accomplished by comparing absolutevalues.4 ) There should be no objection to focusing at-tention on transportation costs where these areimportant cash flows. However, transportation cashflows should not be emphasized to the exclusion ofother cash flows. All relevant cash flows must betaken into accoun t in valuing m ineral reserves.References1Parks, R. D.. Examination and Valuation of Mineral Property,4th ed., Addison-Wesley Publishing Co., Reading, Mass., 1957;pp. 350-53 or Raymond, C. L., "Valuation of Mineral Prop erty,Economics of the Mineral Industries, E. H. Robie, ed., AIME,New York, 1964, p. 133.ZDunn, J. R.. Hudsec. P. P., and Brown S. P., "How ValuableAr e Mineral Resources." Rock Products, S'ep. 1970, p. 85.3 C o l b ~ . . S., and Brooks, D. B., "Mineral Resource Valuationfor Public Policy," Information Circular 8422, 1969, U.S. Bureauof Mines.1 Colby and Brooks, 1969, p. 16.Weston, J. F., and Brigham, E., Essentials of Managerial Fi-nance, 2nd ed., Holt, Rinehart an d Winston, New York , 1971, pp .243-fi8.-.-% D u n , t a l. , a nd Dunn. J. R., "Valuation of High Bulk-LowValue Mineral Depos its" P aper presented a t 1972 SME FallMeet ing, Birmingham. ~ i a . , . 1.7 Ibid., p. 86 and p. 8, respectively.8 Dunn. 1972. D.8.~ u n n ; u d e i . nd Brown. 1910 and Dunn, 1912.10 Dunn, 1972, p. 12.l1 Dunn, 1972, D. 12.la The adaptations are found in Dunn, Hudec, and Brown (1970),P. 86 and Dunn (19721 , P. 16. The more recent version of t hemodel by Dunn (correcting a typographical err or) may be writtenas : Vp = (A-T-Ir) An r v + IP-R) + HVnwhere V, is present value of th e reserve, A is transportation a d-vantage times annua l production (expressed as tQ in Eq. 20), Ir 'is annual interest on present land price at risk rate r', T is an-nual property taxes. P is present land price, R is present valueof the rehabilitation cost, H is estimated land resale value, andVn = (1 + r')-= = present worth of a single paym ent factor.In this equation the relative cash flow term, A, is combinedwith absolute cash flow terms (for example, T) in an attemptto assign an absolute value (V,) o the reserve. This combinationomits all cash flows of production and revenue as well as trans-portation cash flows which are common to the alternative sitesbeing examined."The model in equation form is shown in Ref. 12 ."Bierman Harold Jr. a nd Smidt Seymour The CapitalBudgeting kci is ion. &d ed.. ~ a c ~ i l l a n , ' N e wo r k : 971. pp. 114-115.

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A critical examination of mineral valuation methods in current use - Hoskold and Morkill.pdf