Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III. Practical Problems in Capital Budgeting 10. A Project is Not a Black Box © The McGraw−Hill Companies, 2003 CHAPTER TEN 254 A PROJECT IS NOT A BLACK BOX Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III. Practical Problems in Capital Budgeting 10. A Project is Not a Black Box © The McGraw−Hill Companies, 2003 A BLACK BOX is something that we accept and use but do not understand. For most of us a computer is a black box. We may know what it is supposed to do, but we do not understand how it works and, if something breaks, we cannot fix it. We have been treating capital projects as black boxes. In other words, we have talked as if man- agers are handed unbiased cash-flow forecasts and their only task is to assess risk, choose the right discount rate, and crank out net present value. Actual financial managers won’t rest until they un- derstand what makes the project tick and what could go wrong with it. Remember Murphy’s law, “If anything can go wrong, it will,” and O’Reilly’s corollary, “at the worst possible time.” Even if the project’s risk is wholly diversifiable, you still need to understand why the venture could fail. Once you know that, you can decide whether it is worth trying to resolve the uncertainty. Maybe further expenditure on market research would clear up those doubts about acceptance by con- sumers, maybe another drill hole would give you a better idea of the size of the ore body, and maybe some further work on the test bed would confirm the durability of those welds. If the project really has a negative NPV, the sooner you can identify it, the better. And even if you decide that it is worth going ahead on the basis of present information, you do not want to be caught by surprise if things subsequently go wrong. You want to know the danger signals and the actions you might take. We will show you how to use sensitivity analysis, break-even analysis, and Monte Carlo simulation to identify crucial assumptions and to explore what can go wrong. There is no magic in these tech- niques, just computer-assisted common sense. You don’t need a license to use them. Discounted-cash-flow analysis commonly assumes that companies hold assets passively, and it ig- nores the opportunities to expand the project if it is successful or to bail out if it is not. However, wise managers value these opportunities. They look for ways to capitalize on success and to reduce the costs of failure, and they are prepared to pay up for projects that give them this flexibility. Opportunities to modify projects as the future unfolds are known as real options. We describe several important real op- tions, and we show how to use decision trees to set out these options’ attributes and implications. 255 Uncertainty means that more things can happen than will happen. Whenever you are confronted with a cash-flow forecast, you should try to discover what else can happen. Put yourself in the well-heeled shoes of the treasurer of the Otobai Company in Osaka, Japan. You are considering the introduction of an electrically powered mo- tor scooter for city use. Your staff members have prepared the cash-flow forecasts shown in Table 10.1. Since NPV is positive at the 10 percent opportunity cost of cap- ital, it appears to be worth going ahead. Before you decide, you want to delve into these forecasts and identify the key variables that determine whether the project succeeds or fails. It turns out that the marketing department has estimated revenue as follows: ϭ .1 ϫ 1 million ϭ 100,000 scooters Unit sales ϭ new product’s share of market ϫ size of scooter market NPV ϭϪ15 ϩ a 10 tϭ1 3 11.102 t ϭϩ¥3.43 billion 10.1 SENSITIVITY ANALYSIS Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III. Practical Problems in Capital Budgeting 10. A Project is Not a Black Box © The McGraw−Hill Companies, 2003 The production department has estimated variable costs per unit as ¥300,000. Since projected volume is 100,000 scooters per year, total variable cost is ¥30 billion. Fixed costs are ¥3 billion per year. The initial investment can be depreciated on a straight- line basis over the 10-year period, and profits are taxed at a rate of 50 percent. These seem to be the important things you need to know, but look out for unidentified variables. Perhaps there are patent problems, or perhaps you will need to invest in service stations that will recharge the scooter batteries. The greatest dangers often lie in these unknown unknowns, or “unk-unks,” as scien- tists call them. Having found no unk-unks (no doubt you’ll find them later), you conduct a sen- sitivity analysis with respect to market size, market share, and so on. To do this, the marketing and production staffs are asked to give optimistic and pessimistic estimates for the underlying variables. These are set out in the left-hand columns of Table 10.2. The right-hand side shows what happens to the project’s net present value if the variables are set one at a time to their optimistic and pessimistic values. Your project appears to be by no means a sure thing. The most dangerous variables appear to be market share and unit variable cost. If market share is only .04 (and all other variables are as expected), then the project has an NPV of Ϫ¥10.4 billion. If unit variable cost is ¥360,000 (and all other variables are as expected), then the project has an NPV of Ϫ¥15 billion. Value of Information Now you can check whether an investment of time or money could resolve some of the uncertainty before your company parts with the ¥15 billion investment. Sup- pose that the pessimistic value for unit variable cost partly reflects the production department’s worry that a particular machine will not work as designed and that the operation will have to be performed by other methods at an extra cost of ¥20,000 per unit. The chance that this will occur is only 1 in 10. But, if it does occur, the extra ¥20,000 unit cost will reduce after-tax cash flow by ϭ 100,000 ϫ 20,000 ϫ .50 ϭ ¥1 billion Unit sales ϫ additional unit cost ϫ 11 Ϫ tax rate2 ϭ 100,000 ϫ 375,000 ϭ ¥37.5 billion Revenue ϭ unit sales ϫ price per unit 256 PART III Practical Problems in Capital Budgeting Year 0 Years 1–10 Investment 15 1. Revenue 37.5 2. Variable cost 30 3. Fixed cost 3 4. Depreciation 1.5 5. Pretax profit (1 Ϫ 2 Ϫ 3 Ϫ 4) 3 6. Tax 1.5 7. Net profit (5 Ϫ 6) 1.5 8. Operating cash flow (4 ϩ 7) 3 Net cash flow Ϫ15 ϩ3 TABLE 10.1 Preliminary cash-flow forecasts for Otobai’s electric scooter project (figures in ¥ billions). Assumptions: 1. Investment is depreciated over 10 years straight-line. 2. Income is taxed at a rate of 50 percent. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III. Practical Problems in Capital Budgeting 10. A Project is Not a Black Box © The McGraw−Hill Companies, 2003 It would reduce the NPV of your project by putting the NPV of the scooter project underwater at ϩ3.43 Ϫ 6.14 ϭϪ¥2.71 billion. Suppose further that a ¥10 million pretest of the machine will reveal whether it will work or not and allow you to clear up the problem. It clearly pays to invest ¥10 million to avoid a 10 percent probability of a ¥6.14 billion fall in NPV. You are ahead by Ϫ10 ϩ .10 ϫ 6,140 ϭϩ¥604 million. On the other hand, the value of additional information about market size is small. Because the project is acceptable even under pessimistic assumptions about market size, you are unlikely to be in trouble if you have misestimated that variable. Limits to Sensitivity Analysis Sensitivity analysis boils down to expressing cash flows in terms of key project vari- ables and then calculating the consequences of misestimating the variables. It forces the manager to identify the underlying variables, indicates where additional informa- tion would be most useful, and helps to expose confused or inappropriate forecasts. One drawback to sensitivity analysis is that it always gives somewhat ambigu- ous results. For example, what exactly does optimistic or pessimistic mean? The mar- keting department may be interpreting the terms in a different way from the pro- duction department. Ten years from now, after hundreds of projects, hindsight may show that the marketing department’s pessimistic limit was exceeded twice as often as the production department’s; but what you may discover 10 years hence is no help now. One solution is to ask the two departments for a complete descrip- tion of the various odds. However, it is far from easy to extract a forecaster’s sub- jective notion of the complete probability distribution of possible outcomes. 1 Another problem with sensitivity analysis is that the underlying variables are likely to be interrelated. What sense does it make to look at the effect in isolation of an increase in market size? If market size exceeds expectations, it is likely that a 10 tϭ1 1 11.102 t ϭ ¥6.14 billion, CHAPTER 10 A Project Is Not a Black Box 257 Range NPV, ¥ Billions Variable Pessimistic Expected Optimistic Pessimistic Expected Optimistic Market size .9 million 1 million 1.1 million ϩ1.1 ϩ3.4 ϩ5.7 Market share .04 .1 .16 Ϫ10.4 ϩ3.4 ϩ17.3 Unit price ¥350,000 ¥375,000 ¥380,000 Ϫ4.2 ϩ3.4 ϩ5.0 Unit variable cost ¥360,000 ¥300,000 ¥275,000 Ϫ15.0 ϩ3.4 ϩ11.1 Fixed cost ¥4 billion ¥3 billion ¥2 billion ϩ.4 ϩ3.4 ϩ6.5 TABLE 10.2 To undertake a sensitivity analysis of the electric scooter project, we set each variable in turn at its most pessimistic or optimistic value and recalculate the NPV of the project. 1 If you doubt this, try some simple experiments. Ask the person who repairs your television to state a numerical probability that your set will work for at least one more year. Or construct your own subjec- tive probability distribution of the number of telephone calls you will receive next week. That ought to be easy. Try it. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III. Practical Problems in Capital Budgeting 10. A Project is Not a Black Box © The McGraw−Hill Companies, 2003 demand will be stronger than you anticipated and unit prices will be higher. And why look in isolation at the effect of an increase in price? If inflation pushes prices to the upper end of your range, it is quite probable that costs will also be inflated. Sometimes the analyst can get around these problems by defining underlying variables so that they are roughly independent. But you cannot push one-at-a-time sensitivity analysis too far. It is impossible to obtain expected, optimistic, and pes- simistic values for total project cash flows from the information in Table 10.2. Scenario Analysis If the variables are interrelated, it may help to consider some alternative plausible scenarios. For example, perhaps the company economist is worried about the pos- sibility of another sharp rise in world oil prices. The direct effect of this would be to encourage the use of electrically powered transportation. The popularity of com- pact cars after the oil price increases in the 1970s leads you to estimate that an im- mediate 20 percent price rise in oil would enable you to capture an extra 3 percent of the scooter market. On the other hand, the economist also believes that higher oil prices would prompt a world recession and at the same time stimulate inflation. In that case, market size might be in the region of .8 million scooters and both prices and cost might be 15 percent higher than your initial estimates. Table 10.3 shows that this scenario of higher oil prices and recession would on balance help your new venture. Its NPV would increase to ¥6.5 billion. Managers often find scenario analysis helpful. It allows them to look at differ- ent but consistent combinations of variables. Forecasters generally prefer to give an 258 PART III Practical Problems in Capital Budgeting Cash Flows, Years 1–10, ¥ Billions Base Case High Oil Prices and Recession Case 1. Revenue 37.5 44.9 2. Variable cost 30.0 35.9 3. Fixed cost 3.0 3.5 4. Depreciation 1.5 1.5 5. Pretax profit (1 Ϫ 2 Ϫ 3 Ϫ 4) 3.0 4.0 6. Tax 1.5 2.0 7. Net profit (5 Ϫ 6) 1.5 2.0 8. Net cash flow (4 ϩ 7) 3.0 3.5 PV of cash flows ϩ18.4 ϩ21.5 NPV ϩ3.4 ϩ6.5 Assumptions Base Case High Oil Prices and Recession Case Market size 1 million .8 million Market share .1 .13 Unit price ¥375,000 ¥431,300 Unit variable cost ¥300,000 ¥345,000 Fixed cost ¥3 billion ¥3.5 billion TABLE 10.3 How the NPV of the electric scooter project would be affected by higher oil prices and a world recession. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III. Practical Problems in Capital Budgeting 10. A Project is Not a Black Box © The McGraw−Hill Companies, 2003 estimate of revenues or costs under a particular scenario than to give some ab- solute optimistic or pessimistic value. Break-Even Analysis When we undertake a sensitivity analysis of a project or when we look at alterna- tive scenarios, we are asking how serious it would be if sales or costs turned out to be worse than we forecasted. Managers sometimes prefer to rephrase this question and ask how bad sales can get before the project begins to lose money. This exer- cise is known as break-even analysis. In the left-hand portion of Table 10.4 we set out the revenues and costs of the electric scooter project under different assumptions about annual sales. 2 In the right-hand portion of the table we discount these revenues and costs to give the present value of the inflows and the present value of the outflows. Net present value is of course the difference between these numbers. You can see that NPV is strongly negative if the company does not produce a single scooter. It is just positive if (as expected) the company sells 100,000 scooters and is strongly positive if it sells 200,000. Clearly the zero-NPV point occurs at a lit- tle under 100,000 scooters. In Figure 10.1 we have plotted the present value of the inflows and outflows un- der different assumptions about annual sales. The two lines cross when sales are 85,000 scooters. This is the point at which the project has zero NPV. As long as sales are greater than 85,000, the project has a positive NPV. 3 Managers frequently calculate break-even points in terms of accounting profits rather than present values. Table 10.5 shows Otobai’s after-tax profits at three lev- els of scooter sales. Figure 10.2 once again plots revenues and costs against sales. But the story this time is different. Figure 10.2, which is based on accounting prof- its, suggests a break-even of 60,000 scooters. Figure 10.1, which is based on present values, shows a break-even at 85,000 scooters. Why the difference? When we work in terms of accounting profit, we deduct depreciation of ¥1.5 bil- lion each year to cover the cost of the initial investment. If Otobai sells 60,000 scoot- ers a year, revenues will be sufficient both to pay operating costs and to recover the CHAPTER 10 A Project Is Not a Black Box 259 2 Notice that if the project makes a loss, this loss can be used to reduce the tax bill on the rest of the com- pany’s business. In this case the project produces a tax saving—the tax outflow is negative. 3 We could also calculate break-even sales by plotting equivalent annual costs and revenues. Of course, the break-even point would be identical at 85,000 scooters. Inflows Outflows Year 0 Years 1–10 Unit Sales, Revenue, Variable Fixed PV PV Thousands Years 1–10 Investment Costs Costs Taxes Inflows Outflows NPV 00 1503Ϫ2.25 0 19.6 Ϫ19.6 100 37.5 15 30 3 1.5 230.4 227.0 3.4 200 75.0 15 60 3 5.25 460.8 434.4 26.4 TABLE 10.4 NPV of electric scooter project under different assumptions about unit sales (figures in ¥ billions except as noted). Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III. Practical Problems in Capital Budgeting 10. A Project is Not a Black Box © The McGraw−Hill Companies, 2003 initial outlay of ¥15 billion. But they will not be sufficient to repay the opportunity cost of capital on that ¥15 billion. If we allow for the fact that the ¥15 billion could have been invested elsewhere to earn 10 percent, the equivalent annual cost of the investment is not ¥1.5 billion but ¥2.44 billion. 4 260 PART III Practical Problems in Capital Budgeting Scooter sales, thousands Break-even point: NPV = 0 PV outflows PV inflows 20085 PV, billions of yen 200 19.6 400 FIGURE 10.1 A break-even chart showing the present values of Otobai’s cash inflows and outflows under different assumptions about unit sales. NPV is zero when sales are 85,000. Profit Unit Sales, Variable Fixed Total after Thousands Revenue Costs Costs Depreciation Taxes Costs Tax 0 0 0 3 1.5 Ϫ2.25 2.25 Ϫ2.25 100 37.5 30 3 1.5 1.5 36.0 1.5 200 75.0 60 3 1.5 5.25 69.75 5.25 TABLE 10.5 The electric scooter project’s accounting profit under different assumptions about unit sales (figures in ¥ billions except as noted). 4 To calculate the equivalent annual cost of the initial ¥15 billion investment, we divide by the 10-year annuity factor for a 10 percent discount rate: See Section 6.3. The annual revenues at 85,000 scooters per year are about ¥31.9 billion. You can check that this is sufficient to cover variable costs, fixed costs, and taxes and still leave ¥2.44 billion per year to recover the ¥15 billion initial investment and a 10 percent return on that investment. ϭ 15 6.145 ϭ ¥2.44 billion Equivalent annual cost ϭ investment 10-year annuity factor Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III. Practical Problems in Capital Budgeting 10. A Project is Not a Black Box © The McGraw−Hill Companies, 2003 Companies that break even on an accounting basis are really making a loss—they are losing the opportunity cost of capital on their investment. Reinhardt has described a dramatic example of this mistake. 5 In 1971 Lockheed managers found themselves having to give evidence to Congress on the viability of the company’s L-1011 TriStar program. They argued that the program appeared to be commercially attractive and that TriStar sales would eventually exceed the break-even point of about 200 aircraft. But in calculating this break-even point, Lockheed appears to have ignored the op- portunity cost of the huge $1 billion capital investment on this project. Had it allowed for this cost, the break-even point would probably have been nearer to 500 aircraft. Operating Leverage and Break-Even Points Break-even charts like Figure 10.1 help managers appreciate operating leverage, that is, project exposure to fixed costs. Remember from Section 9.5 that high operating leverage means high risk, other things equal, of course. The electric scooter project had low fixed costs, only ¥3 billion against projected revenues of ¥37.5 billion. But suppose Otobai now considers a different production technology with lower variable costs of only ¥120,000 per unit (versus ¥300,000 per unit) but higher fixed costs of ¥19 billion. Total forecasted production costs are lower (12 ϩ 19 ϭ ¥31 billion versus ¥33 billion), so profitability improves— compare Table 10.6 to Table 10.1. Project NPV increases to ¥9.6 billion. Figure 10.3 is the new break-even chart. Break-even sales have increased to 88,000 (that’s bad), even though total production costs have fallen. A new sensitivity analy- sis would show that project NPV is much more exposed to changes in market size, CHAPTER 10 A Project Is Not a Black Box 261 Scooter sales, thousands Break-even point: Profit = 0 Costs (including depreciation and taxes) Revenues 20060 Accounting revenues and costs, billions of yen 20 60 40 FIGURE 10.2 Sometimes break-even charts are constructed in terms of accounting numbers. After-tax profit is zero when sales are 60,000. 5 U. E. Reinhardt, “Break-Even Analysis for Lockheed’s TriStar: An Application of Financial Theory,” Journal of Finance 28 (September 1973), pp. 821–838. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III. Practical Problems in Capital Budgeting 10. A Project is Not a Black Box © The McGraw−Hill Companies, 2003 market share, or unit price. All of these differences can be traced to the higher fixed costs of the alternative production technology. Is the alternative technology better than the original one? The financial man- ager would have to consider the alternative technology’s higher business risk, and perhaps recompute NPV at a higher discount rate, before making a final decision. 6 262 PART III Practical Problems in Capital Budgeting Year 0 Years 1–10 Investment 15 1. Revenue 37.5 2. Variable cost 12.0 3. Fixed cost 19.0 4. Depreciation 1.5 5. Pretax profit (1 Ϫ 2 Ϫ 3 Ϫ 4) 5.0 6. Tax 2.5 7. Net profit (5 Ϫ 6) 2.5 8. Operating cash flow (4 ϩ 7) 4.0 Net cash flow Ϫ15 ϩ4.0 NPV ϭϪ15 ϩ a 10 tϭ1 4.0 11.12 t ϭϩ¥9.6 billion TABLE 10.6 Cash-flow forecasts and PV for the electric scooter project, here assuming a production technology with high fixed costs but low total costs (figures in ¥ billions). Compare Table 10.1. Scooter sales, thousands Break-even point: NPV = 0 PV outflows PV inflows PV, billions of yen 20088 200 400 68.8 FIGURE 10.3 Break-even chart for an alternative production technology with higher fixed costs. Notice that break-even sales increase to 88,000. Compare Figure 10.1. 6 He or she could use the procedures outlined in Section 9.5 to recalculate beta and come up with a new discount rate. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III. Practical Problems in Capital Budgeting 10. A Project is Not a Black Box © The McGraw−Hill Companies, 2003 Sensitivity analysis allows you to consider the effect of changing one variable at a time. By looking at the project under alternative scenarios, you can consider the ef- fect of a limited number of plausible combinations of variables. Monte Carlo simu- lation is a tool for considering all possible combinations. It therefore enables you to inspect the entire distribution of project outcomes. The use of simulation in cap- ital budgeting was first advocated by David Hertz 7 and McKinsey and Company, the management consultants. Imagine that you are a gambler at Monte Carlo. You know nothing about the laws of probability (few casual gamblers do), but a friend has suggested to you a complicated strategy for playing roulette. Your friend has not actually tested the strategy but is confident that it will on the average give you a 2 1 ⁄2 percent re- turn for every 50 spins of the wheel. Your friend’s optimistic estimate for any series of 50 spins is a profit of 55 percent; your friend’s pessimistic estimate is a loss of 50 percent. How can you find out whether these really are the odds? An easy but possibly expensive way is to start playing and record the outcome at the end of each series of 50 spins. After, say, 100 series of 50 spins each, plot a frequency distribution of the outcomes and calculate the average and upper and lower limits. If things look good, you can then get down to some serious gambling. An alternative is to tell a computer to simulate the roulette wheel and the strat- egy. In other words, you could instruct the computer to draw numbers out of its hat to determine the outcome of each spin of the wheel and then to calculate how much you would make or lose from the particular gambling strategy. That would be an example of Monte Carlo simulation. In capital budgeting we replace the gambling strategy with a model of the project, and the roulette wheel with a model of the world in which the project operates. Let’s see how this might work with our project for an electrically powered scooter. Simulating the Electric Scooter Project Step 1: Modeling the Project The first step in any simulation is to give the com- puter a precise model of the project. For example, the sensitivity analysis of the scooter project was based on the following implicit model of cash flow: This model of the project was all that you needed for the simpleminded sensi- tivity analysis that we described above. But if you wish to simulate the whole proj- ect, you need to think about how the variables are interrelated. For example, consider the first variable—market size. The marketing depart- ment has estimated a market size of 1 million scooters in the first year of the pro- ject’s life, but of course you do not know how things will work out. Actual market Costs ϭ 1market size ϫ market share ϫ variable unit cost2ϩ fixed cost Revenues ϭ market size ϫ market share ϫ unit price Cash flow ϭ 1revenues Ϫ costs Ϫ depreciation2ϫ 11 Ϫ tax rate2ϩ depreciation CHAPTER 10 A Project Is Not a Black Box 263 10.2 MONTE CARLO SIMULATION 7 See D. B. Hertz, “Investment Policies that Pay Off,” Harvard Business Review 46 (January–February 1968), pp. 96–108. [...]... year The company’s tax rate was 35 percent and the cost of capital was 9 percent in nominal terms 283 Visit us at www.mhhe.com/bm7e Brealey−Meyers: Principles of Corporate Finance, Seventh Edition Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 284 PART III III Practical Problems in Capital Budgeting © The McGraw−Hill Companies, 2003 10 A Project is Not a Black Box Practical Problems in... Because risk changes, standard discounted-cash-flow techniques can only approximate the present value of real options We will cover option-valuation methods in Chapter 21 and revisit real options in Chapter 22 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 280 PART III III Practical Problems in Capital Budgeting © The McGraw−Hill Companies, 2003 10 A Project is Not a Black Box Practical... variety of peg shapes In just the same way, it may be worth paying up front for the flexibility to vary the inputs For example, in Chapter 22 we will describe how electric utilities often build in the option to switch be- Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III Practical Problems in Capital Budgeting 10 A Project is Not a Black Box © The McGraw−Hill Companies, 2003 CHAPTER 10. .. which the electric scooter project in Section 10. 1 would break even Calculate the Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III Practical Problems in Capital Budgeting © The McGraw−Hill Companies, 2003 10 A Project is Not a Black Box CHAPTER 10 A Project Is Not a Black Box 281 level of costs at which the project would earn zero profit and at which it would have zero NPV 4 The... chance of high 18 The use of decision trees was first advocated by J Magee in “How to Use Decision Trees in Capital Investment,” Harvard Business Review 42(September–October 1964), pp 79–96 Real options were first identified in S C Myers, “Determinants of Corporate Borrowing,” Journal of Financial Economics 5 (November 1977), pp 146–175 273 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition. .. turboprop has an NPV of $96,000 The piston-engine plane is the better bet Note, however, that the choice would be different if we forgot to take account of the option to expand In that case the NPV of the piston-engine plane would drop from $117,000 to $52,000: 6 1100 2 ϩ 41502 1 .10 6 3.81 4102 ϩ 21180 2 4 ϩ 4 3.412202 ϩ 6 1100 2 4 NPV ϭ Ϫ250 ϩ ϩ 11 .102 2 ϭ ϩ52, or $52,000 The value of the option to expand... There is no provision for expanding to take advantage of good luck 277 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 278 PART III III Practical Problems in Capital Budgeting 10 A Project is Not a Black Box © The McGraw−Hill Companies, 2003 Practical Problems in Capital Budgeting Most simulation models incorporate a business-as-usual strategy, which is fine as long as there are no... lower discount rate for the second piston-engine plane than for the first 275 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition 276 PART III III Practical Problems in Capital Budgeting © The McGraw−Hill Companies, 2003 10 A Project is Not a Black Box Practical Problems in Capital Budgeting The net present value of the investment in the piston-engine plane is therefore $117,000: NPV ϭ... Finance 22 (December 1967), pp 577–590 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III Practical Problems in Capital Budgeting © The McGraw−Hill Companies, 2003 10 A Project is Not a Black Box CHAPTER 10 A Project Is Not a Black Box 2 Technology B uses standard machine tools Labour costs are much higher, but the machinery can be sold for $10 million if the engine doesn’t sell Technology... forecast, year 2 Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III Practical Problems in Capital Budgeting © The McGraw−Hill Companies, 2003 10 A Project is Not a Black Box CHAPTER 10 A Project Is Not a Black Box Notice how we have linked each period’s selling price to the actual selling prices (including forecast error) in all previous periods We used the same type of linkage for . 100 ,000 scooters Unit sales ϭ new product’s share of market ϫ size of scooter market NPV ϭϪ15 ϩ a 10 tϭ1 3 11 .102 t ϭϩ¥3.43 billion 10. 1 SENSITIVITY ANALYSIS Brealey−Meyers: Principles of Corporate. over 10 years straight-line. 2. Income is taxed at a rate of 50 percent. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III. Practical Problems in Capital Budgeting 10. A. subjec- tive probability distribution of the number of telephone calls you will receive next week. That ought to be easy. Try it. Brealey−Meyers: Principles of Corporate Finance, Seventh Edition III.