Profitability Sensitivity Analysis of a Mining Venture

By CHARLES A. BEASLEY ' and E. P. PFLElDERt

SYNOPSIS

A case study of one ore deposit shows that unit operatiTIJ:l and overhead costs, capital structure, capital requirements, and product price levels are the four most important determinantg or venture profitabillty. Productive capacity, loan interest rates and payback period, depletion magnitude and CJCp/oration cost! are determinants with moderate effect o n profitabi lity. Surpris ingly, federal and slale income tax rates and moratoriums and depreciation methods have only sli$ht effect on the rate of return, partly because of the low profitability of Ihe prospect.

Thu ranking ofvenl ll re profitabiiitydctcrnlinants confirms the authors' previous conclusions that the critical cost areas are those most subject to operational and design ejfectiven~5 and managerial contro]. Those areas of cost controlled by larger political and economic fo«es Rre of less sigaificlUlt:e than is normally believed.

rNTRODUCTlON

The object of this paper is to demonstrate through examples the effect on venture profitability of variatioDs in the major cost and design parameters involved in the evaluation of a mineral prospect. In the examples discussed the reasons why these parameters affect profitability, rather than the exact magnitude of change attributable to them, are of prime concern. Details are also provided of the method of mineral deposit evaluation used in the geneml resource to reserve conversion system discussed by Beasley el al (1%9).

A case study of an actual mineral prospect is used to demonstrate the cost and design parameter relationships. The authenticity of the data and the deposit characteristics permit (1) ranking of the cost and design parameters by the magnitude of their ciTeet on venture profitability, and (2) identification of those areas where refinement of technical and financial planning. or cost reduction, would be most beneficial (0 deposit exploitation.

A secondary purpose of the analysis is \0 demonstrate the feasibility of applying computerized evaluation techniques early in an exploration program. Sueh analyses are not inconsistent with the availability of only limited exploration data, aod can indicate throllghout the exploration stage any obviating areas of cost or value. and cost a reas most worthy of further refinement.

CASE STUDY DEPOSIT

A low-grade copper-nickel prospect located in a remote region of the United States was chosen for analysis, The exploration target was the contact zone of a gabbroic stock intruded into amphibole and biotite schists, wi th pyrrhotite, pentlandite and chalcopyrite mineralization in disseminations. veinlels and lenticular masses.

Since the geological nature of the deposit required an under­ground, non-selective, high-volume mining method, sublevel caving was selected as the preliminary exploitation technique. A sfnndnrdTIotation process was deemed capable o(producing a bulk copper-nickel concontrate from the mined ore.

COST FUNCTIONS

Tho operating cost functions for extraction of the ore were assumed to be composed of determinable labor, material and power components. Mill operating costs were derived as a function of mill capacity (Verner, et at (1966). These functions were modified to reflect unique geographic characteristics and inflationary trends.

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Mine capital cost was calculated by the assignment of probable purchase prices to the requisite equipment units determined by the design program, Mill capital costs were assumed to be a function of mill capacity (Miehaclson (1962». Overhead costs were assumed to be a percentage of the direct operating costs of the milling and minins operations, and of the fixed costs for supervision and engineeril\g.

COST ANALYSIS

The analytica1 concept involved computerized expression of the annnal production, revenue and cost data in the form of a cash flow table for each year of the entire investment interval.

The rate of return on equity and total investment, and the present value profiles for various discount rates, were calculated. The return on equity represents the yield on the funds invested in the venture. The return on totat investment COJ1Siders those proceeds paid out to all particip.ants in venture 6nancing.

The incorporation of the mine design and cost analysis calculations into a single computer progrnm made possible the successive calculations required for profitability-sensitivity analysis, and a ranking of cost parametel's in relation to their effect on profitability,

OPTfMUM PLANT CAPACITY

An initial cost aod profitability analysis for the 'standard' operation as designed initially was a necessary first step toward the ultimately desired profitabili ty-sensitivity analysis. The 'standard' operation was expanded, subject to various considerations governing plant size in order to determine the 'optimum' production capacity that (a) involved realistic investment levels, (b) avoided the too-distant discounting of proceeds, and (c) reduced the impact of loog-term economic aod technological uncertainty. This 'optimum' capacity was then used to calculate standard values for the other design functions.

PROFIT ABILITY - SENSITIVITY ANALYSIS

Sixteen m;ijor cost variables, classified either as industry, economic or regulatory profit s timulants, were ~ected for mutually exclusive variation. Table I shows the designed value, variation range and resultant differential return on equity for

• Associate Professor of Mining Engineerina:. Virginia Polytechnic Institute,

t Professor, Mineral Engineering, University or Minnesota.

each of these variables. Al1hougb several variation ranges for each stimulant were used in the analysis, the range shown is considered the most rea list ic. Surprisingly. the several ranges had little effect on the ranking of the variables.

The sensitivity analysis showed the industry group to have the greatest profitability effect, followed by the economic and regulatory groups. The ranking of individual cost parameters shows only slight deviations from tbe general order. Some of the most sensitive variables, and those having less obvious effects, are discussed below.

INDUSTRY STIMUL ANT GROUP

Unit operating and overhead costs

Changes in tbe unit operating and overhead costs are shown in Fig. 1 to have a most significant impact on profitability This is attributable to their effect on the depletion and net income after tax components of net proceeds, relative to fixed investment sums. Decreased costs result in a higher net income, an increased net depletion a llowance, and higher taxes. The additional tax charge. however, is only a fraction of Ihe total increase ia oel income, and is parHy offset by iacreased net depletion allowance.

The equity and total profitability curves intersect at the cost level for which the venture rate of return equals the loan interest ra te. At lower cost levels the return Oil equity exceeds the return on 10la1 investment due 10 favorable ratios of venture return to loan capital cost. This situation reverses itself a t higher cost levels because of the effect of negative leverage.

CAPITAL STRUCTURB

Figure 2 shows that with inereased loan (Dading venture profitability increases, due to the favourable difference between the rate of return on investment and the loan interest

rate, and to the deductibility ofintereSl expense. The increased initial funding requi red by increased leverage, due to the payment of annual interest expense during the development s lage, is offset by carryover or the resultant net loss in the early production stages. Relurn on equity rises rapidly due to the progressively smaUer equity base.

25.----,~---,-----,-----,

20 on Equi ty wi th 50% loan (@

/ ,-/. Inl.

-u ~ 15 z ·

'" :::> r

on Totol /

W

'" 10 LL 0 in~O!'stm~nt.

W t-<t 5 '"

01 2 3 4 5 OPERATING AND OVERHEAD COST,dol1arsAon

Fig. J

TABLE I

RANKtNO OF PRO.FlTASIUTY EFFEcr8 OF mMOll VARIATION

no.ign Variation Differential Profitability Stimuli value B"" return on equity rankilli

%

Industry stimulant group Uuit operating and overhead costs, S/ton 2.75 2.QO-.3.50 '.2 1 Equity~loan st ructure, % . . . . . . . . 50-50E 75-25E 8.6 2' Capital cost requirerttcnls, % of design coat 100 80-120 6.5 3' Loan intere.'lt rate, 1 .,........ 7 3-9 2.5 6 Loan payback perio ,years . . . . . . . . ,. 10-20 1.3 7 Btplora tion costs. SJyear, initial 3-year period · 500000 0-1.5 X 10' 1.1 S

Economic stimulant group Commodity price level, S/lb Cu 0.50 0.45-0.55 6.2 4

S/lb Ni 1.10 I.QO-.1.20 Productive capacity, tonS/day . 20000 15-25 x 10' 3.' 5

Regulotory stlmulanl group .Jnintdc:pJetio.n. .% of net . . . · 50 40-60 1.3 7

% of gro&s . nO! 17-18 23 Ni 18-28

Depletion, % of net ... 50 40-60 1.3 7 Federal income ta}\: rate, % . 48 45-55 0.' S Federal lax moratorium, years 0 0-3 0.' S Depreciation methods . . . .. · DD DD-SYD-SL 0.5 9 State iocome tal!; rate, % or Fede:ral tax 18 12-24 0.3 1. .Depletion, X of gr053 15CU J2-18 0.1 11

23 Ni 18--28 State tax moratorium, )'Can! 0 0-3 0.1 11

. Denotes possibly interchlUllleabJe r.mlc

110

LOAN, PERCENT OF TOTAL CAPITAL o 25 50 75 100

25r-----~----~T_----_T--r_~

- 20 u ~

z "' ~ ~ Il! "-0

"' " "'

\EqUity

15

10 Total investment

iO~0~----~75~-----~t,----~2C5----~O EQUITY PERCENT OF TOTAL CAPITAL

Fig. 2. Ejft!ct of capitaistructure on profitability,

Present value discount rate alld cost oj equity capital

The present-value method of evaluation discounts venture proceeds and expenditures to a common point in time at a discount rate that reflects the investor's value of money. The resultant present value may either be deemed the allowable purchase price of the venture (at a discount rate reflecting the desired return on investment), or a measure of project feasibility relative to other investment opportunities (at arbitrarily selected discount rates).

Figure 3 shows the present value profile for variously assumed discount rates and financial structures, It shows, for example, that the present value of the deposit, utilizing fifty per cent equity financing and a twelve per cent discount rate, is 5.9 million dollars, Alternatively, the zero present value intercept of the profile indicates a rate of return on equity of 13.1:! per cent.

Capital costs

Variation of venture capital requirements (Fig. 4) produces profitability changes so great that even normally acceptable levels of precision could produce errors fatal to the venture, Increased capital requirements result in lower rates of return on both equity and total investment due to increases in both capital sources relative to substantially fixed operating proceeds. Although increased depreciation and interest charges result in lower net income and in decrewoed tax charges, the decrease in taxes is not proportional to the absolute increase in capital cost.

TIle steeper slope of the return on equity curve is due to the damping effect of the larger total investment amount relative to the magnitude of the differential cash flows. The total and equity curves intersect at the point where venture profitability and loan costs are equal.

Loall interest rate

Figure 5 shows the cost of loan capital to have a surprisingly moderate impact on venture profitability. The decrease in the return on equity at higher interest rates is due to increased interest payments that decrease the net proceeds payable to the owners at a given equity-loan ratio. The rate of decrease is determined by the increase in the interest rate as modified by the deductibility of interest payments. In those instances in which net depletion governs, an increase in the nominal interest rate reduces net income before depletion and therefore

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the depletion allowance. This effect is modified in the early years by the tax loss carry-forward that increases with the interest rate. The increase in total profitability is due largely to the add-back of interest as a proceed to the creditor,

Loan payback period

Increased loan life permits smaller annual 'principal plus interest' charges. It results in a larger net income before depletion and an increase in the depletion allowance for the years in which the net income constraint governs. These increases in profitability are modified by the discounting of additional repayment amounts, and by the add-back of loan principal and interest in the return on total investment calculation.

~

0 -x

'" ~ " 0

-0

W ::J -' :if t-z w (f) W et: LL

110

100

90

80

70

60

50

40

30

20

10

0

10

20

30

40 0

100'" equity

-",._.--

5,1 pet

4 8 12 16 DISCOUNT RATE, pet

20

Fig. 3. Effect of capital structure on present value.

25

-u 20 Q.

Z

'" => 15 ~ ,.Equit y UJ et:

"- 10 0 / UJ rotal ~ investment

" 5 et:

~LO---8~0~~IOO~~12~0---IL40~-1~6~0--~180 PERCENT OF STANDARD CAPITAL COST

Pig. 4. Efftc:l 0/ capital cost on profitability

-~20 I I

Z' fa) 50 -to lOCln CC ::0 >-W

/ EQUiIY -CC 15 LL 0

W Totol inve5tment~ 0- lD <{ CC 3 5 7

INTEREST RATE, pct Fig_ 5. Eff.ct o/Ioan mItral rail! 011 prc/ilQ/}ilily.

Annual exploration cost level

The effect on profitability of variation of BMual exploration eXpenditures duriog the latter portion of the exploration phase is pertinent because of the need for increased knowledge of the nature of the deposit, and the closeoess of these expen­ditures 10 p~nt time. Venture profitability decreases sJightly with increased annual exploration costs, due to higher deferred exploration charges and a lower net income. The rate of decrease for equity is greater since exploration costs are arbitrarily satisfied first out of equity funds . This increases the present value of equity requirements relative to the present value of total capital requirements due to the former's occurrence at an earlier point in time.

The legal constraint p laced on the magnitude of exploration expenditures recoverable on a pro rata basis is insignificant in the present case, since total recovery of exploration .exp.enditur.es..res.ult.s in identical_profitabili\y.

BCO NOMIC STIMULANT GROUP

Product price levels

Although initia l comparison of Pig. 6 with Pig. J suggests that a decrease in product price levels produces results similar to an increase in unit operating costs, the two are oot equivalent. A price fluctuation changes both the operating revenue and net income and therefore the basis of calculation of both gross and net depletion. An operating cost fluctuation

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similarly changes net income, but it affects the basis of calculation for depletion only as a percentage of net income.

Changes in the return on equity are more pronounced than changes in the relum on total investment because of the greater ratio of incremental proceeds to investment magnitude. TIle equity and lolal investment curves intersect at the price level for which the venture rales of return equal the loan interest rate, just as they did for variation of operating and overhead costs.

COPPER PRICE,dollars lib

0,~. 4~0 __ ,-~Or·5~0 __ r-~0·r60~-.~0~.70 25'

-20 u Q.

z· Equity

\ et: 15 => ~

w n: 10 ro tol investment lL 0 w 5 ~

'" et:

°aga 1.10 1.30 1.50 NICKEL, dollars lib

Flg. 6. eJftCI of wmmodity prlus all profitability.

Production capacity

Figure 7 shows- ,·the substantial profitability effects of variation of the production capacity from 10 000 to 30 000 tons per day. Although higher rates of return are obtainable at higher production levels, the 20 OOO-ton rate was sdected as the 'standard' on the basis of desired venture life and-because or futurity considecations.

_ 2o,----,-----,----,----, u Q. ~.

Z UJ

~ 15 if] > Z

z 10 o Z et: ::> r

\ Tot o! investment

W et: 51~0 -----+.15~-----,2~0-----2~5~--~30

PRODUCT ION LEVEL t onslday X rn' FW. 7. qccr o!production capaclly on profitability.

REGULATORY STIM ULANT GROUP

Depletion rate

Individual and joint variation of gross and net depletion rates was necessary because of the interrelated effects of these provisions.

Variation of the gross depletion rates for copper and nickel have little or no effect on total deposit profitability for this particular deposit, sincc the net income provision serves as the ultimately limiting value in every year of operating life. Fordcposits with high earnings ~pabjlities, the gross depletion rate would have a pronounced effect. Net cofll rol eJl: ists due to accelerated depreciation charges during the initial Ye"drs, and lower revenue values from exploitation of lesser grade material in later years. T he independent variation of net depletion has slightly more effect than for gross depiction, although con­straint by the gross rate !lcts to limit any significant effect.

Joint variation of the net and gross depletion rates (Fig. 8) results in substantial changes in profilability. It demonstrates that the higher gross depletion allowances for 'strategic' minerals are of limited significance for properties of low to medium earnings potential, and reinforces the conclusion that a change in one depletion provision has limited sig­nificance without a corresponding change in the other.

NICKEL DEPLETION RATE, PERCENT OF GROSS

13 18 23 28 33 38 1;3 2 0 I I I I I •

:s. ~15 ::> -w

'" g, 10

w -;:! 5

I-jqU[ ! ~

-

" Tolo l -w.vul _l

I I I I 3D GO 50 60 70 BD 90

[€PlETlON RATE,PERC ENT OF NET INCOME

I I I 9 12 IS 18 21 24 27

COPPER DEPLH JON RATE, PERCENT OFGROS5

Pig. 8. Effect 0/ joint variance 0/ gross al/d net depletion rates on profitability.

Federal ond srate income tax rales

Figure 9 shows variation of the Fedcra.lalld State income lax ratts to have appreciably less impact on profitability than might be expected, It illustrates a point not widely understood within the minerals industry - that the add-back effect of non-cash expenditures (as depreciation, depletion, deferred exploration and develop.ment), even at extreme rates of taxation, may still enable a venture to yield a substantia] present value and retw"n on investment. The relative aUrae­liveness o f this fealUre is contingent upon the investor's philosophy concerning the utilization of add-back funds, his goals concerning the permanency of corporate operating life, and the stability of depletion and depreciation rates.

Federal and state income tax moratoriums

The consequence of tax moratoriums is to decrease tax expense and increase net income in Ihose vcnture years closest to present time, thereby decreasing venture rjsk: through. a more rapid recovery of expended funds. The greater magnitude of forgivable tax charges, relative to the proceeds that accrue to t he owner and to the total participants, accounts for the steeper slope of the profitability profile for equity than for total investment (Fig. 10).

113

State tax moratoriums are less significant than Federa.1 moratoriums simply because of the lower absolute value of the amounts, although similar tax and net income effects are involved. This shows the State to have le~ power than the Federal government to influence vcnture Altractiveness.

20

o ~

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;:! 5

o

, K~-'_ - - Fe-dHg [ Ig~

- _ _ SIgIl Ig,

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nT otot invutrn ..... t

-- - - -

I 35 50 55

FEOERAL TAX, pc t I I

6 12 18 ~ 30 STATE TAX, PERC ENT OF FEDERAL TAX

Fig. 9. Effect of Federal and State income tax rates on profitability.

20

z

'" 15 => r ~ W

'" Le 0 10 I-w -.. '"

, I

/ Equit y

---- - -

- -- - - -':rDla! KEY investment

--Ffdefo [ incomelQx - - -- State ,ncome

I _l I 2 3

YEARS OF

to.

, 4 5 6 EXEMPTION

-

7

Fir· 10. Effect of Stale or Federal tax moratoriUtfl.S on profitability.

Depreciation method

Table IT shows the limited advantage of an early write-oft' of depreciation charges. Both double-declining balance and the sum-of-the-digits methods result in higher initial depreciation charges and consequently lower taxes during the first years o f venture life. Moreover, the favorable add-back characler­istic of deprecia lion charges is enhanced by their occurrence in the years closest to the time of evaluation. Although the straight-line method yields a lower race of retum due to lower charges in the first years, the shortness of life decreases the expected advantage. .of early write-offmelhads ..

TABLB 11

BFPI!CT OF DIiPRECIATION MCTUOD ON TOTAL DBPOSIT P ROI'ITAlIIUTY

Double-declining balance Sum-or-years digits Straight line

Rate of return, % Equity Tota1 investment

13.8 10.8 13.9 10.9 13.4 10.6

CONCLUSION

Computerized cost studies and profitability sensitivity analyses permit project cost and design variables to be structured according to their effect on venture profitability throughout the exploration and development stages of a mineral prospect. Such analyses are valuable in determining those variables having the greatest effect on profitability.

ACKNOWLEDGEMENTS

Most of the material presented here was developed under the sponsorship of the V.S. Bureau of Mines, Office of Mineral Supply, and represents a portion of a doctoral thesis study by Beasley (1969). Mr Claus Fryberger, Columbia University, assisted with both the programming and the

114

analysis. Mr Richard Dawes, U.S. Bureau of Mines, reviewed much of the information contained herein.

REFERENCES

BEASLEY, C. A. (1969). The conversion of mineral resources to mineral reserves: General and specific process models and a comparative case-study. Doctoral Dissertation, University of Minnesota. July, 1969.

BEASLEY, C. A., DAWE.'l, R. E. and PFLEIDER, E. P. (1969). Mineral resource to reserve conversion: Decision theory and econometric equilibrium models. AIME Annual Meeting, Council of Economics Proceedings, Denver. February, 1969.

MICHAELSON, S. D. (1962). Capital costs of flotation mills. Froth Flotation, AlME, New York, pp 612,658. 1962.

VERNER, W. J. and SHURTZ, R. F. (1966). Mine evaluation - A fresh model. Mill. Engng. Vol. 18 (Il), pp 65-71. November, 1966.