Economic Feasibility Studies in Mineral and Energy Industries1

48

CHAPTER 5 ECONOMIC FEASIBILITY STUDIES IN MINERAL AND ENERGY INDUSTRIES1 "...The mining industry may well be unique in the ratio of the number of projects seriously examined to the number commenced. Ratios of 20:1 are not uncommon, and 40:1 is not unknown. This puts a premium on efficient investigation and much can be done on two fronts, the general approach to seeking out projects, and the evaluation of projects once found..." (Merrett and Sykes, 1963). The objectives of this chapter are to outline, in general terms: (1) the nature and scope of data necessary for conducting a preliminary feasibility study of projects in the mineral and energy industries; (2) once these pertinent data have been collected or carefully estimated, to guide the selection of the proper analytical technique or techniques that will, objectively, evaluate the economic feasibility of these projects and compare them with alternative investment opportunities; and finally, (3) to introduce the basic concepts of estimating risk and uncertainty and show how to incorporate them into the economic analysis. The discussion here is necessarily generalized -- each specific investment project in the extractive industries is unique and deserves a tailor-made analysis to fit its particular circumstances. Nevertheless, this general presentation still provides a basis with which to start a feasibility study and it allows an insight into an understanding of the essential factors of any economic analysis and the techniques by which evaluation can be carried out. Readers who are interested in a much more detailed presentation of economic feasibility studies can find several references at the end of the book. THE NEED FOR ECONOMIC ANALYSIS A need for an economic analysis may arise for various reasons. In most cases such an evaluation will be made prior to: 1) the actual engineering design of the development of a mineral deposit or an oil field; 2)

the acquisition or sale of a working mine or field;

3)

a planned change in the mining or processing methods that consequently may affect the extraction rate (tons of ore per unit of time), the extraction level (tons of contained minerals per

This chapter is a reprint, with permission, from a two-part publication by the author, titled "Economic Feasibility Studies in Mineral and Energy Industries," MIB; part 1 (Vol. 20, No. 2, May 1977) and part 2 (Vol. 20, No. 3, July 1977), Colorado School of Mines, Golden, Colorado. Some revisions and modifications in the material have been introduced by the author for the specific purposes of this book.

49 unit of time, as a result of change in cut-off grades), or other economic conditions under which the particular mine is operating; 4)

an assessment of value of assets for taxation purposes (mostly property and severance taxes); 5) re-evaluation of priorities in the allocation of investment funds by the firm; and 6) the evaluation for the purposes of bidding for leases. Whatever the reason for conducting an economic feasibility study, with limited financial resources and a specific set of corporate objectives, any firm must select the best investment opportunities from among those available. The economic analysis, therefore, should lead toward an unbiased answer to two questions: 1) does the particular investment project seem to satisfy the stated objectives of the firm? 2) how does this project compare with other possible projects? The stated objectives of the mining or energy firm considerably influence the selection of capital investment projects. Maximization of total profits (or loss-minimization for the short-run period) is probably management's principal goal for many firms. In other cases, however, the goal may be expansion in production capacity, an increase in the firm's market share or in the value of its 2 assets, diversification of activities, vertical and horizontal integration, or 3 continuous survival of the firm. Each of these objectives will have an important role in corporate planning and consequently in the economic evaluation of alternative projects. Listing of all available projects according to priority (rank-ordering) ensures that a specific investment is justified and conforms with the firm's objectives. It also provides guidelines for the allocation of limited investment funds. Even if there were only a single investment opportunity under review, it must favorably compare, for optimal allocation of funds, with other profitgenerating activities. This concept of opportunity cost -- the advantage foregone due to alternative use of investment funds -- must be considered as an integral part of all economic analyses.

Vertical integration involves the acquisition or establishment of a subsidiary or a division to deal with a different stage of production or processing (e.g., a steel mill operating its own "captive" mines for iron ore, coking coal, and limestone -- a backward integration toward the resources; a steel mill developing facilities for fabrication of seamless pipes -- a forward integration toward the consumer). Horizontal integration deals with expansion within the same stage of production or processing (e.g., a phosphate rock mining company acquiring another phosphate mine). 3 Continuous survival -- extending the life-span of the firm as much as possible.

50 DEVELOPMENT OF NATURAL RESOURCES -- SPECIFIC CHARACTERISTICS Basically, an investment in a natural resource development project does not differ from any other capital investment. There are, however, additional factors that must be considered in the analysis, and they may well affect the final conclusions. There are four specific factors that relate to natural resources, namely: 1) the long lead time from the geological discovery to the full use of the minerals -- at best, several years; more often -- 8 to 12 years or longer; 2) the political and social environment in the region destined for development; 3) the nonrenewable nature of the mineral resources; and 4) taxation burden and allowances resulting from resource depletion. In the analysis, these factors will show up in terms of a yery long preproduction period, a definite life-time for the project, and specific tax debits (royalties, severance tax) or credits (depletion allowance). The inclusion of these factors in the economic evaluation process is demonstrated in the examples given later. Other factors should also be considered: the heterogeneous nature of mineral and energy deposits (no two deposits are identical) and the finite quantity of commercial mineral (ore) in any specific deposit raise the problem of geological and technical uncertainty. Vulnerability to changing political and social conditions, especially in foreign countries, poses the risk of nationalization, a takeover or expropriation, or the shutdown of the extractive operations. In recent years methods for quantifying uncertainty and risk have been developed; some of these are discussed (and their use demonstrated) later. THE TIME VALUE OF MONEY A yery basic concept in economic analysis is that money has a time value -a given sum of money now is normally worth more than an equal sum at some future date. An investor is ready to give up some rights to present income (or present satisfaction from this income) only if he or she can get a higher future income (or a larger satisfaction in the future). Likewise, firms and individuals borrow money at present, to be repaid -- at a somewhat higher amount -- in the future. The long lead time between the initial investment of funds in exploration and development of large ore bodies or fuel resources and the inflow of revenue when these mines and fields are fully operative requires the incorporation of the time value of money concept in the analysis because of the different time aspects under consideration. Interest Rate This difference between the value (price) of earlier rather than later avail ability of funds is commonly known as the interest rate r. Because present money is almost invariably at a premium compared with future money, the value of the interest rate is almost invariably positive. As a matter of convenience, r is usually expressed as a percent per unit time (e.g., 15 percent per year).

51 The time value of money should not be confused with inflation. Under our current inflationary conditions, it is true that the value of future income will be less than that of the same income at the present, due to a general rise in the price level (which is what inflation is -- you can buy less with the same number of dollars). However, the inflationary effect does augment and magnify the time value of money. Its direct impact is in increasing the magnitude of the interest rate r. Were we living under deflationary conditions, their effect would have been toward lowering the interest rate. Thus, changes in price levels do not create the time value of money; they only influence its magnitude for any given time period. SOURCES OF FINANCE AND THE COST OF CAPITAL There are three possible sources for investment funds -- equity capital, debt financing, and internally generated funds. This section reviews each of these sources and discusses the cost of using them for investment purposes. Equity financing involves partial ownership in the firm through the acquisition of stock. A corporation can raise new equity capital by offering issues of its common or preferred stock. The actual cost of any common stock to the firm is composed of some mechanical expenses (such as registration and legal fees, brokers' commission, and printing costs) and the periodical dividend payments. With preferred stock, there are again the same mechanical costs -- altogether some 2 to 5 percent of the issue -- in addition to the fixed dividend paid to the stockholder whenever a dividend is declared. A firm can raise investment funds by borrowing the money. The sale of bonds -- a long-term loan -- involves periodical payments of interest and principal according to a predetermined schedule and rate. The borrowing of funds from financial institutions, government agencies, or insurance companies represents short and medium-term debt financing and involves the same periodical payments of interest and capital. Unlike dividends, the interest payment! must be met on time, regardless of the state of the firm's operations. The full impact of interest payments as a financing cost to the company is always diluted by the fact that these payments are deductible expenses for tax purposes. The firm's taxable income is reduced by the amount of interest payments and some tax saving occurs. The mechanical costs of debt financing are lower than that of capital equity, at about 1 to 3 percent of the loan value. There are two kinds of internally generated funds: retained earnings are the company's undistributed profits, or what is left after payment of all costs, of taxes, and dividends to the stockholders. Depreciation, amortization, and depletion allowances (see following sections) are noncash charges against the firm's profits and are also available for reinvestment.

52 There are no actual costs involved in the use of these funds, except for the opportunity cost -- what income could have been generated had these funds been used somewhere else. Summing up the discussion of cost of capital, it is clear that each of the sources for investment funds involves some cost for the firm. In general, it can be found that debt financing will cause the lowest cost, followed by internally generated funds and by equity capital. However, the cost of capital is only one factor (although a major one) in planning the financing of investment activities. Other considerations (such as the debt to equity ratio, the current interest rate, existing liabilities of the firm, and the magnitude of the fund-raising effort) will probably lead to the use of at least two different sources of funds, especially for capital-intensive investment projects. Single and Compound Interest The simple interest payment is computed for a single period of time. It measures the difference between the present value of a sum of money and its future value, given a specified interest rate. The most common example is depositing money in a savings account. When the original deposit amounts to P and the interest rate is r percent per one time period, the depositor may then withdraw at the end of this period a sum A, composed of the principal and the interest paid on it, or A = P + Pr = P (1+r)

(1)

For example, a sum of $1,000 deposited for 1 year at an annual interest rate of 7.5 percent will yield at the end of the year A = P (1+r) = $1,000 (1+0.075) = $1,075.00 Whenever the principal is held longer than one period and no interest payment is withdrawn, the bank will pay interest on the original deposit and on the interest accumulated previously. This is a compound interest and it is algebraically derived in the following formulae: A, = P (1+r) for the first time period, A 2 = Α χ (1+r) or P (l+r)(l+r) = P (1+r) 2 for any two periods, and finally, A = P (1+r) , for n discrete time-periods. (2) Conveniently, compound interest tables for varying values of r and n have been compounded and published. Such an abreviated table of compound interest factors (computed at the end of each period n) appears in Table 2 of Appendix A. The intersection of the row (for n) and the column (for r) yields the factor (l+r) n , to be multiplied by the original value of P, to obtain A . For example, a sum of $25,000 invested at the interest rate of 8 percent per year for a period of 4 years will yield A = ($25,000)(1 + 0.08) 4 = ($25,000)(1.3605) = $34,012.50.

53

A Improvement at compound interest

Original principal to be invested

^«n P V

^«*5S

^rf&g P(1+r)

P(1+r) 3 -- Yearly - Interest - Accruals

2

. P(1+r) 2nd year P

1st year P

3rd year P

Etc. P

TIME — Successive valuation dates ι

Fig. 20 : Compound Interest (Source: Fig. 22, p. 161, Parks, 1957). In figure 20, Parks (1957) shows the process of growth of the principal through compound interest. It should be noted that compound interest factors will vary with the time and frequency of compounding -- the factors given in Table 2 in the Appendix are computed once a year at year-end. Other possible compounding frequencies may be once a year at mid-year, semi-annually, quarterly, or continuous compounding. The higher the frequency of compounding within the given time, the higher will be the value of the (1+r) factor. However, the differences are insignificant, provided the magnitude of P is not large. For example, the continuously compounded interest factor for r = 0.08 and n = 4 years is roughly 1.3771 (rather than 1.3605) and the sum of $25,000 will yield at the end of this period $34,427.50 -- an increase of $415.00 over a period of 4 years. Discounting Discounting involves the conversion of future income into present value or present worth. Since immediate availability of resources is usually preferred over future availability of the same resources, one may expect the present value of future income to be somewhat smaller (discounted at the rate of r per period of time). Thus, using equation (1) and looking for P, we get A = P (1+r) or P =

for one discrete time period;

(3)

1+r for n time periods, P=_J] A n (l + r)- n (4) n (l+r) Although the discount factor (l+r)~ n can be easily derived from the compound

54 interest factor, being its reciprocal, a more convenient method is the use of discount factor tables, similar to the one given in Table 1 in Appendix A. Again, the discount factor appearing at the intersection of the row n and the column r is equivalent to (l+r)~ n . The product of this factor and the sum A will yield P. For example, a sum A of $10,000 due 4 years hence at 10 percent interest per year is worth at present P = ($10,000)(1+0.10)'4 = ($10,000)(0.6830) = $6,830.00 The process of discounting is shown in Figure 21 below.

A

I

>

DISCOUNTS FOR SUCCESSIVE

YEARS

Present value

Etc.

\ A (1+r)3

A (1+r)2

A (1+r)

>

Successive valuation dates — T ime

Figure 21: Discounting (Source: Figure 23, p. 165, Parks, 1957) The previous comment about the frequency and timing of compounding during a discrete time period applies also in the case of discounting. The only difference is that the higher the frequency (the shorter is the time period), the lower will be the present value. For instance, the sum of $10,000 continuously discounted at 10 percent for 4 years will yield a present value of only $6,703.00, or $127.00 less than in the case of year-end single discounting. Annuities and Perpetuities The previous section dealt with the conversion of a future income A to its present value P by discounting. In any capital investment project, however, it is more common to compare a series of future income flows with a present investment of I. Thus, if A-, A ? , A~, , A are future income flows arising, respectively,

55 at the end of time periods 0, 1, 2, 3,

, n, and r is the appropriate rate of

discount, then the present value of these income flows is: PV

or

p

A

A

1 + 2 1 (1+r) 2 (1+r) i=n

v =£

Ai

+

A

3 + . . 4. ...+ n 3 (l+r)n (1+r)

(i=0ils 2ϊ3ϊ

A

···" n)

(5)

i i=0 (1+r) The aggregate present value is then compared with I to determine the attractiveness of such an investment opportunity, as discussed later. In the special case when the future income flows are constant for all timeperiods (usually years), these flows are called "annuities." It is easier then to use the annuity formula to compute present value of all future income flows. This formula is P = The term — ^ — * — ^

(A [l - (1+r) "nJ r

(6)

comprises the present value factor of an annuity for

n time periods at r percent per period. Table 3 in Appendix A gives the relevant annuity discount factor values for varying discount rates and time periods. An example for the use of the annuity formula is an investment project to construct a coal cleaning facility to be leased for an annual fee to coal producers for 10 years. Thus, if the annual fee A of $20,000 is paid at year-end and the rate of interest r is assumed to be 8 percent per year, the present value of these annuities is: PV = 20,000 fl - (1+0.08)""1QJ 0.08 = ($20,000)(6.7101) = $134,202.00 When the series of annuities is expected to go on perpetually, equation (6) for present value becomes simply P = f

(7)

n

as n tends toward infinity and (l+r)" tends to zero. This case is referred to as a "perpetuity." Using previous data for computing the present value of future constant income for a perpetuity, PV = $ 2 0 > Q Q Q = $250,000.00 0.08

56 DATA ESTIMATES Any evaluation method, used. This is an important be made to refine, improve, to compute accurately rates

however complex, is as good as the nature of the data point to bear in mind -- at least as much effort must and periodically re-examine all data and estimates as of return or yields.

This section discusses the type of data needed for an economic appraisal of mining or energy projects and some of the difficulties in obtaining or estimating such data. The more detailed and certain are the data, the more reliable will be the results of the economic analysis. However, full knowledge of all details of a mining project is obtainable only after the deposit has been fully depleted and all output sold. It is too late then for evaluation. Thus, the analyst must work with less detailed information when analyzing a potential ore deposit, and the uncertainty increases accordingly. Estimates of Reserves The interest of a firm in a specific deposit or oil field may arise as a result of some exploration work done by the company's own geologists or by outside sources. An early indication of a potential mineralization, if it seems attractive enough following a preliminary appraisal, should be followed by a more thorough geological investigation and supported by drilling and coring. Such an investigation should be summarized with a geological report indicating the extent of the mineralization and its nature. Based on surface and subsurface studies and an adequate number of representative samples (cores), carefully assayed and weighted, the volume of the ore in the deposit and its average metallic content can be estimated. For a detailed example of recoverable ore estimates, please see Chapter 12. Not all of the reserves-in-place are recoverable, and the fraction of the deposit that can be profitably extracted and processed varies with the chamical and physical composition of the deposit, the method of mining and ore treatment used, and the ability of the firm to sell the product at a price that will profit the operator. If the project is undertaken, the sold output should generate, during the life-time of the mine, enough revenue to pay for: 1) the purchase price of the property (or lease bonus and royalty payments); 2) the development costs of the deposit -- removal of overburden and waste material in an open pit; drilling of shafts or drifts and opening of work faces in an underground mine; 3) the cost of equipment, plant, and facilities (extraction equipment, beneficiation, smelting and refining, transportation means, and storage);

57 4) all operating costs (including wages and salaries, overhead expenses, supplies and materials, and treatment costs); 5) an acceptable return on capital investment; and 6) some compensation for time value of money and for risks and uncertainties undertaken by the mining company. In the following sections, some of the cost and revenue items that are pertinent to any economic evaluation are briefly discussed. Rate of Production and Cut-Off Grade The selection of an optimum mine size is based on the interplay of'two different parameters -- rate of production (tonnage per time unit) and cut-off 4 Subject to the limitation of the size of ore body and assuming that the

grade.

market will absorb all output levels considered, there are still a number of technically feasible alternatives of rates and grades for an optimal mine development.

Each of these should be evaluated separately and the best one then compared

with alternative investment opportunities elsewhere.

The assumption that the

market itself is not a limiting factor at any point during the life-time of the mine must be carefully checked and re-examined. Various mining engineers and economists have studied the problem of an optimal mine and plant capacity, as they relate to the ore's cut-off grade.

One of the

earlier scholars of that problem was Donald Carlisle, who was looking for optimal 5 6 design.

By using marginal cost

and average total unit cost

curves and discounting

to account for time value of money, he computed the maximum present values as the optimum for a theoretical metallic mine.

This optimum lies somewhere between the

combination that yields maximum rate of profit per unit and that which generates maximum annual profit (Carlisle 1954).

More about it in Chapter 6.

Once the rate of recovery and the cut-off grade of the ore have been decided, the milling, beneficiation, and processing facilities must be planned accordintly. The goal should be a high use rate with a minimal capital investment.

Yet, the

facilities must have some flexibility to enable the firm to react to changing conditions in the market, in the cost components, or in government policies (such as taxation, import restrictions, stockpile purchases or sales, and reclamation/ pollution abatement requirements). Capital Investment Requirements The selection of mine and plant capacities enables the mining and metallurtical engineers to design a detailed flow sheet and choose the equipment required *4 Cut-off grade is the minimal ore grade that will be mined economically when blended with higher grade ore. 5 Marginal cost (MC) is the cost of increasing output by one additional unit. Average total unit cost (ATUC) is total cost per unit of time, divided by units of output produced during that period.

58 for extraction of the ore, its beneficiation, and processing. It is outside the scope of this chapter to go into details of equipment lists, individual capacities of machinery, etc. A good and experienced engineer can prepare such lists and provide a reliable estimate of their cost, based on the firm's previous plants, manufacturers' and suppliers' price quotations, delivery dates, and price expectations. The analyst would like only to make sure that no major item of investment cost is forgotten. In Table 5, the major items of investment capital in developing a mineral property are listed: Table 5:

Major Items of Investment Capital

FIXED CAPITAL Mineral rights/land acquisition Environmental impact statement and legal fees Further exploration and development drilling removal of overburden and waste (open pit) Construction of shafts or drifts, opening of haulage ways and working faces (underground) Further process development (laboratory and pilot-plant experiments) Plant and equipment: land, water supply, power plant, railroad spur and access roads, waste disposal (tailing ponds), mine plant, beneficiation facilities, smelter plant, refinery, services building, storage, transportation and material handling facilities, engineering costs Townsite or employee housing (where applicable) Environmental protection activities and land restoration WORKING CAPITAL Cash on hand Accounts receivable Inventories (parts and supplies, inventories of finished and semifinished mineral products) START-UP COSTS CONTINGENCY ALLOWANCE AND COST ESCALATION It is worthwhile to note that all expenditures prior to the time of decision (such as preliminary geological survey and process development), usually called "sunk costs," are not part of the final investment analysis. A good estimate of the capital requirement must include working capital and start-up costs. Although estimates of equipment and plant may be based on producers' quotations, the firm must draw on its own experience or the experience of other mining firms, in estimating the working capital and start-up expenditures needed.

59 In some cases, it is possible to get a "turn-key" price for the milling and processing plants. Under such a proposal, an engineering firm will undertake the construction of these plants for a given price. Such a proposal reduces the uncertainty, but does not eliminate it altogether, since most mining firms prefer to plan their own extraction operations. Operating Costs Operating costs refer to the costs incurred in the production of output. These are both cash expenditures and noncash charges for the day-to-day operation of the mine and plant. The magnitude of these costs varies with the nature of the deposit, degree of mechanization, mining method, beneficiation and processing methods, and a host of other factors. It will be meaningless, therefore, to quote a "typical" breakdown of such costs. Instead, a list of the major cost items is given in Table 6 below: Table

6

: Major Operating Costs

LABOR Wages, including overtime Salaries for administrative and clerical staff Vacation and hospitalization payment Fringe b e n e f i t s - - social s e c u r i t y , unemployment insurance, workmen's compensation, other insurance Employer's c o n t r i b u t i o n to the Miner's Welfare Fund ENERGY

Power and fuels SUPPLIES Explosives, timber, lubricants, chemicals, reagents PARTS Spare parts for machinery and equipment MAINTENANCE AND SERVICES Repairs, hauling, professional costs, telephone and telegraph, travel expenses, etc. SELLING EXPENDITURES Advertising, salesmen's commission, brokers' commission ROYALTY PAYMENTS TO LANDOWNERS INTEREST PAYMENTS TO BONDHOLDERS AND CREDITORS NONCASH CHARGES Depreciation and amortization, depletion allowance, capital investment allowance TAXES Local, State, and federal taxes Some of the above items are briefly discussed on the following page.

60 Depreciation and Amortization Depreciation is a noncash charge, deductible from the tax base, which represents a reasonable allowance for the exhaustion, wear and tear, and obsolescence of a depreciable property used in business or held for the production of income. This enables the firm to recover the cost of the depreciable asset during its estimated useful life. There are several methods of computing regular depreciation allowances, but the three methods generally used are: 1) the straight-line; 2) the declining balance; and 3) the sum of the years-digit. Any reasonable method of depreciation is acceptable by the United States government for income tax computations, provided it is consistently applied by the firm. In addition, some assets qualify for special deductions such as accelerated first-year depreciation. Under the straight-line method, the cost of the property less its salvage value is generally deducted in equal annual amounts over the period of its estimated useful 1ife. Under the declining balance method the annual depreciation amount is deducted from the cost of the asset before computing next year's depreciation. Although the rate is constant (usually higher and up to twice the rate used under the straight-line method), it is applied to a declining balance each year. Salvage value is not deducted from the cost of the property in this case. However, total deductions cannot exceed the total cost of the asset less its salvage value. The sum of years-digits method uses a declining rate per year. The rate is determined by a ratio, with the denominator being the sum of the number of useful years of the asset (e.g., for an estimated life of 5 years, the denominator is 1+2+3+4+5=15), while the numerator lists the number of remaining useful years. Thus, in the first year of operation, the ratio (for an expected life-time of 5 years) is 5/15, for the second year, 4/15, and so forth. The rate each year is applied to the total depreciable value of the asset to yield annual depreciation allowances. In Tables 7 to 9 , comparative annual write-offs are shown, using the above three depreciation methods. In preparing the tables, it was assumed that this particular property does not qualify for additional first-year depreciation. Assume that a new bulldozer with an estimated life of 5 years is bought on January 2 of the first year for $16,500. Its salvage value at the end of the fifth year is estimated to be $1,500.

61 Table

Year

1 2 3 4 5

Cost Less Salvage Salvage

$15,000 $15,000 15,000 15,000 15,000 15,000

7 :

S t r a i g h t - L i n e Depreciation Method Annual Rate

1/5=20% 1/5=20%

20% 20% 20% 20% 20% 20% 20% 20%

Annual Allowance Allowance $3,000 $3,000 3,000 3,000 3,000 3,000

Cumulative Allowance, Dec. 31

$ 3,000 6,000 9,000 12,000 15,000

Table 8 : Declining Balance Depreciation Method Recoverable

Year 1 2 3 4 5

Cost, Jan. Jan. 2 Cost, 2

$16,500 $16,500 9,900 5,940 3,564 2,138 2,138

Rate Rate

2/5=40% 2/5=40%

40% 40% 40% 40% 40% 40% 40% 40%

Annual Allowance $6,600 3,960 2,376 1,426 638

Cumulative Dec. 31 $ 6,600 10,560 12,936 14,362 15,000

Only $638 allowance is permissible during the fifth year since the cumulative depreciation value cannot exceed the bulldozer's cost less its salvage value. Table 9 : Sum of Years-Digit Depreciation Method, Constant Base Plan ear

Cost Less Salvage

Ratio

1 2 3 4 5

$15,000 15,000 15,000 15,000 15,000

5/15 4/15 3/15 2/15 1/15

Annual Allowance $5,000 4,000 3,000 2,000 1,000

Cumulative Dec. 31 $ 5,000 9,000 12,000 14,000 15,000

Although the cumulative depreciation, over the life-time of the asset, is the same in all three methods, the distribution of the allowances over time varies; therefore, it has difference impacts on annual cash flows and their discounted present value. The depreciation allowance applies only to property or assets actually used in trade or business, or held and used for generation of income. The original cost of tangible assets (or their value after improvement or casualty losses) is deductible only to the extent that these assets are subject to wear and tear, to decay, to exhaustion, or to obsolescence -- buildings may be depreciated; land may not. The cost of shafts or development work is also charged off as the ore is produced. Some intangible assets actually used by the firm and which have a limited period of usefulness may be depreciated. Such intangible assets may include patents and copyrights, representing a clear-cut case of a limited period of usefulness (17 and 28 years, respectively). For depreciable intangible assets, only the straight-line method is permissible. Amortization applies to certain capital expenditures -- the firm may deduct

62 each year a proportionate part of these expenditures and thus recover them in a manner similar to straight-line depreciation. Some of the capital expenditures that may, under certain conditions, qualify for amortization are premiums paid on partially and fully tax-exempt bonds, organization expenses of a corporation, research and experimental expenses, and trademark and trade name expenditures. For any further information on depreciation and amortization, refer to U.S. Internal Revenue Service documents in the U.S. and to tax guide booklets and regulations in other countries. Depletion Allowance Depletion is the exhaustion or diminution of a natural resource as a result of its extraction. Depletion allowance represents the amount allowed as an annual deduction in arriving at the net income for the taxable year from mineral and timber properties. The depletion allowance is given to the owners of mines, oil and gas wells, other exhaustible natural resources, and standing timber. Only an operating owner or the owner of an economic interest may claim depletion deduction. Thus, royalty owners may claim the allowance; stockholders may not. The Sixteenth Amendment to the U.S. Constitution, when approved by Congress and ratified by three-fourths of the states in 1913, gave Congress the power to lay and collect taxes on incomes from whatever source derived. The first Revenue Act implementing the new income tax made a provision for depletion -- it established an allowance so that receipts resulting from a decline in natural resource value should not be taxed as income. The concept of depletion allowance has been approved by every U.S. Congress since 1913, although the method of computing such allowances and the set limitations on them have been changed somewhat, most recently during 1976 and 1979. The two permissible methods of computing depletion currently are: 1) cost depletion and 2) percentage depletion. The latter has never been applicable for owners of standing timber. Most recently, large oil companies were also restricted to the use of cost depletion. The basis for cost depletion on minerals includes the cost of acquiring a mineral property and the exploration expenditures incurred in discovering this deposit. In determining the cost depletion deduction allowable, the cost of the property is divided by the total estimated remaining and recoverable units (i.e., tons of ore, barrels of oil), and the result is then multiplied by the number of units sold during the tax year (Kennecott, undated). For example, if the price of the property was $500,000, exploration and development costs $200,000, annual sales were 30,000 tons of ore, and the engineering estimate of the recoverable ore is 350,000 tons, the cost depletion for the

63 first year amounts to unrecovered cost of property development remaining recoverable reserves at year end or = οοτΓΤΓπτΓΤΓ^ο $700,000 _ t0 10/+Λη or $500,000 + 200,000 l1mnkU „ as aallowable 0zn ΛΛΛ - on n n A .tons 350,000 30,000 320,000 tons $2.19/ton cQSt depletion> $2.19 per ton x 30,000 tons/year = $65,700 annual cost depletion. The allowance for cost depletion for the second year, assuming no change in the reserves or annual output, amounts to $700,000 - $65,700 = <,K ?, iq iy 290,000 tons and $2.19 per ton x 30,000 tons/yr = $65,700 annual cost of depletion. Percentage depletion permits the deduction of a percentage specified by law, depending on the mineral involved, of the gross relevant income (working interest) from a mineral property to arrive at the taxable income. The deduction for depletion under this method must not, however, exceed 50 percent of taxable income from the property, computed without the deduction for depletion (Balance II below). The following example demonstrates the computation of the allowance, assuming a percentage depletion of 10 percent. Mine A Mine B Total Revenue (working interest) $450,000 $450,000 less Operating Costs 300,000 330,000 Balance I $150,000 $120,000 less Depreciation 50,000 50,000 $100,000 $ 70,000 Balance II less Depletion Allowance 45,000 35,000 Taxable Income $ 55,000 $ 35,000 In the case of Mine A, 10 percent of the relevant revenue is smaller than 50 percent of taxable income before depletion; therefore, it can be used to calculate the depletion allowance. The reverse is correct in the case of Mine B and the limitation of 50 percent of the balance determines the allowance to be deducted. The minimum depletion allowable under the percentage depletion method may never be less than it would be under the cost depletion method. Unlike depreciation charges or cost depletion, in the case of a percentage depletion, even if the owner has recovered the full cost of the property, he or she is still allowed a deduction. The existing depletion allowances play an important role in development of mineral resources by providing the operating owners with relatively inexpensive internal sources of finance for further investment in exploring and developing new reserves. The validity of the depletion allowance concept and, even more so, the

64 determination of the rates for the various minerals were under attack in recent years. As a result of a heated debate in the United States Congress, the rates were reduced somewhat starting January 1, 1970. More recently, Congress approved a graduated phase-out of percentage depletion allowance for large domestic oil companies. Without taking a definite stand in the depletion allowance controversy, which is outside the scope of this study, it is appropriate to review the basic arguments for and against the existing concept and methods of application. Arguments in favor of percentage depletion are: 1) The existing income tax laws do not intend to tax depleting natural resources as a source of income; in this respect, the depletion allowance is yery much like a depreciation allowance on man-made capital assets. 2) The depletion allowance is needed as an incentive to attract investment into the risky activity of exploring and developing mineral resources. 3) Percentage depletion helps assure an adequate supply of minerals essential for the country's economic welfare and for national defense. 4) The profitability of investment in mining is relatively low, considering the risks involved; thus, percentage depletion helps to bring the rate of return to the level of other manufacturing industries. 5) The repeal or reduction of the percentage depletion allowance would adversely affect the extractive industries, investors, consumers, and the government. Opponents of percentage depletion claim that it is a "tax loophole," and as such it causes a loss of revenue to the government, creates an overinvestment in mineral resources, results in misallocation of national resources, and violates the concept of "tax neutrality." These opponents claim that repeal of all depletion allowances would simply mean higher prices, not a decrease in available supply. These higher prices, in turn, would promote more efficient use of resources. In addition, the fact that U.S. mining activities abroad also enjoy some tax advantages seems to contradict the goal of a healthy indigenous mining industry for increased national security and for improved economic welfare. Price Information - Revenue Estimates Price estimates are probably the single most significant factor in any economic evaluation. Any deviation from the expected price may considerably change the results of the analysis; an overestimated price may bring a favorable rate of return to a project which is, otherwise, doubtful. Likewise, an underestimated price of the final product may lead to a rejection of an otherwise sound

65 investment project and to a loss of a profitable opportunity. Yet, in general, price information is the least known item in the assessment and it must be subjectively estimated. A common practice, yet not always a valid one, is to assume that the additional output by the project will be too small to affect the market price. In economic terms, a purely competitive market is assumed. Under these conditions the analyst usually extrapolates the price trend of the past into the life-time of the project. Although simple to apply, this trend extrapolation is based on expectations that the same conditions of the past will exist in the future. A trend extrapolation ignores, therefore, any possible changes in technology, taste, income level, and similar exogenous (outside the system) variables. For example, a trend extrapolation of past lead prices will ignore the possible effects of unleaded gasoline marketing on the demand for this metal and its price in the future. Another method is to apply regression analysis to estimate prices in the future. Price is determined by demand for and supply of the mineral product. If a certain relationship is established between demand (or supply) and a number of independent variables, and their coefficients (first derivative or slope of the curve) are computed on basis of past date, then expected demand (or supply) can be forecasted on the basis of adjusted data. Algebraically, Demand = f (A,B,C,D,

,N), or for a linear equation

Demand = a + bA + cB + dC + eD + + zN + f where a is a constant, b to z are coefficients and JJ is a disturbance term. A,B,....,N are various independent variables that have some influence on the demand (such as level of disposable income, price of the product, prices of all other products and services, and tastes and preference, if quantifiable). Once the coefficients are obtained, pertinent values for the independent variables can be plugged in for any given time and demand forecasted; assuming a certain level of demand, the expected price at that time can be computed. If the doubtful assumption of a purely competitive market is removed, then the possible effect of the additional output on price levels in the market should be carefully analyzed and the impact subjectively quantified. Other considerations to be included in the analysis are possible technological changes affecting this mineral and any other competitive materials, changes in government regulations with respect to import restrictions and pollution control (i.e., the effect of air pollution regulations on base metals smelters and the resulting price increases), and the availability of scrap and other secondary sources of supply. The author is the first to admit that estimating prices is a touchy problem to solve; many firms try to apply teamwork and sometimes use outside consultants to come up with the least-biased price estimate. Occasionally a range of possible prices is quoted, rather than one definite value.

66 When the experts agree on the expected price per unit, it must be converted to f.o.b. at the plant; transportation costs and physical losses during shipment to destination or to the established location of the market must be subtracted (many metals and all petroleum prices are quoted at a given location, such as St. Louis or the East coast). The net price at the mine, smelter, or refinery is then multiplied by the expected annual sales (not output) to provide an estimate of total revenues. Taxes In every profitable operation there is one certainty -- whatever the profit, the government is going to get a share of it. A mining operation, like any other manufacturing or service activity, faces various taxes from three different levels of government -- federal, state, and local. The U.S. federal taxes consist of the following variety: personal income, estate and gift, corporate income, payroll, employment and social security contribution, and sales or excise taxes. Personal income tax, although a burden to each of us, is not discussed in this paper, nor is any estate or gift tax. Payroll taxes -- unemployment compensation and social security contributions by the firm -add to the wages and salaries item in the operating costs. Sales or excise taxes and import duties add to the price of so called "luxury" goods (such as cement and tires) or imported supplies and materials purchased by the firm during the year. The only major specific payment of taxes is for corporate tax. It is usually paid in a lump sum once a year for profit generated during the previous year of operations. The existing U.S. rate is 22 percent of the first $25,000 of net profit, and 48 percent for all profit above this amount. In addition, provisional legislation may change the level of corporate tax by imposing temporary tax cuts or tax surcharge. These temporary changes are difficult to predict, and they may pose a problem to the analyst. As a matter of convenience, the numerical examples given below assume a 50 percent rate for corporate income tax. In an actual appraisal the pertinent rates should be used. The corporate income tax is the largest tax item for every mining firm, but state and local taxes are still important in their own right. Some of the taxes imposed by state and local governments in the U.S. are the property tax, highway user taxes, sales taxes, payroll and business taxes (license fees, wage tax, state corporate income tax), and personal income and inheritance taxes. Of special interest to the mining industry is the existence of a severance tax in some states (see Laing, 1977). Severance tax is a production tax imposed by the state for extraction of exhaustive natural resources and depleting the state's wealth. After a long discussion and in spite of the opposition of the industry, a severance tax was imposed in Colorado in 1977 on selected minerals whose annual revenues exceed a certain minimum. Other countries impose a Value Added tax in lieu of or in

67 addition to the income tax. In the case of an actual evaluation of a potential mineral deposit development, full consideration should be given to all types of taxes. They affect operating costs and reduce the profitability of any project by the amount of taxes paid. The impact of taxation on potential development of natural resources is so large that various countries are ready to grant a "tax holiday" for a couple of years for all new mining activities, to attract investment funds. Other pertinent Data The previous sections described the more essential data items that an analyst needs to make a meaningful economic evaluation.

By necessity, the discussion had

to be generalized and many small items pertinent to specific conditions have been ignored.

These items and many more should be included in an actual evaluation for

a given potential ore deposit. A general summary of this section is presented in Figure 22 below:

PHYSICAL Q U A N T I T Y

REVENUE

Estimated Reserves Expected price (c.i.f.) Expected price (f.o.b.)

X

Recoverable Reserves Rate and level of o u t p u t M i n i n g and Beneficiation losses Annual Output Inventory Adjustments

A n n u a l Sales

T o t a l Revenue

O P E R A T I N G COSTS Non-Cash Charges

Labor

Depreciation and A m o r t i z a t i o n

Energy

Depletion A l l o w a n c e

Supplies Parts Maintenane and Service Selling Expenditures R o y a l t y Payments t o landowner Interest Payments t o boundholders and credits

Capital Investment

Net Cash F l o w

Fig. 22 : List of Sequences for Economic Evaluation

68 Cash Flows vs. Accounting Profits Table 10 below lists the sequences for economic analysis. It provides a good opportunity to present a detailed breakdown of accounting profits for a given time period (in this case, a regular year of operations). The accounting profits will then be covered into a net cash flow -- a more useful indication of return on investment for most of the feasibility analysis studies. The major example used in this part of the chapter is the case of the potential development and extraction of coal by strip mine operations. The full details of this hypothetical example are given in Appendix B. Only data on year 3 of full operations will be included here. For the annual output of 3.1 million metric tons of coal, sold to a public utility under a long-term contract of an f.o.b. price (at the mine, ready to be shipped) of $12.00 per ton, the gross revenue is $37,200,000. One-fifth of this amount is paid as a royalty to the landowner, so that the net gross annual income to the company -- the working interest -- is only $29,760,000. This revenue and other cost items are listed in the table below (for a detailed breakdown of the numerical values, see Appendix B ) : Table 10 : Gross Income, Coal Strip Mine (Values in $1,000) less (1) x .2 = (1) - (2) (4) + (5) (3) - (6) less (7) - (8) (3) x .1 (9) - (10) (11) x .5

(1) (2) (3) (4) (5) (6) (7) (8) (9)

Gross Revenue Royalty Payments Working Interest Expensed investment Operating costs Total costs Gross earnings Depreciation allowance Balance I Depletion allowance Taxable income Tax liability Investment tax credit8 Adjusted tax liability Net Profit after tax

0

16,770

$37,200 7,440 29,760 16,770 12,990 3,358 9,632 2,976 6,656

(10) (11) 3,328 (12) (13) 2£ 3,304 (12) - (13) = (14) $ 3,352 (11) - (14) = (15) Line (15) above shows the estimated accounting net profit (after tax) for this specific year. The derivation of these values is a necessary step in any conventional accounting procedures. However, for many of the more modern economic analyses, the concept of cash flow is more relevant. =

Cash flow measures the actual flow of funds into or out of a specific project. Expensed investment is that annual investment that can be legally deducted as an expense at the time-period it occurred. In most cases, it involves intangible assets and costs of unsuccessful exploration efforts. o

Investment tax credit is an allowance given by the government as a percentage of the investment undertaken through the year, to be deducted from the tax liability.

69 Net cash flow per unit of time will be the excess of income inflows over outlays for operating costs and capital expenditures.

Any new investment project will,

most likely, generate negative cash flows in the earlier (preproduction) time periods, changing into positive flows after production starts, when revenues exceed operating costs and capital investment. The cash flow for any unit of time differs from the accounting net profit for that period in three items -- the depreciation and depletion allowances and the capitalized investment.

The first two allowances must be added back to the

accounting profit because they represent no "out-of-pocket" expenditures of the operation; they are merely bookkeeping adjustments for use of equipment and machinery or for depletable resources.

They are permissible deductions for income

tax purposes, however, and therefore affect the cash flow indirectly. MacKenzie (1969) has noted that "...The treatment of depreciation and other tax allowances is a common source of confusion in cash flow analysis. Depreciation is a premissible deduction for income tax purposes. It is not a real cost of the operation but, rather, is an allowance for capital expenditures that have been incurred. For cash flow purposes, these capital expenditures are accounted for in the time period in which they are incurred..." Q

The capitalized investment is not a permissible deduction item for the period in which it occurred, but being an actual expenditure, it must be deducted in computing the net cash flow. It can be recovered through the annual depreciation allowances and the salvage value. The adjustments needed to get to the expected cash flow for year 3 of the operation are listed in table 11: Table 11 : Adjustments for Year 3 from Accounting Profits to Net Cash Flow (Values in $1,000) (15) Net profit after tax $3,352 add (8) Depreciation allowance 3,358 add (10) Depletion allowance 2,976 6,334 (15) + (8) + (10) =(16) Balance II 9,686 less (17) Capitalized investment 744 add (18) Other cash adjustments* 3_ (16) - (17) + (18)=(19) Net cash flow $8,945 ^Includes either positive or negative cash flows, such as income from salvage, changes in working capital, etc.

Capitalized investment is an investment with an expected life-time and usefulness exceeding one year (e.g. the purchase of a continuous miner machine, with an expected life-time of seven years).

70

METHODS OF INVESTMENT APPRAISAL Several of the more common feasibility study methods are presented in this section of the chapter. Accounting Rate of Return (ARR) It is somewhat ironical to start this review of investment appraisal techniques with a method that totally ignores the time value aspects, nor does it always employ the cash flow concept. Yet, the ARR method is still one of the most common conventional investment evaluation methods in use by the mining industry and elsewhere, and it should be included in this study. The ARR on capital is defined as the ratio of an average accounting profit (net of depreciation and depletion allowance) to the investment capital. This ratio is then compared with the firm's cost of capital to evaluate profitability. There are numerous variants of ARR, but the most common is probably the use of average net of tax profit and initial capital outlay, including working capital, in determining the ratio. Sometimes an average capital employed during the project's life-time is used, rather than total initial investment. A numerical example may clarify the process of computing ARR; data for a simplified hypothetical project are presented below: Initial investment in year 0

$360,000

Working c a p i t a l i n year 0 ( f u l l y recoverable at end of year 6)

40,000

Total investment $400,000 Expected life-time -6 years of operations Straight line depreciation method - $60,000 per year Annual depletion allowance -10 percent of working interest or 50 percent of net profit before tax, whichever is smaller. ITEM Working interest less operating costs Gross earnings less Depreciation allowance Balance I less Depletion allowance* Taxable Income Income tax @ 50% Net Profits after tax Recoverable working

capital

YEAR (values in $1,000) J _ _2_ _3_ _4_ _5_ 450 500 550 600 600 35£ 380_ 390. 42£ 42£ 100 120 160 180 180

_6_ 520 40£ 120

$3,220 2,360 860

60 60 60 60 60 TB" ΊΗΓ OT TZff T2ff

60 60

360, 500

J30_ J £ 60 30 JO J5 30 15

25£ 250 125. 125

_20. JjO. _50 20 30 50 JO _15 J 5 10 15 25 z

1

z

J50 60 JO 30 1

Total Annual Return 10 15 25 30 *50 percent of balance after depreciation

L

TOTAL

JO. 30

55

_JO 165

71 Average annual (accounting) profit after tax is $165,000 τ 6 years = $27,500 per year. ARR is $27,500;$400,000 = 0.069 or about 7 percent on the initial capital investment. When average investment is used to determine the ARR, the unrecovered investment in the midpoint of the porject's life (in the case above, after year 3) is the denominator for the ratio. Therefore, ARR on average is $27,500 ; ($180,000 + 40,000) = 0.125 or 12.5 percent. For a mining or energy investment project, it may be more appropriate to add the depletion allowance to the net of tax profits. Although this allowance serves as a compensation to the operator for the use of depletable natural resources, it still leaves him or her with a larger cash-on-hand share, after the initial investment is fully recovered by annual depreciation charges. In such a case, the returns actually approach cash flows, although time value of money is still ignored. The ARR increases as follows: Total net profits after tax plus

Total d e p l e t i o n allowances

Total return

$165,000 250,000

$415,000

The average annual return is $415,000 τ 6 years = $69,170 and the ARR is $69,170 ; $400,000 = 0.173 or 17.3 percent. The ARR on the average capital is $69,170 T $220,000 = 0.314 or 31.4 percent. Referring back to the example of the the coal strip mine, if it was assumed that year 3 of operations is typical and represents an average, then the ARR is as follows (see the Appendix for details): Annual profit Initial investment (including

$ 3,352,000

working capital) 31,605,000 ARR = $3,352,000 τ $31,605,000 = 0.106 or 10.6 percent. For an average undepreciated investment, the ARR is $3,352,000 τ $17,046,500 = 0.197 or 19.7 percent. By adding depletion the return is increased to $6,328,000 and the ARR to 0.200 or 20.0 percent. All comments about the merits and shortcomings of this specific evaluation method (and all other techniques under review) will be deferred to the latter part of this section. Only then can one compare and contrast the various techniques and evaluate their applicability for particular investment situations. Payback Period (PB) The payback period (PB) evaluation method answers a single question: How long will it take to fully recover all of the initial investment outlay? To answer this question, the annual cash flows are summed up arithmetically until they equal or exceed the initial capital investment. Thus, this method uses cash

72 flow, but not any interest compounding or discounting, even though the emphasis is on time, probing how rapidly is the investment recovered. The derivation in Table 12 uses the data from the first example of the ARR method. Table 12:

Payback Period Analysis (values in $1,000)

Initial Investment $400. Year 2

Net Cash Flows Net profit after tax plus Depreciation plus Depletion plus Recovered working capital Annual cash flows Cumulative cash flows Net Cash Flows Net profit after tax plus Depreciation plus Depletion plus Recovered working capital Annual cash flows Cumulative cash flows

$ 10

$ 15

$ 25

$ 90 $ 90

$105 $195 Year

$135 $330

60 20

60 30

60 50

4

5

6

$ 30

$ 30

$ 15

$150 $480

5150 $630

60 60 -

60 60 -

60 30 40 ΤΪ45~ $775

The payback for this project is about 3 and one-half years (by interpolation) . The relevant derivation for the coal strip mine example is show in Table 13 (only the first four years' cash flows are listed below): Table 13: Payback Period Analysis Derivation for Coal Strip Mine (values in $1,000) Initial Investment $31,605. Year Net profits after tax (Balance II) plus Cash additions less Capitalized investment plus Salvage value plus Working Capital Annual cash flows Cumulative cash flows

3,328 6,334

3,327 6,334

3,352 6,334

3,485 6,334

-

-

744 3

2,543 159

9,662 9,662

9,661 19,323

8,945 28,268

7,435 35,703

Thus, the initial investment in the coal strip mine will be recovered in about 3 years and 5 months.

73 Net Present Value (NPV) The net present value (NPV) or present worth (PW) method is probably the most common evaluation technique in use. It requires a predetermined interest rate, representing the firm's cost of capital and any number of other factors (for example, growth element). Expected net cash flows throughout the life of the project, either negative or positive, are discounted at this rate to a given period (usually it is the present, or year 0; that is where the method got its name) and summed up. A positive aggregate present value above the initial investment indicates an attractive project at the predetermined rate. The derivation of the NPV was briefly explained earlier in this chapter. Equation (5) sums up the future income flows during time periods 0,1,2,3,.... ,n, discounted at the predetermined rate of discount r:

or

i=n A. PV = ΣΖ -J—T i=0 (1+r)1

(1=0,1,2,3

,n)

(5)

i=n PV =ΣΣ A. (1+r)" 1 (i = 0, 1, 2, 3,...., n) (5a) i=0 In order to compute the net present value, the above PV -- present value of future net income flows -- must be compared with I, the present value of cash outlays (investment for the entire expected life of the project, including year 0 ) . Algebraically, then i=n

1

i=n

NPV = 2 2

Ai (1+r)" - £ J

i-0

i=0

ΙΊ. (1+r)"1 (i=0, 1, 2, 3,...., n)

(8)

The first part of equation (8) denotes the net cash inflows and the second the investment outlays, both discounted to their present value at the predetermined discount rate r. Whenever the NPV is positive (NPVv'O), the project is attractive at the rate of r and should be undertaken. A simplified numerical example (Table 14), based on data given under the discussion of the ARR method, illustrates the process of computing the NPV. The predetermined discount rate in this case is assumed to be 12 percent and the relavent discount factors are taken from Table 2 in Appendix A.

74 Table 14: Computing Net Present Value (values in $1,000) ITEM

YEAR

Net p r o f i t s a f t e r tax plus Cash a d d i t i o n s plus Working Capital Cash flow Discount f a c t o r @ 12% NPV @12% Cumulative NPV @12%

(-)360 (-) 40 1. 000 (-)400

10"

0.893 80

(-)320 (-)400

ITEM

5

Net profits after tax plus Cash additions plus Working Capital Cash flow Discount factor @ 12% NPV (? 12% Cumulative NPV @ 12%

4 30

120 ^ 150 0.636 95 (-) 45

25 110

15 90

10 80

ΊϋΓ

(■ -)236 YEAR

30 120 ^ 150 0.567 85 40

135 0.711 96

0. 797 84

6 15 90 40 145 0.507 74 114

(

-)140 Total

The NPV is positive and the project is favorable at a rate of 12 percent. A more realistic example of computing the net present value of a coal strip mine, at 18 percent, is presented in Appendix B. For a project with an expected constant cash inflow for n years after the initial investment, the annuity formula (6) can be used PV = A&-(l+r)-"I

(6)

and the initial investment subtracted from it, to yield the net present value. Thus, equation (6) is modified to NPV = PV - I = A l H 1 + r ) J- I (9) v r ' where PV = present value of constant net annual cash inflows A for n years. I = initial investment in year 0, n = expected life-time of the project, and r = discount rate. The annuity factors ' r ' — for varying time periods and discount rates can be found in many financial handbooks.

75 The following example shows the calculations of NPV for the data below: I = $500,000 in year 0; A = $150,000; n = 5 years; and r = 10% per year. _ 150,000

[ι-α+ο.ιρι -5i

500,000 0.1 NPV = (150,000) x (3.79) - 500,000 = $68,500 Present Value Ratio (PVR)

NPV

One of the objectives of an economic evaluation of investment projects is to enable comparison among alternative opportunities. Rank-ordering of projects on the basis of net present value is meaningful only if the initial investments and the life-time of all projects under consideration are the same. This is one of the drawbacks of tne NPV method, and the PVR technique (also called by others the "productivity index") attempts to correct that situation. The PVR technique provides a measure of "present value per dollar of investment" by dividing the total net present value by the absolute present value of the investment (after MacKenzie, 1969). Algebraically, i=n

i =l

A^l+r) ' —

i=p

I. (1+r)" 1

i=0

li (1+r

(10)

-1

(i = 0, 1, 2, 3, p,

n)

where A. = annual cash flow in year i. I.

investment in year i, r = predetermined discount rate per year, n = total life-time of project, and p = preproduction period in years (initial capital investment). The following simplified example (Table 15) demonstrates the computation of PVR for two alternative projects:

76 Table 15: Computation of Present Value Ratio (value in $1,000) Project A Year

0 1 2 3 4 5

Cash Flow (-) 250 (-) 200

Total NPV

175 250 250 175

Disc._F_actpr @ 14% 1.000 0.877 0.769 0.675 0.592 0.519

NPV (-) 250 (-) 175 (-;) 425

135 169 148 91 118

PVR = .-ran = 0.278

II

Project B

Year

Cash Flow

0 1 2 3 4 5 6

(-) 150 (-) 250 (-) 300

Total NPV PVR = 229 16001

400 400 400 250

Disc. Factor @ 14% 1.000 0.877 0.769 0.675 0.592 0.519 0.456

NPV -) 150 -) 219 -) 231 (-) 600 270 237 208 114 229

0.382

The comparison between the two projects indicates that Project B, in spite of its higher initial investment and longer preproduction period, will yield a higher return per dollar invested. It is important to note that the derivation of the PVR for a single project is meaningless. The importance of this method is in its ability to rank-order alternative projects of unequal initial investment and expected life-time. Such projects, sometimes called "mutually exclusive", involve the undertaking of one project or the other, never both (for example, different mining rates from the same mineral deposit). Under these conditions, the investment alternative yielding the highest present value ratio is the preferred one. M u l t i p l e - R a t e Valuation Formulas

Several evaluation methods use two discount rates for determining the present value of cash flows. The basic assumption underlying these methods is that mining activities should generate a high, speculative rate of return. These inflows can then be invested in a sinking fund, yielding a lower, safe rate of return. A full redemption of the investment capital is anticipated at the end of the current mining activities; an implicit idea here is that mining is a one-time affair -there is no intention on behalf of the mine operators to reinvest the incoming

77 cash flows in developing new deposits to replace the ones being depleted. The better known of the two-rate valuation formulas is the Haskold mine valuation method. It was introduced by H. D. Haskold in 1877 and involved annual uniform accounting profits (annuities) and two discount rates. R. D. Parks, in his famous book Examination and Valuation of Mineral Property (1957), described the method, derived the formula, and provided several examples. Haskold's original formula is as follows: NPV =

§ n

U+i) -l

(11)

+ r

where A = the annuity; i = the safe interest rate; r = the speculative rate; and n = the years of operation. A numerical example is given below: A = $10,000 i = 6% r = 12%; and n = 10 years. NPV

$10,000 ° · 0 6 1n (1.06) -1 _ $10,000 0.0759+0.12

+0.12 =

=

$10,000 0.1959

$10,000 M6 (1.7908-1) _ , M ηςς M φοι,υο^.οι

+

0.12

The discount factors (in our case for i = 6%, r = 12%, and n = 10 years) can be found in Table 7 in Parks (1957). Parks also expanded the use of Haskold's formula to include nonuniform annual profits. It is also possible to use cash flows instead of the accounting profits included in the original formula; however, the resulting NPV in this case will differ considerably from the uniform rate NPV. Discounted Cash Flow (DCF) Rate of Return The discounted cash flow (DCF) method is a fast-spreading technique for evaluating investment projects. Sometimes also called "internal rate of return" or "yield," it incorporates both concepts of time value of money and cash flows, yery much like the NPV method. However, instead of using a predetermined interest rate, the analyst is looking for that interest rate r that makes the present value of the aggregate cash inflows equal to the present value of the combined investment outlays.

78 The DCF method assumed t o t a l NPV to be zero and looks f o r t h a t i n t e r e s t r a t e r t h a t w i l l s a t i s f y the f o l l o w i n g c o n d i t i o n : NPV = 0 = ΈΖ i=0

A.(l+r)

(i=0,

-ΣΖΤ i=0

(1+r)

(12)

1 , 2 , . . . . , n)

The determination of such a rate is a matter of trial and error, without any shortcuts. The analyst starts with one rate, and varies it according to the net result of the NPV. If the NPV is positive, the rate is too low and should be increased; a negative NPV means that the rate used was too high and a lower one is appropriate. Experienced analysts can easily reduce the number of attempts to a minimum. This process is well suited to be run by a computer and many DCF programs are available to the economist. Simple and short series of cash flows can also be calculated in several of the programmed hand calculators now available for use. A simplified numerican example demonstrates the process of determining the proper interest rate r. DCF - Rate of Return Year 0 1 2 3 4 5 6

r=10% Cash Flow Pis.Fact NPV (-)800,000 200,000 200,000 250,000 250,000 100,000 100,000

1.000 0.909 0.826 0.751 0.683 0.620 0.564

(-)800,000 181,800 165,200 187,750 170,750 620,000 56,400

r=ll% Pis.Fact NPV 1.000 0.901 0.812 0.731 0.659 0.593 0.535

r=12%. Pis.Fact NPV

(-)800,000 1.000 180,200 0.893 162,400 0.797 182,750 0.711 164,750 0.636 59,300 0.567 53,500 0.507

Total 23,900 By interpolation we find that r = 11.25%.

5,900

(-)800,000 178,600 159,400 177,750 159,000 56,700 50,700 (-) 17,850

The Advantages and Shortcomings of Various Methods After presenting a review of some of the more common evaluation techniques in use by the mining and energy industries, it is appropriate to sum up by comparing the different approaches. The interest here is in the specific merits of each of the methods and how well it fits with the given set of corporate objectives and capital investment conditions. The accounting rate of return (ARR) was for many years the most common evaluation method. It is still in use by various companies which enjoy its relative simplicity and the fact that the ARR yields one finite result (for example, ARR equals 7 percent on the initial investment). The disadvantages of the ARR technique are many: the time value of money is ignored; there is no use of cash flow (although it is possible to add depreciation and depletion allowances to the accounting return and then compute an adjusted ARR); it considers only the depreciable life of the venture, not its

79 economic life-time; and finally, the use of averages obscures the year-to-year changes in income and return. Merrett and Sykes (1963) summarize the shortcomings of the ARR method by pointing out the failure of this technique to allow for the incidence of capital outlays and earnings -- projects with the same initial capital investment but different distribution of income may yield the same ARR but will considerably differ in NPV or DCF rate of return. They also point out that "...another factor neglected by the method is the gestation or preproduction period between the commencement of a project and the time when it begins to produce an income..." (p. 221). Since the time lag between discovery of an ore body and its actual exploitation varies from one deposit to another, it should affect the profitability of the projects; it does not when the ARR method is used. The payback period (PB) method is probably the simplest to compute, thus it is one of the most popular methods of investment appraisal. The method has obvious applications to industries with rapid technological changes -- if a new plant tends to become obsolete long before the end of its physical life because of the advent of superior types of new plants, then for investment in this plant to be justified, it must promise sufficiently high profits over a very short period. The use of a well-chosen payback period could, therefore, be yery appropriate under these circumstances. PB method is also applicable, to some degree, for measuring risk. However, the risk should be of predominantly time-related nature -- the risk that a project will go exactly as planned for a certain period and will then suddenly cease altogether to exist and be worth nothing. These risk conditions may occur in the case of expropriation or nationalization of foreign activities without compensation. PB method is not suitable to measure adequately any other, more common, types of risks. The apparent disadvantages of the payback period method are that no consideration to time value of money is allowed; because returns beyond the payback period are neglected, the method really does not give a satisfactory indication of profitability -- the projects with the fastest paybacks are not necessarily the most profitable (Wei born 1969). Only in the case where projects give rise to the same net cash flow patterns, and have identical lives, is the relationship between the payback period and profitability an indication for rank-ordering. Under these conditions the relationship is inverse -- the shorter the payback period, the higher the profitability. As mentioned earlier, the PB method has some limited application as an initial screening device to save time and money -- any project that fails to pay for itself over a period of 12 - 15 years is unlikely to be an attractive investment opportunity. Net Present Value (NPV) method allows for the time value of money and uses cash flows. The technique discriminates among investments with different income

80 patterns over time and considers the full economic life of the venture. Comparison among alternative projects is meaningful only if the initial investment and the useful life-time of all projects are identical. The main problem in using the NPV method is to determine the "proper" discount rate. What is the cost of capital for the company? Is it constant throughout the economic life of the project? If not, later changes in the discount rate, if estimated at the time of evaluation, should be incorporated into the analysis. Another problem is that concern about liquidity of the firm is downgraded by this method in order to emphasize profit maximization exclusively. Some of the shortcomings of the NPV method are corrected by the present value ratio (PVR) technique -- although there is still the need for a predetermined rate, comparison among alternative projects with different initial investment outlays becomes possible. The PVR simply modifies the NPV method by providing a measure of present value per dollar of investment. The Hoskold Formula uses two rates of interest -- a "safe" one to be used with a sinking fund to recoup the initial investment and a "speculative" rate. "...When Mr. Hoskold developed his method, sinking funds were common and thus a correct assumption in those times. The apparent error in using profits rather than cash flows was probably not too significant since mines were very laborintensive and the depreciable and amortizable assets may have been small compared to total profits..." (Berry 1970) These conditions have changed since then and a sinking fund is not common in modern financial management. The effect of a safe rate for the sinking fund is that it reduces the amounts allocated to the speculative rate and thus reduces overall profitability estimates. The speculative rate does not increase over time to compensate the firm for the declining effect of the lower safe rate. From an economic theory point-of-view, it is doubtful if two different rates of interest could exist in the same market unless speculative returns are considered. The frequently-heard claim that the higher rate is supposed to be indicative of a higher risk possibility is theoretically unjustified. Risk probabilities should be measured by other means, not through establishing different interest rates. The attractiveness of the DCF rate of return method as an evaluation technique is three-fold: 1) it provides a more useful measure of expected profitability, and thus comparison among alternative projects is more meaningful; 2) it gives the real "internal" rate of return on capital investment; and 3) it seems to eliminate the need to determine an acceptable cost of capital for the firm. The method, although somewhat more cumbersome than NPV, is flexible enough to discriminate among investments with different cash flow patterns over time and it considers the full economic life of the venture. The weakness of the method is its implicit assumption that all the cash flows

81 generated by the project can be reinvested in opportunities that yield a comparable rate of return -- a valid assumption only in certain circumstances. In many other cases the rate of return for individual investment may be highly variable. Another possible problem may arise in the case of massive outlays of funds (negative cash flows) during several time periods during the life-time of the project, resulting in a possible dual rate of return. A brief discussion of the "optimal" method of evaluation is presented later in this chapter. Sequential Evaluation Processes The decision to go ahead and develop a given ore body (or any other capital investment decision) has consequences that affect subsequent decisions. It is a process of continuous optimization -- the selection, at any given time period, of the best case from a number of alternatives. The process of sequential selection among alternative decisions and the possible outcome can be show in a "decision tree." Figure 23 shows such a tree dealing with the problem of developing a natural gas field. The point from which two or more branches eminate is called a "node". Such a node, when surrounded by a square, denotes a decision node -- a point at which the decision maker dictates which branch is followed. An encircled node is a chance node -- a point where chance determines the outcome (Newendorp and Campbell 1968). The sequence of decisions starts at the left side (Figure 23) with the first problem -- whether or not to buy acerage; once a decision has been reached to go ahead and buy the land (and this involves a certain investment), in the next decision node there is the need to determine if the company should run a seismic survey (at the expense of so many thousand dollars) or drill immediately on the basis of available geologic data. The flow of decisions is always forward -- it is not reversible. The estimated costs associated with the decision nodes and the expected payoffs (or disappointments) of the chance nodes (modified by a subjective probability distribution of occurrence) -- all discounted to a common point of time -determine the course of action prior to the initial investment decision. The decision tree can also be used to follow the course of events and the progress of activity on that project. Once the activities have reached a decision node, if conditions have changed, the remaining alternatives must be adjusted accordingly and then reanalyzed to develop a new strategy from that point forward. The analysis then must consider only future investments versus expected payoffs -all costs that accrued previously should not be included in the evaluation. At A more detailed discussion of probability distribution is presented in the following section.

82 the decision node of "run of buying the acreage are relevance of this capital permissible deduction for

seismic" or "drill on geologic control", all expenses irrelevant with respect to this decision. The sole expenditure is, if the project were started, as a income tax purposes.

Fig. 23: A Decision Tree Data Source:

Newendorp and Campbell, 1968.

83 RISK ANALYSIS Uncertainty and Risk The previous section dealt with various evaluation techniques and provided several examples, given assumed full certainty. Consequently, no explicit measures of the degree of risk in the project were included. It can be argued that the "most likely value" estimates, as subjectively determined by the analyst, have been used for variables of the investment opportunities. When these data are then evaluated by a DCF Rate of Return method or similar modern techniques, the discounted return on an investment could be calculated to a fraction of a percent, \lery often this result, based on a single value data estimate, is presented as the solution of the investment analysis. And, yet, however impressive is the derived expected profitability measure, its precision is only illusory. All DCF calculations are necessarily based on data estimates that are far from being so precise; some uncertainty is associated with them and this uncertainty is in no way reflected in the derived rate of return when single value data estimates are used. In the past some economists used to define "risk" as an uncertain situation in which numerical probabilities can be assigned to possible outcomes; "uncertainty" then was a situation in which outcome probabilities were not known. This distinction is not significant anymore. Rather, the emplasis now is on the casual relationship between the two terms -- risk is the consequential effect of possible uncertain outcomes. Because future outcome of an investment decision is not known with certainty, there is a risk for the investor of a nonprofitable venture. Future costs and revenues in capital investment projects seldom can be estimated with certainty. The magnitude of uncertainties in a mine development project is even larger than in most other manufacturing industries. On the basis of samples and geologic maps, a decision must be reached about development of a mine, its capacity in terms of rate and level of output, a processing plant, and a smelter/refinery complex. Uncertainties can arise in the estimates of reserves and their average metallic content, in the expected demand and prices for the mineral, in government policies, and in any other aspect of operations. The combined effect of all these uncertainties influences the cash flows and the rate of return. Although the individual uncertainties can be small (have a low probability of occurrence), their cumulative effect may be large; if each of six independent "best estimates" in an investment analysis has a two-thirds chance of being correct, there is less than a 9 percent chance for all six to be correct (i.e., (2/3) 6 = 64/729 = 0.088).

84 Klausner (1969) comments on the need to point out the uncertainties: "...Increasing the decision maker's understanding of the uncertainty surrounding the key investment variables, and the effect of this uncertainty on the overall outcome of an investment, would certainly improve the basis upon which an investment decision could be made. Bringing underlying uncertainties out into the open and incorporating them into the investment evaluation therefore should be the hallmark of an adequate riskanalysis technique..." (p. 15) It is as important to measure the uncertainty and risk of investment opportunity as it is to compute its expected profitability. An uncertainty dimension must be incorporated into the expected profitability measure. Yet, uncertainties cannot easily be quantitatively estimated. Three methods of estimation and incorporation of uncertainties and risk into the feasibility studies are presented here -- risk adjusted rate of return, sensitivity analysis, and assigning a probability distribution (either subjective or Objective) to the variables in the evaluation. Risk-Adjusted Return An arbitrary adjustment for risk, such as raising the minimum discount rate because the project is "risky", is a common practice and is made almost intuitively. Often one can see the predetermined discount rate for a feasibility study raised (e.g., from 18 to 22 percent) because uncertainty is higher in this specific project. Thus, while 18 percent is the minimum expected return on a riskfree project, a premium will be added to it to "take care" of the risk. Even though risk-adjustment is a common practice, at least conceptually this method of handling risk is misleading: "...expected profitability and uncertainty are essentially independent indicators of the worth of an investment alternative. Thus, they should be separately measured. To combine them in the evaluation is to obscure the true basis for the mine development decision..." (MacKenzie 1969). Another problem facing the analyst in risk-adjusting is the magnitude of the "premium" to be added to the minimal (acceptable) return, when no effort is actually made to estimate the risk. Therefore, the author rejects this method and would prefer to use alternate methods of risk and uncertainty analysis. Sensitivity Analysis The purpose of a sensitivity analysis is to identify those critical variables that, if changed, could considerably affect the profitability measure. In a sensitivity analysis, selective individual variables are changed -- one at a time -- and the effect of such a change on the expected rate of return is computed. A simplified example is used to demonstrate the process of carrying out a

85 sensitivity analysis.

The basic data on the most likely (no risk) project are

as follows: $25,000,000 5 years $ 5,000,000 Straight-Line 10% of Working Interest, not to exceed 50% of Balance I 75,000 tons of concentrates $220 per ton of concentrates $115 per ton of concentrates 50% of accounting profits

Capitalized Investment in Year 0 Life-time of Mine (years 1-5) Salvage Value at end of Operations Depreciation Method Allowed Depletion Allowance Annual Output and Sales f.o.b. Price Production Cost Corporate Income Tax Rate

The annual cash flows and NPV at 15 percent discount rate for this base case are as follows: Cash flows and NPV (in $1,000)

less less less plus less plus

Item/Year

0

Total Revenue Total Costs Depreciation Balance I Depletion Taxable income Tax 1 lability Balance II Cash additions Capitalized investment Salvage value

0 0 0 0 0 0 0 0 0

Total Cash flow

1-4 16,500 8,625 4,000 3,875 1,650 2,225 1,112.5 1,112.5 5,650

Total

16,500 8,625 4,000 3,875 1,650 2,225 1,112.5 1,112.5 5,650

25,000 0_ (-)25,000

6,762.5

0 5,000 11,762.5

1.000 (-)25,000

2.856 19,314

0.497 5,846

0

g_

Discount factor at 15% NPV @ 15% NPV ρ 16%

+ 160 (-)480

By interpolation, the DCF rate of return is 15.24 percent. Five possible changes are considered in the following sensitivity analysis: (1)

in the capital investment;

(2)

in the price of concentrates;

(3)

in the operating costs;

(4)

in the preproduction period; and

(5)

in the expected life-time of the mine.

86 The table below lists several of the possible changes and summarizes their effect on the NPV at 15 percent and the DCF Rates of Return. Change NPV @ 15% DCFROR (% change (in $1,000) (%) Base-Case + 160 0 15.24% l.a. +5% in investment (-)1,090 13.36 (·)12 l.b. +10% in investment (-)2,340 11.61 (-)24 2.a. +10% in price + 3,197 19.91 + 31 2.b. -5% in price (-)1,437 12.74 (-)16 3.a. +10% in cost (-)1,531 12.59 (-)17 3.b. -5% in cost + 877 16.36 + 7 4.a. 2 years of preproduction (-)1,496 12.85 (-)16 5.a. 6 years of operation + 1,890 17.65 + 16 The profitability of any project is probably most sensitive to changes in prices of the sold output; other strategic variables are the initial investment estimate, the duration of the preproduction period, sales forecasts, and estimates of operating costs. In the mineral industry, profitability also may be sensitive to the average ore grade and recovery rates -- small variations in the metallic content of the ore (the level of extraction) may considerably change the profitability of the project. Once all of the important strategic variables have been identified, they can be given a special attention by the decision-makers, in the form of additional research and development effort on recovery rates, more earlier negotiations on sales contracts, or very careful watch on investment costs and timing. Sensitivity analysis by itself cannot, however, and will not measure the uncertainty of an investment alternative '-- it provides no estimate of the probability that the contemplated change will really occur. In addition, it is desirable to know the cumulative effect on profitability of simultaneous variations in all or several of the variables -- what will be the effect of price increase combined with an increase in operating costs? This combined effect is not shown in the sensitivity analysis. As mentioned previously, sensitivity analysis provides useful information on the variables that go into a feasibility study. However, it is not the proper method to quantify uncertainties and risks and to incorporate them into the analysis. Subjective Probability Distribution One way of quantifying the uncertainty and risk associated with an investment opportunity is to assign an expected probability distribution to the variations in the values of the variables. The probability distribution utilizes numbers in the range of zero to one. For an event that is certain to happen, a probability of occurrence of 1.0 is assigned; if the event cannot occur at all, its probability is 0.0. The probability of a head on the flip of a fair coin is

87 0.5.

The combined probabilities of different outcomes must add up to 1.0. Using a simplified example by MacKenzie (1969), involving only two variables, the use of a subjective probability distribution will be demonstrated here; the use of an objective probability distribution will be presented in the next section. The above example deals with the mining and sale of ore and the only two variables considered are mining costs and the price of the ore. The chief mining engineer expects the average cost per ton of ore to be $9; however, cost may vary within a minimum of $6 and a maximum of $12 per ton. The marketing manager expects an average price of $13 per ton, but this price may vary between $9 and $17 per ton. With an expected value for the price (EV ) of $13 and for the cost (EV ) of $9, the expected value of the profit per ton (EV^-) is $4; but what is the expected value of the profit if there are variations in the two variables of cost and price? Subjective Probability Distribution assigns probability distribution factors to each of the variations. This is usually done by going to the person who knows best -- in our case the mining engineer for mining costs and the marketing director for price variations, for estimating these probabilities. Suppose the following estimates are obtained from the experts: Price

Total weighted average

prob.

Cost

prob.

$ 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00

0.04 0.07 0.12 0.16 0.20(EVJ p 0.15 0.11 0.09 0.06

$ 6.00 7.00 8.00 9.00 10.00 11.00 12.00

0.05 0.15 0.22 0.27 (EVJ c 0.16 0.10 0.05

$13.11

1.00

$ 8.84

1.00

The weighted averages for both price and cost are more representative of future behavior. With a weighted average of $13.11 for the price and $8.84 for the cost, the expected profit (EV.Ü changes then from $4.00 to $4.27 per ton of ore. The strongest aspect of subjective probability distribution -- going to the people who should know best -- is also the method's weakest aspect. It is only human nature for the people directly involved to introduce some biases in their own favor. The mining engineer will tend, intuitively, to estimate the probability distribution in such a way as to overemphasize efficient mining, even though the EV stays the same (a diagram showing this distribution skewed to the left of the EV ). The marketing manager will tend to suggest a distribution curve that is

88 skewed to the right of the EV . The net results are that the expected profit EVjp using the weighted averages for the price and cost, will be larger than the earlier estimate of $4 per ton. To solve the problem of biases, mineral and energy firms will usually go to outside consultants to get their objective estimates of probability distribution around the expected value. These values are then used to recalculate the weighted average rate of return. Objective Probability Distribution (Monte Carlo Simulation Technique) When it can be reasonably assumed that there is a random pattern of variations in the value of a variable, the Monte Carlo method can simulate such random variations through the use of random numbers. The result of such a simulation is a normal distribution, within a predetermined range of values, around the expected value (that is, if plotted on a graph, it will have the shape of a symmetrical bell, with its highest point at the expected value). Figure 24 shows a normal distribution (a bell-shaped curve around the expected value), while Figure 25 presents the cumulative probability distribution curve for the same range of values. Using the previous simple example on the cost and price of a ton of ore, the use of the Monte Carlo Simulation technique can be demonstrated. Again, the expected value of the price (EV ) is $13 per ton, but it can wary between $9 and $17 per ton. If we are interested in a confidence limit of 90 percent (90 percent of the area underneath the normal distribution curve), then the range of price values narrows to between $10 and $16 per ton. Likewise, EV is $9 per ton, with variations between $6 and $12 (or for a 90 percent confidence limit $7 to $11). A 90 percent confidence level can be calculated by establishing an upper and a lower limit; that is, EV + (1.645) x (the standard deviation of the sample). For the example in front of us: $1

s

=

s

= μ

c

^ ^4^3 = $1.83 per ton, and

}.645

= $1

· 2 2 Per

ton

·

Because of symmetry the standard deviations are the same on both sides of the expected values. lnrough the use of published tables of random normal deviates, it is possible to compute random normal samples. $13 and s

For example, if revenue estimates are EV =

= $1.83, and cost estimates are EVQ = $9.00 and SQ = $1.22, then

This method was developed during the second World War for a secret project, code-named Monte Carlo, where a roulette device was used to simulate the probable behavior of neutron diffusion.

89

Normal Distribution

Shaded arta _ Unshaded under curve ~" under curve

Figure 24 :

Normal D i s t r i b u t i o n of

Probabilities

Prob
1 .0

0.8 Probability Distribution

0.6 0.4 0.2 0

0 0 Deviation from expected value

Figure 25 :

Cumulative P r o b a b i l i t y

+

90 their corresponding random normal samples, using the random normal deviates detailed below, are as follows: EV + (Normal Deviate)

EV + (Normal Deviate) x (s ) 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00 13.00

+ + + + + + + + + + + + + + + -

0.106)x 0.837)x 0.104)x 0.376)x 0.695)x 1.260)x 0.953)x 0.632)x 0.202)x 0.542)x 0.431)x 0.716)x 0.463)x 0.092)x 1.344)x 0.187)x 0.118)x 0.628)x 0.354)x 1.046)x 0.501)x 0.780)x 1.006)x 0.259)x 1.267)x 0.083)x 0.209)x 0.437)x 0.041)x 0.136)x 0.618)x

c ftr),

Cost (C)

Price (P)

1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83) 1.83)

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

12.81 14.53 13.19 12.31 14.27 10.69 11.26 14.16 12.63 13.99 12.21 11.69 13.85 13.17 10.54 12.66 13.22 11.85 13.65 14.91 12.08 14.43 11.16 12.53 15.32 12.85 13.88 12.20 13.08 13.25 11.87

9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00 9.00

+ + + + + + + + + + + + + +

835) x(l .22) 63Γ x(l .22) 279 x(l .22) 497 x(l .22) 424 x(l .22) 163 x(l .22) 142 x(l .22) 52Γ x (1 .22) 267 x(l .22) 960 > x(l .22) 061 x(l .22) 754 x(l .22) 449 x(l .22) 461 x(l .22) 680 x(l .22) 331 x(l .22) 502 x(l .22) 089 x(l .22) 410 Λ x(l .22) 108 x(l .22) 316 x(l .22) 744 x(l .22) 995 x(l .22) 355 x(l .22) 267 x(l .22) 856 x(l .22) 783 x(l .22) (1 .050 x(l .22) 046 x(l .22) (1 211 x(l .22) .379 x(l .22)

(0 (0 (1 (0 (1 (0 (1 (0 (0 (0 (0 (0 (0 (1 (0 (0 (0 (1 (0 (0 (1 (0 (0 (1

(o (o (o (o (o

Profit Per Unit = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

7.98 8.23 10.56 8.39 7.26 9.20 10.39 8.36 9.33 7.83 9.07 9.92 8.45 10.78 8.17 8.60 9.61 7.67 8.50 9.13 7.33 9.91 7.79 10.65 9.33 7.96 8.04 10.28 8.94 7.52 9.46

4.83 6.30 2.63 3.92 7.01 1.49 0.87 5.80 3.30 6.16 3.14 1.77 5.40 2.39 2.37 4.06 3.61 4.18 5.15 5.78 4.69 4.52 3.38 1.88 5.99 4.89 5.34 1.92 4.14 5.73 2.41 121.91

Total

3.93 rr 2 593.78 τπ -

Average Profit N

=

31

whereΣΓΤΓis total profits; 7f*is the mean profit; Χ.ΤΓ is the sum of the profits squared; and N is the frequency (number of samples). This process of selecting random normal samples must be repeated at least thirty times for each variable to reduce the possibility of any sampling errors due to a small sample size.

The larger the sample size, the closer will be the

average profit 7f to $4.00 per ton.

91 The estimated expected profit will be the sum of random normal samples of profit, divided by the sample size. The estimated standard deviation of the profit is computed by the equation

* ·ψ£ ■ Ψ\

(Ι3)

where TTis the random normal sample of profit and N is the sample size. For the numerical example given above, ^ψ-

=

$3.93/ton for N = 31, the standard deviation for profit

was $1.93/ton. For 90 percent confidence interval, the limits are EV + (1.645) x {sn)9 or Upper Limit = $4.00 + (1.645) x 1.93 = $7.17 and Lower Limit = $4.00 - (1.645) x 1.93 = $0.83 For a larger confidence interval of 95 percent, the limits are EV + (1.96) x ( s ^ ) and the Upper Limit = $4.00 + (1.96) x (1.93) = $7.78; Lower Limit = $4.00 - (1.96) x (1.93) = $0.22 The estimated confidence limits reflect the uncertainty with which expected profitability is held -- in this example, there was more than a 95 percent chance of at least breaking even on the sale of ore. These estimates of the expected profitability and degree of uncertainty associated with them can now be compared with results of alternative projects and the optimum selected on the basis of both the expected return and the degree of risk. A final word on the Monte Carlo Simulation technique. Most real-life projects involve many more than two variables and to do the simulation for all manually becomes a cumbersome and time-consuming effort. There are today computer programs to generate normal probability distributions for any given degrees of value and for any desired number of variables. If the analysts expect normal distribution and a Monte Carlo simulation deems desirable, the use of these programs will generate the upper and lower limits for any given confidence limit fast and inexpensively. The generalized discussion of probability distribution was intentionally kept simple and was aimed at explaining the concept rather than serving as a handbook of how to measure uncertainties under real conditions. There is much more to probability theory and the use of Monte Carlo simulation technique. For example, the assumption of normal distribution of the variations around the expected value is not usually realistic. Thus, methods have been developed to deal with a skewed and even with a discrete distribution pattern. These methods are

92 outside the scope of this book, however. The interested reader can follow them in books and articles that specifically deal with measurement of uncertainty and risk in investment projects. SUMMARY AND CONCLUSIONS It is appropriate now to sum up the discussion by briefly dealing with two specific questions: 1) is there a common "acceptable" rate of return for the energy and mining industries? 2) what is the "optimal" method of economic evaluation? An Acceptable Rate of Return Suppose the analysts went through the exercise and computed DCF rate of return for a number of alternative projects. They went on to estimate also their degree of uncertainty and came out with expected values and standard deviations. Are the results they have on hand now satisfactory for all potential investors under all circumstances? Will e^jery "attractive" mining project for company A at the present time be of interest to company B (or, for that matter -- to company A a year hence)? Where can they place the cut-off rate of return for screening alternative projects -- is it 20 percent, 15 percent, or 10 percent? Will one cut-off criterion be acceptable by all others? The definite answer to all of these questions is in the negative. A certain engineering consulting firm rejected all possible projects that did not yield the firm an expected rate of return of at least 32 percent. The author is sure that many mining and energy firms would be more than satisfied if they could commence on projects yielding two thirds of that rate. MacKenzie remarked: "...Corporate preference depends on the interplay between the profit, growth and survival objectives of the company and the capital and skilled resources that it is able to direct toward their realization..." (1969) As conditions change over time and differ from one mining company to another preferences may vary. This is especially the case when there is no clear-cut situation, when a highly expected profitability is paired with a high level of uncertainty, or vice versa. The preferred alternative of one company then is not necessarily the same as that of another. It is not uncommon then that a deposit given up as uneconomical by one company is picked up by another mining firm and eventually developed as a successful project. The rate of return is not the sole or ultimate criterion for decision, although it is usually one of the important factors considered by the firm's management. As a matter of practice, personal judgment, established criterions within the corporation, and personal intuition contribute to determining corporate preferences. All these factors may conceptually be expressed in the form of a

93 Utility curve, using both rate of return and confidence limits as parameters. This approach is not practical, however, because many of the factors are unquantifiable. The "Optimal" Method of Economic Evaluation The answer to the question of the best, foolproof and always appropriate method of appraisal is also in the negative. There just is no such method. Although modern investment evaluation techniques, using cash flows and allowing for time value of money, are definitely superior to the traditional methods of ARR or payback, they are still not perfect. Furthermore, their degree of applicability varies with the stated objectives of the analysis. They must also be supplemented by estimates of uncertainty and risk if their purpose is to present adequately the full investment picture before the decision makers. Nevertheless, the net present value (with present value ratio) and the discounted cash flow methods still present two alternatives, economically viable methods of analysis. The author's personal bias is toward the use of DCF whenever possible, supplemented by another technique if so desired. Under normal circumstances, this method is able to handle the specific situations; it provides the best possible measure of profitability and easy rank-ordering of alternative projects. As a matter of general practice, it is adviseable always for the analysts to evaluate a potential project by using two different methods (such as NPV and PB or DCF rate of return and PB). When the results obtained from both methods are similar, this reinforces the analysts' conclusion of the feasibility of the project. If the results obtained seem to contradict each other, the analysts must go to somewhat more sophisticated appraisal methods (such as incremental analysis) to solve the apparent contradiction.