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CHAPTER 5.2

Economic Principles for Decision Making

Ian Runge

Mining used to be a business primarily focused on the technical aspects of getting valuable ore out of the ground and extracting the minerals in a metallurgically efficient way. Without deny-ing the importance of these skills, a narrow focus on technical issues is no longer sufficient to guarantee success, even in rich ore bodies. Skill in economics is an essential partner to tech-nical skill in every step of the mining process. The economic way of thinking starts before the first drill hole is put in the ground and includes not just the most economic way of mining but also the most economic method of assessing mining proj-ects. Economics directs mining strategy and takes into account changes in worldwide demand for mineral products.

This chapter introduces the economic approach to deci-sion making and focuses on how individuals engaged in mining enterprises make decisions using sound economic principles. While the better decisions and the more successful enterprises are adopted and copied by others, the less-successful enter-prises fail or are taken over, and outdated practices disappear. Thus the structure of the industry evolves. This chapter pres-ents these economically based decisions in three parts.

The first section, “Mining Economics and Strategy,” looks at the industry from a strategic perspective—the broad trends in the mining world and the way that much of the world is interconnected—and highlights and challenges some common misconceptions of mining economics. For long-term success, practitioners must at least be cognizant of these broader influences.

The second section, “Costs,” follows a narrower approach. Fortunately, most economic assessments in mines do not require a broad understanding of the whole financial world but can achieve reliable answers focused on what is happening in the company, the mine site, or just one part of the mine. This section focuses on costs and how the understand-ing of costs is critical for decision making—from day-to-day choices at the mine face to long-term life-of-mine planning.

The third section, “Time Value of Money,” examines one of the most important aspects of assessment in all but the sim-plest of mines: understanding what is happening in the mine over an extended period of time. Investing in new, bigger machinery at the start can reduce costs and provides benefits over the rest of the mine life. Mining the richest ore first can

increase profits and reduce debt but can also impact mine life. Understanding these issues requires economic tools to assess the time value of money.

MINING ECONOMICS AND STRATEGYMost approaches to economics assume that one person or one company’s actions do not affect the whole market. This assumption is usually quite reasonable, because even the biggest mining companies usually only account for a small proportion of world production. A single extra ton of cop-per produced at one mine will not change the world price of copper. Yet the world is interconnected, and the results for one participant in such an interconnected marketplace often depend on the choices (strategies) of all the other participants. Perhaps that extra ton of copper will not affect the world price, but if the changed economic forces that allow this mine to expand production also apply to its competitors, then maybe they too will expand their production. If everyone expands production, then perhaps the world price will change.

For many decisions in operating mines, the standard (non-strategic) approach of ignoring what competitors are doing and using conventional economic models is quite appropriate. If an electric rope shovel is more economical than a diesel-powered hydraulic excavator in a mine, this choice is unlikely to be wrong even when the outside world changes quite sub-stantially, or even if other mines elsewhere in the world favor a different choice.

Nevertheless, there are many areas of mining and mining-specific applications where the use of conventional models must be used cautiously. One such area is in the understanding of risk and return. With financial investments (in the stock mar-ket, for example), low-risk, lower-return opportunities form part of a continuous spectrum to higher-risk and higher-return opportunities. In this style of market, the choice of a higher (expected) return opportunity is synonymous with greater uncertainty and higher risk. With individual mine investment, this risk/return trade-off is not so clear-cut. The uniqueness of each ore body and the idiosyncratic risk attached to each project means that higher returns are not necessarily synony-mous with higher risk. This creates opportunities for operators who understand the characteristics of the ore body, and who

Ian Runge, Founder, Runge Ltd., Brisbane, Queensland, Australia

310 SME Mining Engineering Handbook

understand the risks associated with mining it, to potentially make higher-than-normal returns without exposing the com-pany to any higher risk. It also inhibits some decision making when projects are evaluated using conventional models that are founded on efficient market risk/return characteristics.

Strategic considerations are also important because of high sunk costs in mining—a characteristic of mining that is less important in most other industries. If a company has high sunk costs but low cash costs and the market price declines quite sub stantially, the company is unlikely to go out of busi-ness or even to reduce production. With lower prices, cash flow is still likely to be positive, and even though the company might be reporting losses (from an accounting perspective), reducing production will result in even larger losses.

This raises two important strategic issues. If poten tial competitors have knowledge of a company’s capital struc-ture, acting rationally, they might be deterred from entering the same market, knowing that the company will not easily be put out of busi ness. With less competition, the company may be able to gain a price premium. However, this compara-tive advantage can also work against the company if custom-ers also know about the company’s capital structure. If they believe the company will continue producing so long as price exceeds the company’s cash cost, the company is vulnerable to exploi tation. What should the company’s strategy be? Can the company assume that its customers and competitors will act rationally? One must ask if one’s own corporate structure promotes or inhibits rational choices for one’s actions?

Conventional but incorrect economic thinking pervades many other areas of mining, often in critical areas such as reserve definitions and the change in costs as reserves are depleted. With few exceptions, mines commence at the shal-lowest and/or highest-grade sections of the ore body and prog-ress to parts that are less economically attractive. Moreover, new discoveries are generally deeper and lower grade than existing mines. This suggests that the cost of mining and, with it, the price of mineral commodities must rise over time. Thus, for example, renewable sources of energy (solar, wind) are commonly seen as the inevitable successors to today’s coal, oil, and uranium supplies.

Yet even this intuitively obvious trend hasn’t proven cor-rect over the last century, and economics provides much of the explanation. For example, Baumol and Blackman (1993) describe work by themselves and others demonstrating that “the real cost (price) of extraction for a sample of thirteen min-erals had declined for all but two between 1870 and 1956” and that “the price of fifteen resources for the period 1900 to 1986 until the ‘energy crises’ of the 1970 [showed] negligible upward trend in the real (inflation-adjusted) prices.” Practitioners who have spent a long time in the industry know this well.

The extraordinary growth in living standards since the industrial revolution has driven the demand for minerals, but the same technological developments that have underpinned this growth have also expanded the effective stocks of natural resources at a rate faster than their rate of exploitation. There is no guarantee that this historical trend will prevail in the future, but a long-term strategy that simply adopts the common view rather than one founded on the economics of supply and demand risks incorrect choices and over- or underinvestment.

COSTSTo most people the concept of cost is subject to no ambiguity. It is the amount of money one has to take out of their billfold,

purse, or bank account to buy something. Day-to-day trans-actions seldom require any further discernment, because pur-chasing a small item on its own does not evidently preclude the purchase of anything else later on. For larger expenditures, the real cost is more evident. An overseas vacation might mean delaying the purchase of a new car for another year; in deciding to spend the money on the vacation, one must be comfortable with the idea of driving the old car for longer. The decision—the real cost of the vacation and the one that influ-ences choice—is based on the imagined loss of enjoyment and utility from driving around in the new car that much sooner.

In economics, the cost of anything is the highest-valued opportunity necessarily forsaken. This chapter looks at cost from this economic perspective. Unlike accounting costs, which are historical, the economic view of costs is a forward-looking one. Costs in this sense inform decision making, choosing between the imagined value a person will enjoy from following one path and the value of an alternative path. The tools described in this chapter and in the following econom-ics chapters are aimed at understanding this value in order to help make these decisions. This chapter introduces the con-cepts of marginal, average, variable, fixed, and sunk costs. It illustrates why the marginal cost calculation is such a vital one in pit optimization and in determining the scale of investments and why certain costs are excluded or included in cash-flow calculations.

Types of CostsTo make sensible business decisions, every business needs to know its costs to produce its products. Of the variety of ways to measure costs, some cost concepts are more appropriate for certain problems than others. This section explores these different cost concepts and some subtleties in understanding them.

Every business incurs costs that do not vary with output and costs that do. A fixed cost is an expense that does not vary with the level of output—for example, an annual payment to maintain a mining lease (assuming the payments are inde-pendent of production). The portion of a fixed cost that is not recoverable is a sunk cost. Sunk costs should not affect subse-quent decisions and are excluded in preparing a cash flow of a mining property

Example 1. You have spent $15 million evaluating a mining property over a long period of time, and the project looks (almost) viable. Your accounting policy requires you to allocate the $15 million across the proven reserves, but when this cost is included, the project fails to meet your required investment return. Should the exploration costs be included or excluded?

Solution. The exploration costs should not enter into the decision to proceed or not. If you proceed with the project, your accountants will report a loss on the project (because they will write off the cost of exploration and assign it to the project), but if you do not proceed, your accountants will still report a loss. The $15 million is common to all alternatives because it has already been expended and is unrecoverable.

Are these costs truly unrecoverable? The exploration costs in this example may have already been spent, but they do not automatically become sunk costs. You might not be able to recover your whole $15 million of expenditure, for example, but the property might be salable for $10 million. Only $5 mil-lion of the original $15 million is a sunk cost, and $10 million is a recoverable cost.

Economic Principles for Decision Making 311

How does one treat the cost of what is already owned, such as the exploration property in the preceding example or one’s existing equipment? Such choices are common in operating mines, particularly when underutilized equipment is owned and can potentially be used in new, though less-than-ideal ways. In these cases, the company must use the eco-nomic cost to help make the decision, defined by the value of the opportunity that is forsaken. The choice is between using the equipment and doing without the equipment, and each alternative has var ious money costs and benefits. In the finance literature, these true economic costs are referred to as opportunity costs.

Example 2. You have some older equipment that cannot be used for overburden removal, and you propose to use it for reclamation. You already own it, so there is no purchase price and no cash flow. If you do not use it for reclamation, you could sell it for $1 million. Should the $1 million be included in the cash-flow analysis and in the decision to use it for reclamation?

Solution. Yes. The alternative case has its costs, plus a revenue of $1 million (minus taxes) from the sale of the equip-ment, so this potential revenue is lost in the first case.

Lost revenues (from the alternate scenarios) are called opportunity costs because, by accepting the project, other opportunities for using the assets are foregone. These true economic costs should be used regardless of the value that the accounting system places on the asset in question.

Variable costs change with the level of output. Typically, as output increases, so does the need for labor, fuel, elec-tricity, and materials, so variable costs depend on the wages and prices that a firm must pay for these inputs. Although variable costs are commonly called operating costs, in the day-to-day decisions one cannot assume a one-to-one corre-spondence between what an accountant calls an operating cost and what is truly a variable cost. Whether a cost is a fixed or a variable cost depends on the time frame of the decision. For yearly budgeting, labor costs are a variable cost, because labor requirements can usually be increased or decreased in line with yearly production requirements. But on a day-to-day basis, most labor costs are fixed. If a truck driver has reported to work and there is no truck available, then this labor cost cannot be avoided.

Thus, even if the production manager (making day-to-day decisions) and the planning engineer (making life-of-mine decisions) both have the same objective—to maximize com-pany profit—the way they make their choices might be quite different. For a production manager, almost all costs are fixed on a day-to-day basis, so from that perspective the lowest cost per ton is achieved when the production is at a maximum. Thus the normal and entirely rational objective for a production manager is to forget about costs and just maximize produc-tion. From the perspective of a long-range planning engineer, few costs are fixed. There is scope to buy and sell equipment, change equipment mix, and change the extraction sequence. Decisions must be made not only on production requirements but also on optimization of costs, both capital and operating.

Any new mining development also includes costs that the decision maker does not take into account. For example, following commencement of a new mine, the increased traf-fic might require higher costs of local road maintenance. Dust and noise pollution might impose costs on people quite removed from the project. This style of cost is termed an externality. Externalities can be both positive and negative.

A supermarket valued at $0.5 million before a mine com-mences might be valued at $1 million after the mine starts due to the increased business it enjoys from mine personnel. Externalities are changes in value incurred by others outside of the company that are not explicitly taken into account in any decision within the company.

There is a risk that economic assessments which do not take into account significant externalities might lead to incor-rect choices. Many large firms already extend their assess-ments to include externalities on social responsibility grounds even if no legislated requirement has mandated this.

Marginal CostsIn economics, few concepts are more important than the con-cept of marginal cost.

The marginal cost is the change in total cost. The counter-part to marginal cost is marginal revenue. Marginal revenue is the change in total revenue.

One can consider almost any production process, which will involve some fixed and some variable costs. As produc-tion expands, the fixed costs are unchanged, so the average per-unit cost of production attributable to this component declines. If this were the only trend, then the highest pro-duction case would be the lowest overall cost of production. However, few production processes work this way. The fixed parts of the process can only service a limited range of vari-able parts. As production expands for the same fixed compo-nents, the efficiency of the system declines. Each increment of production incurs a little more variable costs than the previous increment.

For example, a loader/truck system is the archetypal system in mining. The haul road establishment costs, loader capital costs, and most of the loader operating costs are the fixed components, and the trucks are the variable component. When only one truck is paired to the loader, the average cost of production is high because the fixed costs of owning and operating the loader are spread over a relatively small produc-tion. The loader spends a lot of time idle while the one truck is hauling the material to be dumped. When two trucks are allocated, production will increase—but not quite to double the previous amount, because there will be queuing at the start of the shift. The only extra costs are for the extra truck. As additional trucks are added, production will increase further but by a declining amount as the increasing numbers of trucks interfere with each other.

Figure 5.2-1 shows the idealized situation for this style of production process using sample production and production cost numbers for illustration.

The average cost of production is initially high at low levels of production, and each increment of production has a low but increasing marginal cost. If the marginal cost is less than the average cost, the average cost declines with increases in production. The production rate that yields the lowest aver-age unit cost of production occurs where the marginal cost curve crosses the average cost curve (30 units of production in Figure 5.2-1).

Although the lowest average unit cost of production is certainly a desirable objective, usually the objective is to maximize profits (or minimize losses). If the selling price is $2.33, for example, production can be expanded to 40 units and the additional production still yields a return higher than the marginal cost. Indeed, this is the rule: Expand production until the marginal cost equates to the (marginal) revenue. If in

312 SME Mining Engineering Handbook

this pricing scenario the production was expanded to 60 units, with an average cost of $2.33/unit, then the mine would still be profitable. However the production from the first 40 units would be subsidizing the last 20 units of production. Profits cannot be improved by increases in production rate where the marginal cost exceeds the marginal revenue.

A similar situation occurs for mines in a loss-making sit-uation. In Figure 5.2-1, if the selling price is $0.81/unit, for example, the mine cannot avoid losses at any output level. But the losses are minimized at the point where the marginal cost equates to the selling price (about 15 units of production), not at the lowest point on the average cost curve (30 units of production).

For some simpler assessments (selecting loader/truck fleets, for example), reliable computer simulation packages are available. For most assessments, however, the compilation of a graph similar to Figure 5.2-1 is a lengthy process. The marginal cost curve normally cannot be calculated directly, because as the production expands, the process employed to undertake it frequently changes. If this example involved a loader/truck fleet, for example, the size of loader and truck selected might be quite different for an output of 60 units of production compared to an output of 20 units. Thus, a desired production rate of 60 units requires design of a system appro-priate to this rate and its attendant costs, whereas a desired production rate of 30 units requires a system design appropri-ate to this lower rate—presumably using smaller equipment. The marginal cost is the change in total cost—calculated by multiplying the average cost at the higher production rate by this output and subtracting the equivalent total cost at the lower production rate.

In this example, the selling price was assumed to be inde-pendent of production. For many mineral commodities such as gold and silver, this is an appropriate assumption because gold and silver are readily transportable and freely traded on world markets, and the production from any one mine—even the biggest mines—is small compared to the size of the world market. But for many other commodities, price is dependent

on production because the cost of transport to supply into larger and more distant markets reduces the mine gate price. Most industrial minerals are in this category, as well as bulk commodities such as coal. How then can the optimum output be determined?

In these cases (where price cannot be assumed constant), the same logic and the same rule applies: Select an output level where the marginal cost equates to the (marginal) rev-enue. In this case the marginal revenue is not a constant; it too must be calculated. Example 3 illustrates how the marginal revenue calculation can be addressed.

Example 3. Consider a mine currently producing 8 Mt (million metric tons) of coal per year under a mix of spot sales and contracts to a variety of regional customers. At any one time customers are all paying slightly different prices for the same coal, but in due course prices become more widely known and these influences reduce. Long-term contracts have price variation clauses that adjust to market conditions. The average selling price for the existing out-put is $10/t. You can expand production by 1 Mt/yr at an operating cost (for this extra coal) of $6/t with only a small amount of capital. Repaying this extra capital, you can still make your required return on investment at a selling price of only $9/t. You believe you can find additional custom-ers who will purchase the extra 1 Mt/yr at $9/t. Should you proceed?

Solution. This seems to be a clear-cut case. If the sell-ing price exceeds the marginal cost, profits increase with each increase in production. The risk is that, lacking any ability to keep prices secret (never a good strategy, in any case) for any length of time or to differentiate the new coal from the old coal, all of the output from the mine will be priced downward. Your customers themselves have incentives to do this. For instance, what is to stop your new customer from selling some of your new coal to one of your old customers (at perhaps $9.50/t), with both of them being better off?

In this example, prices are not independent of produc-tion. Selling some coal below average price makes it harder to

0 10 20 30 40 50Output (Production)

$ pe

r Uni

t of P

rodu

ctio

n

60 70 80 90 1000.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

Marginal Cost Average Cost

$2.33/unit

$1.57/unit

$0.81/unit

Figure 5.2-1 Average and marginal cost curves

Economic Principles for Decision Making 313

maintain the price of your existing supply. Perhaps you only risk downward price revision by 5%, but this reduced price applies to all of your output, if not immediately, then cer-tainly in the near future. The marginal revenue is the change in total revenue, and this is not the same as the proposed $9/t selling price that the new customer is initially prepared to pay. Expansion is only viable to the point where marginal cost equates to marginal revenue. Table 5.2-1 shows this calculation.

The additional output has an effective selling price (mar-ginal revenue) of just $5.50/t—a price at which the expanded production is not viable because it is less than the marginal cost of $9/t. Of course, real-life cases always have additional complexities that are not included in this example, but the principle applies. The change in total cost and total revenue should be applied to the change in production, and this result should guide the decision of whether or not to proceed, not the narrowly defined costs and revenues associated just with the extra production.

The confusion between average, incremental, and mar-ginal payoffs can work the other way, too. Most managers naturally hesitate to throw good money after bad, but if an existing project is already making a loss, this may be irrel-evant in the decision regarding incremental expenditure on it. Sometimes an existing project is yielding poor returns because of a bottleneck in the production chain, and small incremental investments to remove such bottlenecks can yield large mar-ginal returns.

Whenever optimization is the objective, marginal costs should be the focus.

Procedures aimed at pit optimization (in open-pit mines) and cutoff grade calculations (in all types of mines) apply this identical principle. Starting from an initial ore body, they examine extensions to the ore body in all dimensions to ascer-tain whether the marginal revenues from the extension exceed the marginal cost of extracting the additional ore and waste. The optimum limit of mining is where, at the margins, the return equates to the cost.

TIME VALUE OF MONEYMoney tomorrow is not as valuable as money today. Given the choice of having the same amount of money in the future or right now, everyone would prefer to have it now. Money received in the future has some risk that it might not mate-rialize, but even if there was no such risk, it is still worth more if it is available for use now. If it is available now, the things that one might conceivably do with the money are as broad as possible. If it is not available until some time in the future, then the opportunity set is limited to a smaller subset of this first set. Maximum freedom to choose is always worth something—particularly in more uncertain environments. Therefore, money to be received in the future must include a premium if it is to be considered equivalent to money in hand today. Future cash flows (money) must be discounted in order to compare with present cash flows.

Almost every economic decision in mining involves cash flows (spending money, receiving money) occurring at differ-ent points of time. Consequently, economic evaluations must incorporate a way for equating these money values at some constant point in time (usually, now). For simple calculations, future values are derived by taking current values and mul-tiplying by the interest rate (compounded). Or, equivalently, future values (anticipated cash flows) are turned into the

equivalent present value by discounting—that is, dividing by the compounded interest rate.

For meaningful calculations of mining investment propo-sitions, a complete tabulation is normally prepared for all of the cash flows through each year of the project’s life. The aggregate cash flow (the sum of the expected positive and negative cash flows) in each year is calculated first, and this value is turned into a present value via the applied discount rate. To account for uncertainty and other factors, the discount rate is usually greater than the long-term interest rate.

Valuation at Constant Point in TimeThe first series of time-value calculations apply simple formu-las to bring anticipated cash flows to an equivalent time ref-erence basis for calculation. Simple calculations are grouped into two categories:

1. How to turn a future value into the equivalent present value and vice versa, and

2. How to turn a regular series of equal values occurring over several years into an equivalent single amount in the present and vice versa.

The two functions used to relate present values to future val-ues and vice versa are

1. Compound amount function (future value), and2. Present value function.

The future value is determined by the following formula:

FV = PV × (1 + i) n

where FV = future value PV = present value i = interest rate (in the time period) n = number of time periods (years) (1 + i)n = compound factor

Example 4. Your company has to pay a reclamation bond to the government for each hectare (ha) of disturbed land. The funds are held in trust, earning interest at 6% compounded annually until reclamation is complete, whereupon they are returned. If you disturb 40 ha of land this year and the bond is $50,000/ha, how much do you expect to get back when recla-mation is completed in 3 years’ time?

Solution.Present value: $50,000 # 40(of money paid out now) = $2.0 million

Compound factor: (1 + 0.06)3

= 1.191Therefore,Future value: $2,382,000

Table 5.2-1 Marginal revenue calculation

Production Scenario

Total Production,

Mt/yrEstimated Average Selling Price per t

Total Annual Revenue, millions

Current mine 8 $10.00 $80.0After expansion 9 $9.50 $85.5 Extra output 1 $5.50

Unit marginal revenue$5.5

Marginal revenue

314 SME Mining Engineering Handbook

The present value function is used to move a future value estimate back to the present and is the inverse of the future value function:

PVi

FV1 n=+^ h

where

i11

n+^ h = present value function

Example 5. You have received bids from two manufac-turers for purchase of a new dragline. The first bid (A) is com-petitive but from a company that requires payment in full on placement of order. The second bid (B) is for a higher price, but no payment is required until the machine starts digging in 3 years. Which is the preferred option?

Dragline A bid price (payment today): $30,000,000Dragline B bid price (payment 3 years’ time): $40,000,000Required return on capital (discount rate): 15%Time n: 3 years

Solution. Present value (of purchasing Dragline B 3 years into future) $40,000,000

# 0.6575$26,300,000

Dragline B has a lower cost than Dragline A in present value terms.

Functions are also used to relate a regular series of equal values occurring over several years into an equivalent single amount. The most useful of these is the capital recovery func-tion. Used to spread a present value amount evenly over a period of n years, it produces a series of equal values occur-ring at the end of each year for the time period specified.

( )i

i

i

i i

11

1 1 1

1capital recovery factorn

n

n=-

+

=+ -

+]

]

g

g

Example 6. The expected life of a rope shovel is 16 years, after which time the mine will close and the salvage value will be effectively zero. What is the annual owning cost, including allowance for return on your capital invested in the rope shovel? If the shovel works 6,000 hours per year, what is the hourly cost?

Required return on capital (discount rate): 15%Cost of rope shovel: $7,000,000Time (n): 16 years

Solution.Capital recovery factor: 0.15/[1 – (1/1.15)16] = 0.15/[1 – 0.1069] = 0.1679

Equivalent annual cost of = $7,000,000 # 0.1679shovel over 16 years = $1,175,300/yr

Therefore, hourly cost = $1,175,300/6,000 = $195.88 per hour

Almost all scientific or engineering calculators and spreadsheets now include functions capable of undertaking these calculations directly.

Discounted Cash-Flow AnalysisAlthough all of the functions discussed in the previous sec-tion are important in determining values for activities occur-ring over time, their usefulness is limited because they do not take taxation effects into account and need regular cash flows. Since almost all real-life cases involve taxation, and operat-ing costs and revenues vary over time, an alternative evalu-ation method must be used. The method universally used for almost all mining and other business evaluations is the dis-counted cash flow (DCF) technique. (This technique is only briefly introduced for a simple case; however, Chapter 2.4 in the handbook addresses this technique from a broader per-spective.) In Mining Economics and Strategy (Runge 1998), comprehensive examples of the DCF technique are set out for a wide range of mining applications.

A big difference exists between corporate finance (i.e., costing, economics, and capital investment decisions) and financial accounting, which stresses incomes and earnings. While accounting procedures document what has happened, mining economics aims at informed decisions on what to do. For accounting purposes, all expenditures are normally appor-tioned over the period that the expenditure translates into use-ful work. For planning and operating a business, there is no apportionment—allowance has to be made when the expense actually occurs.

Example 7. Consider the purchase of a dozer for $600,000 paid for today. The entire $600,000 is an immediate cash out-flow. An amount of $600,000 has to be available at the time the dozer is delivered—before it has done any useful work. However, assuming straight-line depreciation over the 6-year life of the dozer, only $100,000 is considered an account-ing expense in each year. Current earnings (reported profits) for this year are reduced only by $100,000. The remaining $500,000 is expensed (counted as an operating cost) over the following 5 years.

To run the business, what is important is cash flow, not accounting profit. In Example 7, the company supplying the dozer requires the full purchase price to be paid now, not just the amount of depreciation that the accountant attributes to this year’s cost of production. Furthermore, capital expendi-tures always occur before any production, whereas accounting conventions only assign their costs (and revenues) during or after production has taken place.

The objective of a cash-flow analysis is to simulate all of the anticipated cash flows over the project’s life (and express them in present value terms) to help make a decision to pro-ceed or not. The most obvious cash flows are

• Revenues from sale of the products,• Expenses incurred in producing the products, and• Capital expenditures necessary to bring about production.

Capital expenditures are tabulated in the cash flow in the year prior to their use. The plant or equipment must be operational before any production takes place (the start of the

Economic Principles for Decision Making 315

period). With the end-of-year convention, capital expenditures are therefore placed at the end of the preceding year.

Cash-flow tabulations should normally commence with production tabulated on the top or near to the top of the table, because almost all of the revenue and many of the operating expenses are related to production. Revenues (the primary cash inflow) are also tabulated at the top of the table.

To obtain the operating profit, operating costs are sub-tracted from the operating revenues. All operating expenses are included in a cash-flow calculation, even if some of the costs pertain to production in following years. This differs from the way operating costs are treated for accounting pur-poses, where expenses that pertain to production in succeed-ing time periods (e.g., advance stripping) are apportioned to the period in which they directly relate to production.

A sample discounted cash-flow tabulation for a mining project is set out in Table 5.2-2. In this tabulation, a hypotheti-cal gold mine with a 5-year life produces up to 50,000 oz/yr and expects to sell all of the output at $500/oz. The main back-ground data needed for this tabulation (or any discounted cash-flow tabulation) are set out in Table 5.2-3.

In Table 5.2-3 the data has been deliberately chosen for illustrative purposes so that the selling price of $500/oz yields a net present value of zero at a discount rate of 15%. This discount rate is just a guideline and is usually determined by senior company finance personnel weighing the relative risks and the cost of capital between this project and any alternative projects that the company might otherwise choose to apply its resources to. Thus, in this example, if the gold price exceeded $500/oz, the internal rate of return would exceed this (oppor-tunity) cost of capital, and the project could proceed.

Although the format for cash-flow tabulations in real-life applications—even for large projects—is similar to Table 5.2-2, even simple assessments include many more ele-ments than shown. Elements commonly built into the DCF tabulation include exchange rate factors, expected escalation and de-escalation of cost and revenue components (inflation adjustments), and finance charges.

REFERENCESBaumol, W.J., and Blackman, S.A.B. 1993. Natural resources.

In The Fortune Encyclopaedia of Economics. Edited by D.R. Henderson. New York: Warner Books. pp. 40–41.

Runge, I.C. 1998. Mining Economics and Strategy. Littleton, CO: SME.

Table 5.2-3 Base data for discounted cash-flow calculation

Item Value

Initial capital cost $15,000,000

Life of project 5 yearsSalvage value at end of life At written-down valueProduction per year VariesSelling price $500/ozAnnual operating expenses As shownDepreciation rate for tax purposes (declining balance)

27.5%

Tax rate 35%Discount rate 15%

Table 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. Tax depreciation this year at 27.5% (declining balance) — $4,125 $2,991 $2,168 $1,572 $1,140

7. End-of-year written-down valuefor tax purposes

— $10,875 $7,884 $5,716 $4,144 $3,005

8. Salvage value (= 7) — — — — — $3,005

9. Taxable profit (4 – 6) — $277 $4,247 $3,493 $2,355 $478

10. Income tax payable at 35% tax rate — $97 $1,486 $1,223 $824 $167

11. After-tax profit (9 – 10) — $180 $2,760 $2,270 $1,531 $311

12. Net cash flow (4 – 5 + 8 – 10) ($15,000) $4,305 $5,751 $4,439 $3,103 $4,455

13. Discount factor (at 15% ROI†) 1.0000 0.8696 0.7561 0.6575 0.5718 0.4972

14. Discounted cash flow (12 × 13) ($15,000) $3,744 $4,349 $2,919 $1,774 $2,215

15. Net present value $0 — — — — —

*All annual cash flows are in thousands, rounded to nearest thousand.†ROI = return on investment.