Economic principles of decision making


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Economic principles of decision making

  1. 1. CHAPTER 5.2 Economic Principles for Decision Making Ian RungeMining used to be a business primarily focused on the technical increase profits and reduce debt but can also impact mine life.aspects of getting valuable ore out of the ground and extracting Understanding these issues requires economic tools to assessthe minerals in a metallurgically efficient way. Without deny- the time value of the importance of these skills, a narrow focus on technicalissues is no longer sufficient to guarantee success, even in rich MINING ECONOMICS AND STRATEGYore bodies. Skill in economics is an essential partner to tech- Most approaches to economics assume that one person ornical skill in every step of the mining process. The economic one company’s actions do not affect the whole market. Thisway of thinking starts before the first drill hole is put in the assumption is usually quite reasonable, because even theground and includes not just the most economic way of mining biggest mining companies usually only account for a smallbut also the most economic method of assessing mining proj- proportion of world production. A single extra ton of cop-ects. Economics directs mining strategy and takes into account per produced at one mine will not change the world price ofchanges in worldwide demand for mineral products. copper. Yet the world is interconnected, and the results for This chapter introduces the economic approach to deci- one participant in such an interconnected marketplace oftension making and focuses on how individuals engaged in mining depend on the choices (strategies) of all the other make decisions using sound economic principles. Perhaps that extra ton of copper will not affect the world price,While the better decisions and the more successful enterprises but if the changed economic forces that allow this mine toare adopted and copied by others, the less-successful enter- expand production also apply to its competitors, then maybeprises fail or are taken over, and outdated practices disappear. they too will expand their production. If everyone expandsThus the structure of the industry evolves. This chapter pres- production, then perhaps the world price will change.ents these economically based decisions in three parts. For many decisions in operating mines, the standard (non- The first section, “Mining Economics and Strategy,” strategic) approach of ignoring what competitors are doinglooks at the industry from a strategic perspective—the broad and using conventional economic models is quite appropriate.trends in the mining world and the way that much of the If an electric rope shovel is more economical than a diesel-world is interconnected—and highlights and challenges some powered hydraulic excavator in a mine, this choice is unlikelycommon misconceptions of mining economics. For long- to be wrong even when the outside world changes quite sub-term success, practitioners must at least be cognizant of these stantially, or even if other mines elsewhere in the world favorbroader influences. a different choice. The second section, “Costs,” follows a narrower Nevertheless, there are many areas of mining and mining-approach. Fortunately, most economic assessments in mines specific applications where the use of conventional modelsdo not require a broad understanding of the whole financial must be used cautiously. One such area is in the understandingworld but can achieve reliable answers focused on what is of risk and return. With financial investments (in the stock mar-happening in the company, the mine site, or just one part of the ket, for example), low-risk, lower-return opportunities formmine. This section focuses on costs and how the understand- part of a continuous spectrum to higher-risk and higher-returning of costs is critical for decision making—from day-to-day opportunities. In this style of market, the choice of a higherchoices at the mine face to long-term life-of-mine planning. (expected) return opportunity is synonymous with greater The third section, “Time Value of Money,” examines one uncertainty and higher risk. With individual mine investment,of the most important aspects of assessment in all but the sim- this risk/return trade-off is not so clear-cut. The uniquenessplest of mines: understanding what is happening in the mine of each ore body and the idiosyncratic risk attached to eachover an extended period of time. Investing in new, bigger project means that higher returns are not necessarily synony-machinery at the start can reduce costs and provides benefits mous with higher risk. This creates opportunities for operatorsover the rest of the mine life. Mining the richest ore first can who understand the characteristics of the ore body, and who Ian Runge, Founder, Runge Ltd., Brisbane, Queensland, Australia 309
  2. 2. 310 SME Mining Engineering Handbookunderstand the risks associated with mining it, to potentially purse, or bank account to buy something. Day-to-day trans-make higher-than-normal returns without exposing the com- actions seldom require any further discernment, because pur-pany to any higher risk. It also inhibits some decision making chasing a small item on its own does not evidently precludewhen projects are evaluated using conventional models that the purchase of anything else later on. For larger expenditures,are founded on efficient market risk/return characteristics. the real cost is more evident. An overseas vacation might Strategic considerations are also important because of mean delaying the purchase of a new car for another year;high sunk costs in mining—a characteristic of mining that is in deciding to spend the money on the vacation, one must beless important in most other industries. If a company has high comfortable with the idea of driving the old car for longer. Thesunk costs but low cash costs and the market price declines decision—the real cost of the vacation and the one that influ-quite sub­ tantially, the company is unlikely to go out of busi- s ences choice—is based on the imagined loss of enjoyment andness or even to reduce production. With lower prices, cash utility from driving around in the new car that much sooner.flow is still likely to be positive, and even though the company In economics, the cost of anything is the highest-valuedmight be reporting losses (from an accounting perspective), opportunity necessarily forsaken. This chapter looks at costreducing production will result in even larger losses. from this economic perspective. Unlike accounting costs, This raises two important strategic issues. If poten­ ialt which are historical, the economic view of costs is a forward-competitors have knowledge of a company’s capital struc- looking one. Costs in this sense inform decision making,ture, acting rationally, they might be deterred from entering choosing between the imagined value a person will enjoy fromthe same market, knowing that the company will not easily following one path and the value of an alternative path. Thebe put out of busi­ ess. With less competition, the company n tools described in this chapter and in the following econom-may be able to gain a price premium. However, this compara- ics chapters are aimed at understanding this value in order totive advantage can also work against the company if custom- help make these decisions. This chapter introduces the con-ers also know about the company’s capital structure. If they cepts of marginal, average, variable, fixed, and sunk costs. Itbelieve the company will continue producing so long as price illustrates why the marginal cost calculation is such a vital oneexceeds the company’s cash cost, the company is vulnerable in pit optimization and in determining the scale of investmentsto exploi­ ation. What should the company’s strategy be? Can t and why certain costs are excluded or included in cash-flowthe company assume that its customers and competitors will calculations.act rationally? One must ask if one’s own corporate structurepromotes or inhibits rational choices for one’s actions? Types of Costs Conventional but incorrect economic thinking pervades To make sensible business decisions, every business needs tomany other areas of mining, often in critical areas such as know its costs to produce its products. Of the variety of waysreserve definitions and the change in costs as reserves are to measure costs, some cost concepts are more appropriatedepleted. With few exceptions, mines commence at the shal- for certain problems than others. This section explores theselowest and/or highest-grade sections of the ore body and prog- different cost concepts and some subtleties in understandingress to parts that are less economically attractive. Moreover, discoveries are generally deeper and lower grade than Every business incurs costs that do not vary with outputexisting mines. This suggests that the cost of mining and, with and costs that do. A fixed cost is an expense that does not varyit, the price of mineral commodities must rise over time. Thus, with the level of output—for example, an annual payment tofor example, renewable sources of energy (solar, wind) are maintain a mining lease (assuming the payments are inde-commonly seen as the inevitable successors to today’s coal, pendent of production). The portion of a fixed cost that is notoil, and uranium supplies. recoverable is a sunk cost. Sunk costs should not affect subse- Yet even this intuitively obvious trend hasn’t proven cor- quent decisions and are excluded in preparing a cash flow ofrect over the last century, and economics provides much of a mining propertythe explanation. For example, Baumol and Blackman (1993) Example 1. You have spent $15 million evaluating adescribe work by themselves and others demonstrating that mining property over a long period of time, and the project“the real cost (price) of extraction for a sample of thirteen min- looks (almost) viable. Your accounting policy requires you toerals had declined for all but two between 1870 and 1956” and allocate the $15 million across the proven reserves, but whenthat “the price of fifteen resources for the period 1900 to 1986 this cost is included, the project fails to meet your requireduntil the ‘energy crises’ of the 1970 [showed] negligible upward investment return. Should the exploration costs be includedtrend in the real (inflation-adjusted) prices.” Practitioners who or excluded?have spent a long time in the industry know this well. Solution. The exploration costs should not enter into the The extraordinary growth in living standards since the decision to proceed or not. If you proceed with the project,industrial revolution has driven the demand for minerals, but your accountants will report a loss on the project (becausethe same technological developments that have underpinned they will write off the cost of exploration and assign it to thethis growth have also expanded the effective stocks of natural project), but if you do not proceed, your accountants will stillresources at a rate faster than their rate of exploitation. There report a loss. The $15 million is common to all alternativesis no guarantee that this historical trend will prevail in the because it has already been expended and is unrecoverable.future, but a long-term strategy that simply adopts the common Are these costs truly unrecoverable? The explorationview rather than one founded on the economics of supply and costs in this example may have already been spent, but they dodemand risks incorrect choices and over- or underinvestment. not automatically become sunk costs. You might not be able to recover your whole $15 million of expenditure, for example,COSTS but the property might be salable for $10 million. Only $5 mil-To most people the concept of cost is subject to no ambiguity. lion of the original $15 million is a sunk cost, and $10 millionIt is the amount of money one has to take out of their billfold, is a recoverable cost.
  3. 3. Economic Principles for Decision Making 311 How does one treat the cost of what is already owned, A supermarket valued at $0.5 million before a mine com-such as the exploration property in the preceding example mences might be valued at $1 million after the mine startsor one’s existing equipment? Such choices are common in due to the increased business it enjoys from mine personnel.operating mines, particularly when underutilized equipment Externalities are changes in value incurred by others outsideis owned and can potentially be used in new, though less-than- of the company that are not explicitly taken into account inideal ways. In these cases, the company must use the eco- any decision within the company.nomic cost to help make the decision, defined by the value There is a risk that economic assessments which do notof the opportunity that is forsaken. The choice is between take into account significant externalities might lead to incor-using the equipment and doing without the equipment, and rect choices. Many large firms already extend their assess-each alternative has var­ ous money costs and benefits. In the i ments to include externalities on social responsibility groundsfinance literature, these true economic costs are referred to as even if no legislated requirement has mandated this.opportunity costs. Example 2. You have some older equipment that cannot Marginal Costsbe used for overburden removal, and you propose to use it In economics, few concepts are more important than the con-for reclamation. You already own it, so there is no purchase cept of marginal cost.price and no cash flow. If you do not use it for reclamation, The marginal cost is the change in total cost. The counter-you could sell it for $1 million. Should the $1 million be part to marginal cost is marginal revenue. Marginal revenue isincluded in the cash-flow analysis and in the decision to use it the change in total revenue.for reclamation? One can consider almost any production process, which Solution. Yes. The alternative case has its costs, plus a will involve some fixed and some variable costs. As produc-revenue of $1 million (minus taxes) from the sale of the equip- tion expands, the fixed costs are unchanged, so the averagement, so this potential revenue is lost in the first case. per-unit cost of production attributable to this component Lost revenues (from the alternate scenarios) are called declines. If this were the only trend, then the highest pro-opportunity costs because, by accepting the project, other duction case would be the lowest overall cost of production.opportunities for using the assets are foregone. These true However, few production processes work this way. The fixedeconomic costs should be used regardless of the value that the parts of the process can only service a limited range of vari-accounting system places on the asset in question. able parts. As production expands for the same fixed compo- Variable costs change with the level of output. Typically, nents, the efficiency of the system declines. Each increment ofas output increases, so does the need for labor, fuel, elec- production incurs a little more variable costs than the previoustricity, and materials, so variable costs depend on the wages increment.and prices that a firm must pay for these inputs. Although For example, a loader/truck system is the archetypalvariable costs are commonly called operating costs, in the system in mining. The haul road establishment costs, loaderday-to-day decisions one cannot assume a one-to-one corre- capital costs, and most of the loader operating costs are thespondence between what an accountant calls an operating cost fixed components, and the trucks are the variable component.and what is truly a variable cost. Whether a cost is a fixed When only one truck is paired to the loader, the average costor a variable cost depends on the time frame of the decision. of production is high because the fixed costs of owning andFor yearly budgeting, labor costs are a variable cost, because operating the loader are spread over a relatively small produc-labor requirements can usually be increased or decreased in tion. The loader spends a lot of time idle while the one truckline with yearly production requirements. But on a day-to-day is hauling the material to be dumped. When two trucks arebasis, most labor costs are fixed. If a truck driver has reported allocated, production will increase—but not quite to doubleto work and there is no truck available, then this labor cost the previous amount, because there will be queuing at the startcannot be avoided. of the shift. The only extra costs are for the extra truck. As Thus, even if the production manager (making day-to-day additional trucks are added, production will increase furtherdecisions) and the planning engineer (making life-of-mine but by a declining amount as the increasing numbers of trucksdecisions) both have the same objective—to maximize com- interfere with each other.pany profit—the way they make their choices might be quite Figure 5.2-1 shows the idealized situation for this style ofdifferent. For a production manager, almost all costs are fixed production process using sample production and productionon a day-to-day basis, so from that perspective the lowest cost cost numbers for illustration.per ton is achieved when the production is at a maximum. Thus The average cost of production is initially high at lowthe normal and entirely rational objective for a production levels of production, and each increment of production has amanager is to forget about costs and just maximize produc- low but increasing marginal cost. If the marginal cost is lesstion. From the perspective of a long-range planning engineer, than the average cost, the average cost declines with increasesfew costs are fixed. There is scope to buy and sell equipment, in production. The production rate that yields the lowest aver-change equipment mix, and change the extraction sequence. age unit cost of production occurs where the marginal costDecisions must be made not only on production requirements curve crosses the average cost curve (30 units of productionbut also on optimization of costs, both capital and operating. in Figure 5.2-1). Any new mining development also includes costs that Although the lowest average unit cost of production isthe decision maker does not take into account. For example, certainly a desirable objective, usually the objective is tofollowing commencement of a new mine, the increased traf- maximize profits (or minimize losses). If the selling price isfic might require higher costs of local road maintenance. $2.33, for example, production can be expanded to 40 unitsDust and noise pollution might impose costs on people quite and the additional production still yields a return higher thanremoved from the project. This style of cost is termed an the marginal cost. Indeed, this is the rule: Expand productionexternality. Externalities can be both positive and negative. until the marginal cost equates to the (marginal) revenue. If in
  4. 4. 312 SME Mining Engineering Handbook 4.00 3.50 Marginal Cost Average Cost 3.00 $ per Unit of Production 2.50 $2.33/unit 2.00 1.50 $1.57/unit 1.00 $0.81/unit 0.50 0.00 0 10 20 30 40 50 60 70 80 90 100 Output (Production) Figure 5.2-1  Average and marginal cost curvesthis pricing scenario the production was expanded to 60 units, on production because the cost of transport to supply intowith an average cost of $2.33/unit, then the mine would still larger and more distant markets reduces the mine gate profitable. However the production from the first 40 units Most industrial minerals are in this category, as well as bulkwould be subsidizing the last 20 units of production. Profits commodities such as coal. How then can the optimum outputcannot be improved by increases in production rate where the be determined?marginal cost exceeds the marginal revenue. In these cases (where price cannot be assumed constant), A similar situation occurs for mines in a loss-making sit- the same logic and the same rule applies: Select an outputuation. In Figure  5.2-1, if the selling price is $0.81/unit, for level where the marginal cost equates to the (marginal) rev-example, the mine cannot avoid losses at any output level. enue. In this case the marginal revenue is not a constant; it tooBut the losses are minimized at the point where the marginal must be calculated. Example 3 illustrates how the marginalcost equates to the selling price (about 15 units of production), revenue calculation can be addressed.not at the lowest point on the average cost curve (30 units of Example 3. Consider a mine currently producing 8 Mtproduction). (million metric tons) of coal per year under a mix of spot For some simpler assessments (selecting loader/truck sales and contracts to a variety of regional customers. Atfleets, for example), reliable computer simulation packages any one time customers are all paying slightly differentare available. For most assessments, however, the compilation prices for the same coal, but in due course prices becomeof a graph similar to Figure  5.2-1 is a lengthy process. The more widely known and these influences reduce. Long-termmarginal cost curve normally cannot be calculated directly, contracts have price variation clauses that adjust to marketbecause as the production expands, the process employed to conditions. The average selling price for the existing out-undertake it frequently changes. If this example involved a put is $10/t. You can expand production by 1 Mt/yr at anloader/truck fleet, for example, the size of loader and truck operating cost (for this extra coal) of $6/t with only a smallselected might be quite different for an output of 60 units of amount of capital. Repaying this extra capital, you can stillproduction compared to an output of 20 units. Thus, a desired make your required return on investment at a selling priceproduction rate of 60 units requires design of a system appro- of only $9/t. You believe you can find additional custom-priate to this rate and its attendant costs, whereas a desired ers who will purchase the extra 1 Mt/yr at $9/t. Should youproduction rate of 30 units requires a system design appropri- proceed?ate to this lower rate—presumably using smaller equipment. Solution. This seems to be a clear-cut case. If the sell-The marginal cost is the change in total cost—calculated by ing price exceeds the marginal cost, profits increase with eachmultiplying the average cost at the higher production rate increase in production. The risk is that, lacking any ability toby this output and subtracting the equivalent total cost at the keep prices secret (never a good strategy, in any case) for anylower production rate. length of time or to differentiate the new coal from the old In this example, the selling price was assumed to be inde- coal, all of the output from the mine will be priced downward.pendent of production. For many mineral commodities such Your customers themselves have incentives to do this. Foras gold and silver, this is an appropriate assumption because instance, what is to stop your new customer from selling somegold and silver are readily transportable and freely traded on of your new coal to one of your old customers (at perhapsworld markets, and the production from any one mine—even $9.50/t), with both of them being better off?the biggest mines—is small compared to the size of the world In this example, prices are not independent of produc-market. But for many other commodities, price is dependent tion. Selling some coal below average price makes it harder to
  5. 5. Economic Principles for Decision Making 313maintain the price of your existing supply. Perhaps you only Table 5.2-1  Marginal revenue calculationrisk downward price revision by 5%, but this reduced price Totalapplies to all of your output, if not immediately, then cer- Production Production, Estimated Average Total Annualtainly in the near future. The marginal revenue is the change Scenario Mt/yr Selling Price per t Revenue, millionsin total revenue, and this is not the same as the proposed Current mine 8 $10.00 $80.0$9/t selling price that the new customer is initially prepared After expansion 9 $9.50 $85.5to pay. Expansion is only viable to the point where marginal Extra output 1 $5.50 $5.5cost equates to marginal revenue. Table 5.2-1 shows this Unit marginal revenue Marginal revenuecalculation. The additional output has an effective selling price (mar-ginal revenue) of just $5.50/t—a price at which the expanded equivalent present value by discounting—that is, dividing byproduction is not viable because it is less than the marginal the compounded interest rate.cost of $9/t. Of course, real-life cases always have additional For meaningful calculations of mining investment propo-complexities that are not included in this example, but the sitions, a complete tabulation is normally prepared for all ofprinciple applies. The change in total cost and total revenue the cash flows through each year of the project’s life. Theshould be applied to the change in production, and this result aggregate cash flow (the sum of the expected positive andshould guide the decision of whether or not to proceed, not the negative cash flows) in each year is calculated first, and thisnarrowly defined costs and revenues associated just with the value is turned into a present value via the applied discountextra production. rate. To account for uncertainty and other factors, the discount The confusion between average, incremental, and mar- rate is usually greater than the long-term interest rate.ginal payoffs can work the other way, too. Most managersnaturally hesitate to throw good money after bad, but if an Valuation at Constant Point in Timeexisting project is already making a loss, this may be irrel- The first series of time-value calculations apply simple formu-evant in the decision regarding incremental expenditure on it. las to bring anticipated cash flows to an equivalent time ref-Sometimes an existing project is yielding poor returns because erence basis for calculation. Simple calculations are groupedof a bottleneck in the production chain, and small incremental into two categories:investments to remove such bottlenecks can yield large mar- 1. How to turn a future value into the equivalent presentginal returns. value and vice versa, and Whenever optimization is the objective, marginal costs 2. How to turn a regular series of equal values occurringshould be the focus. over several years into an equivalent single amount in the Procedures aimed at pit optimization (in open-pit mines) present and vice versa.and cutoff grade calculations (in all types of mines) applythis identical principle. Starting from an initial ore body, they The two functions used to relate present values to future val-examine extensions to the ore body in all dimensions to ascer- ues and vice versa aretain whether the marginal revenues from the extension exceed 1. Compound amount function (future value), andthe marginal cost of extracting the additional ore and waste. 2. Present value function.The optimum limit of mining is where, at the margins, thereturn equates to the cost. The future value is determined by the following formula:TIME VALUE OF MONEY FV = PV × (1 + i) nMoney tomorrow is not as valuable as money today. Given wherethe choice of having the same amount of money in the future FV = future valueor right now, everyone would prefer to have it now. Money PV = present valuereceived in the future has some risk that it might not mate- i = interest rate (in the time period)rialize, but even if there was no such risk, it is still worth n = number of time periods (years)more if it is available for use now. If it is available now, the 1 + i)n = compound factor (things that one might conceivably do with the money are asbroad as possible. If it is not available until some time in the Example 4. Your company has to pay a reclamation bondfuture, then the opportunity set is limited to a smaller subset to the government for each hectare (ha) of disturbed land. Theof this first set. Maximum freedom to choose is always worth funds are held in trust, earning interest at 6% compoundedsomething—particularly in more uncertain environments. annually until reclamation is complete, whereupon they areTherefore, money to be received in the future must include a returned. If you disturb 40 ha of land this year and the bond ispremium if it is to be considered equivalent to money in hand $50,000/ha, how much do you expect to get back when recla-today. Future cash flows (money) must be discounted in order mation is completed in 3 years’ time?to compare with present cash flows. Solution. Almost every economic decision in mining involves cash Present value:   $50,000 # 40flows (spending money, receiving money) occurring at differ- (of money paid out now) = $2.0 millionent points of time. Consequently, economic evaluations mustincorporate a way for equating these money values at some Compound factor:   (1 + 0.06)3constant point in time (usually, now). For simple calculations, = 1.191future values are derived by taking current values and mul- Therefore,tiplying by the interest rate (compounded). Or, equivalently, Future value:   $2,382,000future values (anticipated cash flows) are turned into the
  6. 6. 314 SME Mining Engineering Handbook The present value function is used to move a future value Therefore, hourly cost = $1,175,300/6,000estimate back to the present and is the inverse of the future = $195.88 per hourvalue function: FV Almost all scientific or engineering calculators and PV = spreadsheets now include functions capable of undertaking ^1 + ihn these calculations directly.where 1 = present value function Discounted Cash-Flow Analysis ^1 + ihn Although all of the functions discussed in the previous sec- tion are important in determining values for activities occur- Example 5. You have received bids from two manufac- ring over time, their usefulness is limited because they do notturers for purchase of a new dragline. The first bid (A) is com- take taxation effects into account and need regular cash flows.petitive but from a company that requires payment in full on Since almost all real-life cases involve taxation, and operat-placement of order. The second bid (B) is for a higher price, ing costs and revenues vary over time, an alternative evalu-but no payment is required until the machine starts digging in ation method must be used. The method universally used for3 years. Which is the preferred option? almost all mining and other business evaluations is the dis- counted cash flow (DCF) technique. (This technique is only Dragline A bid price briefly introduced for a simple case; however, Chapter 2.4 in    (payment today): $30,000,000 the handbook addresses this technique from a broader per- Dragline B bid price spective.) In Mining Economics and Strategy (Runge 1998),    (payment 3 years’ time): $40,000,000 comprehensive examples of the DCF technique are set out for Required return on capital a wide range of mining applications.    (discount rate): 15% A big difference exists between corporate finance (i.e., Time n: 3 years costing, economics, and capital investment decisions) and financial accounting, which stresses incomes and earnings. Solution. While accounting procedures document what has happened, P resent value (of purchasing mining economics aims at informed decisions on what to do. Dragline B 3 years into future)  $40,000,000 For accounting purposes, all expenditures are normally appor-   # 0.6575 tioned over the period that the expenditure translates into use- $26,300,000 ful work. For planning and operating a business, there is no apportionment—allowance has to be made when the expense Dragline B has a lower cost than Dragline A in present actually occurs.value terms. Example 7. Consider the purchase of a dozer for $600,000 Functions are also used to relate a regular series of equal paid for today. The entire $600,000 is an immediate cash out-values occurring over several years into an equivalent single flow. An amount of $600,000 has to be available at the timeamount. The most useful of these is the capital recovery func- the dozer is delivered—before it has done any useful work.tion. Used to spread a present value amount evenly over a However, assuming straight-line depreciation over the 6-yearperiod of n years, it produces a series of equal values occur- life of the dozer, only $100,000 is considered an account-ring at the end of each year for the time period specified. ing expense in each year. Current earnings (reported profits) for this year are reduced only by $100,000. The remaining capital recovery factor = i i ]1 + ign $500,000 is expensed (counted as an operating cost) over the ]1 + ign - 1 = 1- 1 following 5 years. (1 + i) n To run the business, what is important is cash flow, not Example 6. The expected life of a rope shovel is 16 accounting profit. In Example 7, the company supplying theyears, after which time the mine will close and the salvage dozer requires the full purchase price to be paid now, not justvalue will be effectively zero. What is the annual owning cost, the amount of depreciation that the accountant attributes toincluding allowance for return on your capital invested in the this year’s cost of production. Furthermore, capital expendi-rope shovel? If the shovel works 6,000 hours per year, what is tures always occur before any production, whereas accountingthe hourly cost? conventions only assign their costs (and revenues) during or after production has taken place. Required return on capital (discount rate): 15% The objective of a cash-flow analysis is to simulate all of Cost of rope shovel: $7,000,000 the anticipated cash flows over the project’s life (and express Time (n): 16 years them in present value terms) to help make a decision to pro- ceed or not. The most obvious cash flows are Solution. • Revenues from sale of the products, Capital recovery factor:   0.15/[1 – (1/1.15)16] • Expenses incurred in producing the products, and = 0.15/[1 – 0.1069] • Capital expenditures necessary to bring about production. = 0.1679 Capital expenditures are tabulated in the cash flow in Equivalent annual cost of = $7,000,000 # 0.1679 the year prior to their use. The plant or equipment must be shovel over 16 years = $1,175,300/yr operational before any production takes place (the start of the
  7. 7. Economic Principles for Decision Making 315Table 5.2-2  Sample discounted cash flow Year* 0 1 2 3 4 5  1.  Production, oz — 32,000 50,000 50,000 50,000 45,000  2.  Operating revenue at $500/oz — $16,000 $25,000 $25,000 $25,000 $22,500  3.  Operating expenses — $10,598 $17,762 $19,339 $21,073 $20,882  4.  Operating profit (2 – 3) — $4,402 $7,238 $5,661 $3,927 $1,618  5.  Capital expenditure $15,000 — — — — —  6.  ax depreciation this year at 27.5% (declining balance) T — $4,125 $2,991 $2,168 $1,572 $1,140  7.  nd-of-year written-down value E — $10,875 $7,884 $5,716 $4,144 $3,005 for tax purposes  8.  Salvage value (= 7) — — — — — $3,005  9.  Taxable profit (4 – 6) — $277 $4,247 $3,493 $2,355 $47810. ncome tax payable at 35% tax rate I — $97 $1,486 $1,223 $824 $16711.  After-tax profit (9 – 10) — $180 $2,760 $2,270 $1,531 $31112.  Net cash flow (4 – 5 + 8 – 10) ($15,000) $4,305 $5,751 $4,439 $3,103 $4,45513.  Discount factor (at 15% ROI†) 1.0000 0.8696 0.7561 0.6575 0.5718 0.497214.  Discounted cash flow (12 × 13) ($15,000) $3,744 $4,349 $2,919 $1,774 $2,21515.  Net present value $0 — — — — —*All annual cash flows are in thousands, rounded to nearest thousand.†ROI = return on investment.period). With the end-of-year convention, capital expenditures Table 5.2-3  Base data for discounted cash-flow calculationare therefore placed at the end of the preceding year. Item Value Cash-flow tabulations should normally commence with Initial capital cost $15,000,000production tabulated on the top or near to the top of the table, Life of project 5 yearsbecause almost all of the revenue and many of the operatingexpenses are related to production. Revenues (the primary Salvage value at end of life At written-down valuecash inflow) are also tabulated at the top of the table. Production per year Varies To obtain the operating profit, operating costs are sub- Selling price $500/oztracted from the operating revenues. All operating expenses Annual operating expenses As shownare included in a cash-flow calculation, even if some of the Depreciation rate for tax purposes 27.5%costs pertain to production in following years. This differs   (declining balance)from the way operating costs are treated for accounting pur- Tax rate 35%poses, where expenses that pertain to production in succeed- Discount rate 15%ing time periods (e.g., advance stripping) are apportioned tothe period in which they directly relate to production. A sample discounted cash-flow tabulation for a mining Although the format for cash-flow tabulations in real-project is set out in Table 5.2-2. In this tabulation, a hypotheti- life applications—even for large projects—is similar tocal gold mine with a 5-year life produces up to 50,000 oz/yr Table 5.2‑2, even simple assessments include many more ele-and expects to sell all of the output at $500/oz. The main back- ments than shown. Elements commonly built into the DCFground data needed for this tabulation (or any discounted cash- tabulation include exchange rate factors, expected escalationflow tabulation) are set out in Table 5.2-3. and de-escalation of cost and revenue components (inflation In Table 5.2-3 the data has been deliberately chosen for adjustments), and finance charges.illustrative purposes so that the selling price of $500/oz yieldsa net present value of zero at a discount rate of 15%. This REFERENCESdiscount rate is just a guideline and is usually determined by Baumol, W.J., and Blackman, S.A.B. 1993. Natural resources.senior company finance personnel weighing the relative risks In The Fortune Encyclopaedia of Economics. Edited byand the cost of capital between this project and any alternative D.R. Henderson. New York: Warner Books. pp. 40–41.projects that the company might otherwise choose to apply its Runge, I.C. 1998. Mining Economics and Strategy. Littleton,resources to. Thus, in this example, if the gold price exceeded CO: SME.$500/oz, the internal rate of return would exceed this (oppor-tunity) cost of capital, and the project could proceed.