Having read our earlier chapters on capital budgeting, you may have concluded that the choice of which projects to accept or reject is a simple one. You just need to draw up a set of cash-flow forecasts, choose the right discount rate, and crank out net present value. But finding projects that create value for the shareholders can never be reduced to a mechanical exercise. We therefore devote the next three chapters to ways in which companies can stack the odds in their favor when making investment decisions.
When managers are presented with investment proposals, they do not accept the cash flow forecasts at face value. Instead, they try to understand what makes a 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.”
Once you know what makes a project tick, you may be able to reconfigure it to improve its chances of success. And if you understand why a venture may fail, you can decide whether it is worth trying to rule out the possible causes of failure. Maybe further expenditure on market research would clear up those doubts about acceptance by consumers, 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 without further analysis, you do not want to be caught by surprise if things go wrong later. You want to know the danger signals and the actions that you might take.
Our first task in this chapter is to show how managers use sensitivity analysis, break-even analysis, and Monte Carlo simulation to identify the crucial assumptions in investment proposals and to explore what can go wrong. There is no magic in these techniques, just computer-assisted common sense. You do not need a license to use them.
Discounted cash-flow analysis commonly assumes that companies hold assets passively, and it ignores the opportunities to expand the project if it is successful or to bail out if it is not. However, wise managers recognize these opportunities when considering whether to invest. They look for ways to capitalize on success and 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. In the final section of the chapter, we describe several important real options, and we show how to use decision trees to set out the possible future choices.
10-1Sensitivity and Scenario Analysis
Uncertainty means that more things can happen than will happen. Therefore, whenever managers are given a cash-flow forecast, they try to determine what else may happen and the implications of these possible surprise events. This is called sensitivity analysis.
Put yourself in the well-heeled shoes of the financial manager of the Otobai Company in Osaka. You are considering the introduction of a high-performance electric scooter for city use. Your staff members have prepared the cash-flow forecasts shown in Table 10.1. Since NPV is positive at the 20% opportunity cost of capital, it appears to be worth going ahead, but before you decide, you want to delve into these forecasts and identify the key variables that determine whether the project succeeds or fails.
TABLE 10.1 Preliminary cash-flow forecasts for Otobai’s electric scooter project (figures in ¥ billions unless stated otherwise)
The project requires an initial investment of ¥15 billion in plant and machinery, which will have negligible further value when the project comes to an end. As sales build up in the early and middle years of the project, the company will need to make increasing investments in net working capital, which is recovered in later years. After year 6, the company expects sales to tail off as other companies enter the market, and the company will probably need to reduce the price of the scooter. The cost of goods sold is forecast to be 50% of sales; in addition, there will be fixed costs each year that are unrelated to the level of sales. Taxes at a 40% rate are computed after deducting straight-line depreciation.
These seem to be the important things you need to know, but look out for unidentified variables that could affect these estimates. Perhaps there could be 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 scientists call them.
BEYOND THE PAGE
Try It! Scooter project spreadsheets
mhhe.com/brealey13e
Having found no unk-unks (no doubt you will find them later), you conduct a sensitivity analysis with respect to the required investment in plant and working capital and the forecast unit sales, price, and costs. To do this, the marketing and production staffs are asked to give optimistic and pessimistic estimates for each of the underlying variables. These are set out in the second and third columns of Table 10.2. For example, it is possible that sales of scooters could be 25% below forecast, or you may be obliged to cut the price by 15%. The fourth and fifth columns of the table 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 are cost of goods sold and unit sales. If the cost of goods sold is 70% of sales (and all other variables are as expected), then the project has an NPV of – ¥10.7 billion. If unit sales each year turn out to be 25% less than you forecast (and all other variables are as expected), then the project has an NPV of – ¥5.9 billion.
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
Trendy consultants sometimes use a tornado diagram such as Figure 10.1 to illustrate the results of a sensitivity analysis. The bars at the summit of the tornado show the range of NPV outcome due to uncertainty about the level of sales. At the base of the tornado you can see the more modest effect of uncertainty about investment in working capital and the level of fixed costs.1
FIGURE 10.1 Tornado diagram for electric scooter project
Value of Information
The world is uncertain, and accurate cash-flow forecasts are unattainable. So, if a project has a positive NPV based on your best forecasts, shouldn’t you go ahead with it regardless of the fact that there may be later disappointments? Why spend time and effort focusing on the things that could go wrong?
Sensitivity analysis is not a substitute for the NPV rule, but if you know the danger points, you may be able to modify the project or resolve some of the uncertainty before your company undertakes the investment. For example, suppose that the pessimistic value for the cost of goods sold partly reflects the production department’s worry that a particular machine will not work as designed and that the operation will need to be performed by other methods. The chance of this happening is only 1 in 10. But, if it does occur, the extra cost would reduce the NPV of your project by ¥2.5 billion, putting the NPV underwater at +2.02 – 2.50 = – ¥0.48 billion. Suppose that a ¥100 million pretest of the machine would resolve the uncertainty and allow you to clear up the problem. It clearly pays to invest ¥100 million to avoid a 10% probability of a ¥2.5 billion fall in NPV. You are ahead by –0.1 + .10 × 2.5 = ¥0.15 billion. On the other hand, the value of additional information about working capital is small. Because the project is only marginally unprofitable, even under pessimistic assumptions about working capital, 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 variables and then calculating the consequences of misestimating those variables. It forces the manager to identify the crucial determinants of the project’s success and indicates where additional information would be most useful or where design changes may be needed.
One drawback to sensitivity analysis is that it always gives somewhat ambiguous results. For example, what exactly does optimistic or pessimistic mean? The marketing department may be interpreting the terms in a different way from the production 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 that of the production department, but what you may discover 10 years hence is no help now. Of course, you could specify that when you use the terms “pessimistic” and “optimistic,” you mean that there is only a 10% chance that the actual value will prove to be worse than the pessimistic figure or better than the optimistic one. However, it is far from easy to extract a forecaster’s notion of the true probabilities of possible outcomes.2
Another problem with sensitivity analysis is that the underlying variables are likely to be interrelated. For example, if inflation pushes prices to the upper end of your range, it is quite probable that costs will also be inflated. And if sales are unexpectedly high, you may need to invest more in working capital. Sometimes the analyst can get around these problems by defining underlying variables so that they are roughly independent. For example, it made more sense for Otobai to look at cost of goods sold as a proportion of sales rather than as a dollar value. But you cannot push one-at-a-time sensitivity analysis too far. It is impossible to obtain expected, optimistic, and pessimistic values for total project cash flows from the information in Table 10.2.
Sensitivity analysis boils down to expressing cash flows in terms of key project variables and then calculating the consequences of misestimating the variables. It forces the manager to identify the underlying variables, indicates where additional information would be most useful, and helps to expose inappropriate forecasts.
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 possibility of a sharp rise in world oil prices. The direct effect of this would be to encourage the use of electrically powered transportation. The popularity of hybrid cars after a recent oil price increases leads you to estimate that an immediate 20% rise in the price of oil would enable you to increase unit sales by 10% a year. On the other hand, the economist also believes that higher oil prices would stimulate inflation, which would affect selling prices, costs, and working capital. Table 10.3 shows that this scenario of higher oil prices and higher inflation would on balance help your new venture. Its NPV would increase to ¥6.9 billion.
TABLE 10.3 How the NPV of the electric scooter project would be affected by higher oil prices and increased inflation (figures in ¥billions unless stated otherwise)
Managers often find such scenario analysis helpful. It allows them to look at different, but consistent, combinations of variables. Forecasters generally prefer to give an estimate of revenues or costs under a particular scenario than to give some absolute optimistic or pessimistic value.
10-2Break-Even Analysis and Operating Leverage
Break-Even Analysis
When we undertake a sensitivity analysis of a project or when we look at alternative scenarios, we are asking how serious it would be if sales or costs turn out to be worse than we forecasted. Managers sometimes prefer to rephrase this question and ask how bad things can get before the project NPV turns negative. This exercise is known as break-even analysis.
We saw earlier that the profitability of Otobai’s project could be severely damaged if unit sales are unexpectedly low. Therefore, management might look at how far unit sales could fall before the project becomes a loser. A 1% annual shortfall in unit sales would turn NPV from ¥2.02 to –¥1.70, a decline of ¥0.32. So NPV would be exactly zero if each year sales fell by 1% × (2.02)/(0.32) = 6.3% below forecast.
Table 10.4 shows the break-even points for each of the other variables. You can see, for example, that quite small errors in your forecasts for unit sales, price, and variable costs could cause your project to become a loser. On the other hand, the project would still break even (NPV = 0) if you have underestimated working capital by 60.1%.
BEYOND THE PAGE
Break-even analysis of Otobai’s electric scooter project
mhhe.com/brealey13e
Table 10.4 defines break-even as the point at which NPV would be exactly zero. But managers frequently calculate break-even points in terms of accounting profits rather than net present values. For example, look at Table 10.5, which shows the minimum level of sales that Otobai needs each year to avoid a loss on its scooter project. You can see that in year 1, Otobai needs sales of ¥11.80 billion to cover costs and depreciation. In year 2, the break-even sales level rises to ¥12.06 billion.3
Should Otobai’s manager be relaxed if the project breaks even each year in accounting terms? It is true that its revenues will then be sufficient to cover the operating costs and repay the initial investment. But they will not be sufficient to repay the opportunity cost of capital on that ¥15 billion. A project that breaks even in accounting terms will surely have a negative NPV.
|
Change in Estimated Value |
|
|
Capital investment |
+16.2% |
|
Working capital |
+60.1 |
|
Sales |
–6.3 |
|
Cost of goods sold (% of sales) |
+3.2 |
|
Fixed costs |
+14.5 |
TABLE 10.4 The percentage change in the estimated value of each variable that produces an NPV of zero for the electric scooter project
TABLE 10.5 A project’s accounting break-even point is the minimum level of sales required to avoid an accounting loss
Operating Leverage and the Break-Even Point
A project’s break-even point depends on the extent to which its costs vary with the level of sales. Suppose that electric scooters fall out of favor. The bad news is that Otobai’s sales revenue is less than you had hoped, but you have the consolation that the cost of goods sold is also lower. But, any costs that are fixed do not decline along with sales, and, therefore, any shortfall in sales has a greater impact on profitability. Of course, a high proportion of fixed costs is not all bad. The firm whose costs are fixed fares poorly when demand is low but makes a killing during a boom.
A business with high fixed costs is said to have high operating leverage. Operating leverage is usually defined in terms of accounting profits rather than cash flows4 and is measured by the percentage change in profits for each 1% change in sales. Thus the degree of operating leverage (DOL) is
The following simple formula5 shows how DOL is related to the business’s fixed costs (including depreciation) as a proportion of pretax profits:
For example, in year 2 of the scooter project,
A 1% increase in the project’s year-2 revenues would result in a 4.5% rise in profits.
10-3Monte Carlo Simulation
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 effect of a limited number of plausible combinations of variables. Monte Carlo simulation is a tool for considering all possible combinations. It therefore enables you to inspect the entire distribution of project outcomes.
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 2.5% return for every 50 spins of the wheel. Your friend’s optimistic estimate for any series of 50 spins is a profit of 55%; your friend’s pessimistic estimate is a loss of 50%. 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 strategy. In other words, you could instruct the computer to draw numbers out of its digital 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 us 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 computer a precise model of the project. For example, the sensitivity analysis of the scooter project was based on the following implicit model of each year’s cash flow:
This model of the project was all that you needed for the simpleminded sensitivity analysis that we described above. But if you wish to simulate the whole project, you need to think about how the variables are interrelated. For example, consider the unit sales variable. The marketing department has estimated sales of 6.8 million scooters in the first year of the project’s life; of course, you do not know how things will work out. Actual sales will exceed or fall short of expectations by the amount of the department’s forecast error:
Sales, year 1 = expected sales, year 1 × (1 + forecast error, year 1)
You expect the forecast error to be zero, but it could turn out to be positive or negative. Suppose, for example, that actual sales turn out to be 7.48 million. That means a forecast error of 10%, or +.1:
Sales, year 1 = 6.8 × (1 + .1) = 7.48 million
You can write sales in the second year in exactly the same way:
Sales, year 2 = expected sales, year 2 × (1 + forecast error, year 2)
At this point, you must consider how the expected sales in year 2 are affected by what happens in year 1. If scooter sales are below expectations in year 1, it is likely that they will continue to be below in subsequent years. Suppose that a shortfall in year 1 leads you to revise down your forecast of sales in year 2 by a like amount. Then:
Expected sales, year 2 = actual sales, year 1
Now you can rewrite sales in year 2 in terms of the actual sales in the previous year plus a forecast error:
Sales, year 2 = sales, year 1 × (1 + forecast error, year 2)
In the same way, you can describe the expected sales in year 3 in terms of sales in year 2 and so on. This set of equations illustrates how you can describe interdependence between different periods. But you also need to allow for interdependence between different variables. For example, if sales are high, the price of electrically powered scooters is likely to be above forecast. Suppose that this is the only uncertainty and that a 10% addition to sales would lead you to predict a 3% increase in price. Then you could model the first year’s price as follows:
Price, year 1 = expected price, year 1 × (1 + .3 × error in sales forecast, year 1)
Then, if variations in sales exert a permanent effect on price, you can define the second year’s price as
Price, year 2 = expected price, year 2 × (1 + .3 × error in sales forecast, year 2) = actual price, year 1 × (1 + .3 × error in sales forecast, year 2)
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 sales. These linkages mean that forecast errors accumulate; they do not cancel out over time. Thus, uncertainty increases with time: The farther out you look into the future, the more the actual price or sales may depart from your original forecast. The complete model of your project would include a set of equations for each of the variables: sales, price, variable cost, fixed cost, and investment in working capital. Even if you allowed for only a few interdependencies between variables and across time, the result would be quite a complex list of equations. Perhaps that is not a bad thing if it forces you to understand what the project is all about. Model building is like spinach: You may not like the taste, but it is good for you.
Step 2: Specifying Probabilities Remember the procedure for simulating the gambling strategy? The first step was to specify the strategy, the second was to specify the numbers on the roulette wheel, and the third was to tell the computer to select these numbers at random and calculate the results of the strategy:
The steps are just the same for your scooter project:
Think about how you might go about specifying your possible errors in forecasting market size. You expect sales in year 1 to be 6.8 million scooters. You obviously don’t think you are underestimating or overestimating, so the expected forecast error is zero. On the other hand, the marketing department has given you a range of possible estimates. Sales in year 1 could be as low as 5.7 million scooters or as high as 8.2 million scooters. Thus the forecast error has an expected value of 0 and a range of plus or minus 20%. If the marketing department has, in fact, given you the lowest and highest possible outcomes, actual market size should fall somewhere within this range with near certainty.6
That takes care of market size; now you need to draw up similar estimates of the possible forecast errors for each of the other variables that are in your model.
Step 3: Simulate the Cash Flows The computer now samples from the distribution of the forecast errors, calculates the resulting cash flows for each period, and records them. After many iterations, you begin to get accurate estimates of the probability distributions of the project cash flows—accurate, that is, only to the extent that your model and the probability distributions of the forecast errors are accurate. Remember the GIGO principle: “garbage in, garbage out.”
Step 4: Calculate Present Value The distributions of project cash flows should allow you to calculate the expected cash flows more accurately. In the final step, you need to discount these expected cash flows to find present value.
Simulation, though complicated, has the obvious merit of compelling the forecaster to face up to uncertainty and to interdependencies. Once you have set up your simulation model, it is a simple matter to analyze the principal sources of uncertainty in the cash flows and to see how much you could reduce this uncertainty by improving the forecasts of sales or costs. You may also be able to explore the effect of possible modifications to the project.
Simulation may sound like a panacea for the world’s ills, but, as usual, you pay for what you get. Sometimes you pay for more than you get. It is not just a matter of the time spent in building the model. It is extremely difficult to estimate interrelationships between variables and the underlying probability distributions, even when you are trying to be honest. But in capital budgeting, forecasters are seldom completely impartial and the probability distributions on which simulations are based can be highly biased.
In practice, a simulation that attempts to be realistic will also be complex. Therefore, the decision maker may delegate the task of constructing the model to management scientists or consultants. The danger here is that even if the builders understand their creation, the decision maker cannot and therefore does not rely on it. This is a common but ironic experience.
10-4Real Options and Decision Trees
When you use discounted cash flow (DCF) to value a project, you implicitly assume that the firm will hold the assets passively. But managers are not paid to be dummies. After they have invested in a new project, they do not simply sit back and watch the future unfold. If things go well, the project may be expanded; if they go badly, the project may be cut back or abandoned altogether. Projects that can be modified in these ways are more valuable than those that do not provide such flexibility. The more uncertain the outlook, the more valuable this flexibility becomes.
That sounds obvious, but notice that sensitivity analysis and Monte Carlo simulation do not recognize the opportunity to modify projects.7 For example, think back to the Otobai electric scooter project. In real life, if things go wrong with the project, Otobai would abandon to cut its losses. If so, the worst outcomes would not be as devastating as our sensitivity analysis and simulation suggested.
Options to modify projects are known as real options. Managers may not always use the term “real option” to describe these opportunities; for example, they may refer to “intangible advantages” of easy-to-modify projects. But when they review major investment proposals, these option intangibles are often the key to their decisions.
The Option to Expand
Long-haul airfreight businesses such as UPS need to move a massive amount of goods each day. To handle the growing demand, UPS announced in 2016 that it had agreed to buy 14 Boeing freighter aircraft to add to its existing fleet of more than 500 planes. If business continued to expand, UPS would need more aircraft. But rather than placing additional firm orders, the company secured a place in Boeing’s production line by acquiring options to buy a further 14 aircraft at a predetermined price. These options did not commit UPS to expand but gave it the flexibility to do so.
Figure 10.2 displays UPS’s expansion option as a simple decision tree. You can think of it as a game between UPS and fate. Each square represents an action or decision by the company. Each circle represents an outcome revealed by fate. In this case, there is only one outcome—when fate reveals the airfreight demand and UPS’s capacity needs. UPS then decides whether to exercise its options and buy the additional aircraft. Here the future decision is easy: Buy the airplanes only if demand is high and the company can operate them profitably. If demand is low, UPS walks away and leaves Boeing with the problem of finding another customer for the planes that were reserved for UPS.
FIGURE 10.2 UPS’s expansion option expressed as a simple decision tree
You can probably think of many other investments that take on added value because of the further options they provide. For example,
· When launching a new product, companies often start with a pilot program to iron out possible design problems and to test the market. The company can evaluate the pilot project and then decide whether to expand to full-scale production.
· When designing a factory, it can make sense to provide extra land or floor space to reduce the future cost of a second production line.
· When building a four-lane highway, it may pay to build six-lane bridges so that the road can be converted later to six lanes if traffic volumes turn out to be higher than expected.
· When building production platforms for offshore oil and gas fields, companies usually allow ample vacant deck space. The vacant space costs more up front but reduces the cost of installing extra equipment later. For example, vacant deck space could provide an option to install water-flooding equipment if oil or gas prices are high enough to justify this investment.
Expansion options do not show up on accounting balance sheets, but managers and investors are well aware of their importance. For example, in Chapter 4 we showed how the present value of growth opportunities (PVGO) contributes to the value of a company’s common stock. PVGO equals the forecasted total NPV of future investments. But it is better to think of PVGO as the value of the firm’s options to invest and expand. The firm is not obliged to grow. It can invest more if the number of positive-NPV projects turns out high, or it can slow down if that number turns out low. The flexibility to adapt investment to future opportunities is one of the factors that makes PVGO so valuable.
The Option to Abandon
If the option to expand has value, what about the decision to bail out? Projects do not just go on until assets expire of old age. The decision to terminate a project is usually taken by management, not by nature. Once the project is no longer profitable, the company will cut its losses and exercise its option to abandon the project.
Some assets are easier to bail out of than others. Tangible assets are usually easier to sell than intangible ones. It helps to have active secondhand markets, which exist mainly for standardized items. Real estate, airplanes, trucks, and certain machine tools are likely to be relatively easy to sell. On the other hand, the knowledge accumulated by a software company’s research and development program is a specialized intangible asset and probably would not have significant abandonment value. (Some assets, such as old mattresses, even have negative abandonment value; you have to pay to get rid of them. It is costly to decommission nuclear power plants or to reclaim land that has been strip-mined.)
EXAMPLE 10.1 
Bailing Out of the Outboard-Engine Project
Managers should recognize the option to abandon when they make the initial investment in a new project or venture. For example, suppose you must choose between two technologies for production of a Wankel-engine outboard motor.
1. Technology A uses computer-controlled machinery custom-designed to produce the complex shapes required for Wankel engines in high volumes and at low cost. But if the Wankel outboard does not sell, this equipment will be worthless.
2. Technology B uses standard machine tools. Labor costs are much higher, but the machinery can be sold for $17 million if demand turns out to be low.
Just for simplicity, assume that the initial capital outlays are the same for both technologies. If demand in the first year is buoyant, technology A will provide a payoff of $24 million. If demand is sluggish, the payoff from A is $16 million. Think of these payoffs as the project’s cash flow in the first year of production plus the value in year 1 of all future cash flows. The corresponding payoffs to technology B are $22.5 million and $15 million:
|
Payoffs from Producing Outboard ($ millions) |
||
|
Technology A |
Technology B |
|
|
Buoyant demand |
$24.0 |
$22.5 |
|
Sluggish demand |
16.0 |
15.0a |
a Composed of a cash flow of $1.5 million and a PV in year 1 of 13.5 million.
Technology A looks better in a DCF analysis of the new product because it was designed to have the lowest possible cost at the planned production volume. Yet you can sense the advantage of the flexibility provided by technology B if you are unsure whether the new outboard will sink or swim in the marketplace. If you adopt technology B and the outboard is not a success, you are better off collecting the first year’s cash flow of $1.5 million and then selling the plant and equipment for $17 million.
Figure 10.3 summarizes Example 10.1 as a decision tree. The abandonment option occurs at the right-hand boxes for technology B. The decisions are obvious: Continue if demand is buoyant, abandon otherwise. Thus the payoffs to technology B are
FIGURE 10.3 Decision tree for the Wankel outboard motor project. Technology B allows the firm to abandon the project and recover $18.5 million if demand is sluggish.
Technology B provides an insurance policy: If the outboard’s sales are disappointing, you can abandon the project and receive $18.5 million. The total value of the project with technology B is its DCF value, assuming that the company does not abandon, plus the value of the option to sell the assets for $17 million. When you value this abandonment option, you are placing a value on flexibility.
Production Options
When companies undertake new investments, they generally think about the possibility that they may wish to modify the project at a later stage. After all, today everybody may be demanding round pegs, but, who knows, tomorrow square ones may be all the rage. In that case, you need a plant that provides the flexibility to produce a 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 between burning oil and burning natural gas. We refer to these opportunities as production options.
Timing Options
The fact that a project has a positive NPV does not mean that it is best undertaken now. It might be even more valuable to delay.
Timing decisions are fairly straightforward under conditions of certainty. You need to examine alternative dates for making the investment and calculate its net future value at each of these dates. Then, to find which of the alternatives would add most to the firm’s current value, you must discount these net future values back to the present:
The optimal date to undertake the investment is the one that maximizes its contribution to the value of your firm today. This procedure should already be familiar to you from Chapter 6, where we worked out when it was best to cut a tract of timber.
In the timber-cutting example, we assumed that there was no uncertainty about the cash flows, so that you knew the optimal time to exercise your option. When there is uncertainty, the timing option is much more complicated. An investment opportunity not taken at t = 0 might be more or less attractive at t = 1; there is rarely any way of knowing for sure. Perhaps it is better to strike while the iron is hot even if there is a chance that it will become hotter. On the other hand, if you wait a bit you might obtain more information and avoid a bad mistake. That is why you often find that managers choose not to invest today in projects where the NPV is only marginally positive and there is much to be learned by delay.
More on Decision Trees
We will return to all these real options in Chapter 22, after we have covered the theory of option valuation in Chapters 20 and 21. But we will end this chapter with a closer look at decision trees.
Decision trees are commonly used to describe the real options imbedded in capital investment projects. But decision trees were used in the analysis of projects years before real options were first explicitly identified. Decision trees can help to illustrate project risk and how future decisions will affect project cash flows. Even if you never learn or use option valuation theory, decision trees belong in your financial toolkit.
The best way to appreciate how decision trees can be used in project analysis is to work through a detailed example.
EXAMPLE 10.2 A Decision Tree for Pharmaceutical R&D
Drug development programs may last decades. Usually hundreds of thousands of compounds may be tested to find a few with promise. Then these compounds must survive several stages of investment and testing to gain approval from the Food and Drug Administration (FDA). Only then can the drug be sold commercially. The stages are as follows:
1. Phase I clinical trials. After laboratory and clinical tests are concluded, the new drug is tested for safety and dosage in a small sample of humans.
2. Phase II clinical trials. The new drug is tested for efficacy (Does it work as predicted?) and for potentially harmful side effects.
3. Phase III clinical trials. The new drug is tested on a larger sample of humans to confirm efficacy and to rule out harmful side effects.
4. Prelaunch. If FDA approval is gained, there is investment in production facilities and initial marketing. Some clinical trials continue.
5. Commercial launch. After making a heavy initial investment in marketing and sales, the company begins to sell the new drug to the public.
Once a drug is launched successfully, sales usually continue for about 10 years, until the drug’s patent protection expires and competitors enter with generic versions of the same chemical compound. The drug may continue to be sold off-patent, but sales volume and profits are much lower.
The commercial success of FDA-approved drugs varies enormously. The PV of a “blockbuster” drug at launch can be 5 or 10 times the PV of an average drug. A few blockbusters can generate most of a large pharmaceutical company’s profits.8
No company hesitates to invest in R&D for a drug that it knows will be a blockbuster. But the company will not find out for sure until after launch. Occasionally, a company thinks it has a blockbuster only to discover that a competitor has launched a better drug first.
Sometimes the FDA approves a drug but limits its scope of use. Some drugs, though effective, can only be prescribed for limited classes of patients; other drugs can be prescribed much more widely. Thus the manager of a pharmaceutical R&D program has to assess the odds of clinical success and the odds of commercial success. A new drug may be abandoned if it fails clinical trials—for example, because of dangerous side effects—or if the outlook for profits is discouraging.
Figure 10.4 is a decision tree that illustrates these decisions. We have assumed that a new drug has passed phase I clinical trials with flying colors. Now it requires an investment of $18 million for phase II trials. These trials take two years. The probability of success is 44%.
FIGURE 10.4 A simplified decision tree for pharmaceutical R&D. A candidate drug requires an $18 million investment for phase II clinical trials. If the trials are successful (44% probability), the company learns the drug’s scope of use and updates its forecast of the drug’s PV at commercial launch. The investment required for the phase III trials and prelaunch outlays is $130 million. The probability of success in phase III and prelaunch is 80%.
If the trials are successful, the manager learns the commercial potential of the drug, which depends on how widely it can be used. Suppose that the forecasted PV at launch depends on the scope of use allowed by the FDA. These PVs are shown at the far right of the decision tree: an upside outcome of NPV = $700 million if the drug can be widely used, a most likely case with NPV = $300 million, and a downside case of NPV = $100 million if the drug’s scope is greatly restricted.9 The NPVs are the payoffs at launch after investment in marketing. Launch comes three years after the start of phase III if the drug is approved by the FDA. The probabilities of the upside, most likely, and downside outcomes are 25%, 50%, and 25%, respectively.
A further R&D investment of $130 million is required for phase III trials and for the prelaunch period. (We have combined phase III and prelaunch for simplicity.) The probability of FDA approval and launch is 80%.
Now let’s value the investments in Figure 10.4. We assume a risk-free rate of 4% and market risk premium of 7%. If FDA-approved pharmaceutical products have asset betas of .8, the opportunity cost of capital is 4 + .8 × 7 = 9.6%.
We work back through the tree from right to left. The NPVs at the start of phase III trials are:
Since the downside NPV is negative at –$69 million, the $130 million investment at the start of phase III should not be made in the downside case. There is no point investing $130 million for an 80% chance of a $100 million payoff three years later. Therefore the value of the R&D program at this point in the decision tree is not –$69 million, but zero.
BEYOND THE PAGE
Try It! Figure 10.4: Decision tree for the pharmaceutical project
mhhe.com/brealey13e
Now calculate the NPV at the initial investment decision for phase II trials. The payoff two years later depends on whether the drug delivers on the upside, most likely, or downside: a 25% chance of NPV = +$295 million, a 50% chance of NPV = +$52 million, and a 25% chance of cancellation and NPV = 0. These NPVs are achieved only if the phase II trials are successful: There is a 44% chance of success and a 56% chance of failure. The initial investment is $18 million. Therefore, NPV is
Thus the phase II R&D is a worthwhile investment, even though the drug has only a 33% chance of making it to launch (.44 × .75 = .33, or 33%).
Notice that we did not increase the 9.6% discount rate to offset the risks of failure in clinical trials or the risk that the drug will fail to generate profits. Concerns about the drug’s efficacy, possible side effects, and scope of use are diversifiable risks, which do not increase the risk of the R&D project to the company’s diversified stockholders. We were careful to take these concerns into account in the cash-flow forecasts, however. The decision tree in Figure 10.4 keeps track of the probabilities of success or failure and the probabilities of upside and downside outcomes.10
Figures 10.3 and 10.4 are both examples of abandonment options. We have not explicitly modeled the investments as options, however, so our NPV calculation is incomplete. We show how to value abandonment options in Chapter 22.
Pro and Con Decision Trees
Any cash-flow forecast rests on some assumption about the firm’s future investment and operating strategy. Often that assumption is implicit. Decision trees force the underlying strategy into the open. By displaying the links between today’s decisions and tomorrow’s decisions, they help the financial manager to find the strategy with the highest net present value.
The decision tree in Figure 10.4 is a simplified version of reality. For example, you could expand the tree to include a wider range of NPVs at launch, possibly including some chance of a blockbuster or of intermediate outcomes. You could allow information about the NPVs to arrive gradually, rather than just at the start of phase III. You could introduce the investment decision at phase I trials and separate the phase III and prelaunch stages. You may wish to draw a new decision tree covering these events and decisions. You will see how fast the circles, squares, and branches accumulate.
The trouble with decision trees is that they get so ____ complex so ____ quickly (insert your own expletives). Life is complex, however, and there is very little we can do about it. It is therefore unfair to criticize decision trees because they can become complex. Our criticism is reserved for analysts who let the complexity become overwhelming. The point of decision trees is to allow explicit analysis of possible future events and decisions. They should be judged not on their comprehensiveness but on whether they show the most important links between today’s and tomorrow’s decisions. Decision trees used in real life will be more complex than Figure 10.4, but they will nevertheless display only a small fraction of possible future events and decisions. Decision trees are like grapevines: They are productive only if they are vigorously pruned.
SUMMARY
Good capital budgeting practice tries to identify the major uncertainties in project proposals. An awareness of these uncertainties may suggest ways that the project can be reconfigured to reduce the dangers, or it may point to some additional research that will confirm whether the project is worthwhile.
There are several ways in which companies try to identify and evaluate the threats to a project’s success. The first is sensitivity analysis. Here the manager considers in turn each forecast or assumption that drives cash flows and recalculates NPV at optimistic and pessimistic values of that variable. The project is “sensitive to” that variable if the resulting range of NPVs is wide, particularly on the pessimistic side.
Sensitivity analysis often moves on to break-even analysis, which identifies break-even values of key variables. Suppose the manager is concerned about a possible shortfall in sales. Then it may be helpful to calculate the sales level at which the project just breaks even (NPV = 0) and to consider the odds that sales will fall that far. Break-even analysis is also done in terms of accounting income, although we do not recommend this application. Projects with a high proportion of fixed costs are likely to have higher break-even points. Because a shortfall in sales results in a larger decline in profits when the costs are largely fixed, such projects are said to have high operating leverage.
Sensitivity analysis and break-even analysis are easy, and they identify the forecasts and assumptions that really count for the project’s success or failure. The important variables do not change one at a time, however. For example, when raw material prices are higher than forecasted, it’s a good bet that selling prices will be higher too. The logical response is scenario analysis, which examines the effects on NPV of changing several variables at a time.
Scenario analysis looks at a limited number of combinations of variables. If you want to go whole hog and look at all possible combinations, you will have to turn to Monte Carlo simulation. In that case, you must build a financial model of the project and specify the probability distribution of each variable that determines cash flow. Then you ask the computer to draw random values for each variable and work out the resulting cash flows. In fact, you ask the computer to do this thousands of times in order to generate complete distributions of future cash flows. With these distributions in hand, you can get a better handle on expected cash flows and project risks. You can also experiment to see how the distributions would be affected by altering project scope or the ranges for any of the variables.
Elementary treatises on capital budgeting sometimes create the impression that once the manager has made an investment decision, there is nothing to do but sit back and watch the cash flows unfold. In practice, companies are constantly modifying their operations. If cash flows are better than anticipated, the project may be expanded; if they are worse, it may be contracted or abandoned altogether. Options to modify projects are known as real options. In this chapter, we introduced the main categories of real options: expansion options, abandonment options, timing options, and options providing flexibility in production.
Good managers take account of real options when they value a project. One convenient way to summarize real options and their cash-flow consequences is to create a decision tree. You identify the things that could happen to the project and the main counteractions that you might take. Then, working back from the future to the present, you can consider which action you should take in each case.
Decision trees can help to identify the possible impact of real options on project cash flows, but we largely skirted the issue of how to value real options. We return to this topic in Chapter 22, after we have covered option-valuation methods in the preceding two chapters.
FURTHER READING
Three not-too-technical references on real options are listed below. Additional references follow Chapter 22.
A. Dixit and R. Pindyck, “The Options Approach to Capital Investment,” Harvard Business Review 73 (May–June 1995), pp. 105–115.
W. C. Kester, “Today’s Options for Tomorrow’s Growth,” Harvard Business Review 62 (March–April 1984), pp. 153–160.
A. Triantis and A. Borison, “Real Options: State of the Practice,” Journal of Applied Corporate Finance 14 (Summer 2001), pp. 8–24.
PROBLEM SETS
Select problems are available in McGraw-Hill’s Connect. Please see the preface for more information.
1. Terminology* Match each of the following terms to one of the definitions or descriptions listed below: sensitivity analysis, scenario analysis, break-even analysis, operating leverage, Monte Carlo simulation, decision tree, real option, tornado diagram.
a. Recalculation of project NPV by changing several inputs to new but consistent values.
b. Opportunity to modify a project at a future date.
c. Analysis of how project NPV changes if different assumptions are made about sales, costs, and other key variables.
d. The degree to which fixed costs magnify the effect on profits of a shortfall in sales.
e. A graphical technique for displaying possible future events and decisions taken in response to those events.
f. A graphical technique that is often used to display the results of a sensitivity analysis.
g. Determination of the level of future sales at which project profitability or NPV equals zero.
h. Method for calculating the probability distribution of possible outcomes.
2. Project analysis True or false?
a. Sensitivity analysis is unnecessary for projects with asset betas that are equal to zero.
b. Sensitivity analysis can be used to identify the variables most crucial to a project’s success.
c. If only one variable is uncertain, sensitivity analysis gives “optimistic” and “pessimistic” values for project cash flow and NPV.
d. The break-even sales level of a project is higher when break-even is defined in terms of NPV rather than accounting income.
e. Risk is reduced when most of the costs are fixed.
f. Monte Carlo simulation can be used to help forecast cash flows.
3. Sensitivity analysis Otobai’s staff (see Section 10-1) has come up with the following revised estimates for the electric scooter project:
|
Optimistic |
Pessimistic |
|
|
% change in capital investment |
–20.00 |
60.00 |
|
% change in working capital |
–50.00 |
50.00 |
|
% change in units sold |
25.00 |
–20.00 |
|
% change in price |
20.00 |
–25.00 |
|
Cost of goods sold as % of sales |
40.00 |
75.00 |
|
% change in fixed costs |
–50.00 |
70.00 |
4. Conduct a sensitivity analysis using the spreadsheets (available in Connect). What are the principal uncertainties in the project?
5. Sensitivity analysis The Rustic Welt Company is proposing to replace its old welt-making machinery with more modern equipment. The new equipment costs $9 million (the existing equipment has zero salvage value). The attraction of the new machinery is that it is expected to cut manufacturing costs from their current level of $8 a welt to $4. However, as the following table shows, there is some uncertainty both about future sales and about the performance of the new machinery:
|
Pessimistic |
Expected |
Optimistic |
|
|
Sales (millions of welts) |
0.4 |
0.5 |
0.7 |
|
Manufacturing cost with new machinery (dollars per welt) |
6 |
4 |
3 |
|
Economic life of new machinery (years) |
7 |
10 |
13 |
6. Conduct a sensitivity analysis of the replacement decision, assuming a discount rate of 12%. Rustic Welt does not pay taxes.
7. Sensitivity analysis Use the spreadsheet for the guano project in Chapter 6 to undertake a sensitivity analysis of the project. Make whatever assumptions seem reasonable to you. What are the critical variables? What should the company’s response be to your analysis?
8. Sensitivity analysis Emperor’s Clothes Fashions can invest $5 million in a new plant for producing invisible makeup. The plant has an expected life of five years, and expected sales are 6 million jars of makeup a year. Fixed costs are $2 million a year, and variable costs are $1 per jar. The product will be priced at $2 per jar. The plant will be depreciated straight-line over five years to a salvage value of zero. The opportunity cost of capital is 10%, and the tax rate is 40%.
a. What is project NPV under these base-case assumptions?
b. What is NPV if variable costs turn out to be $1.20 per jar?
c. What is NPV if fixed costs turn out to be $1.5 million per year?
d. At what price per jar would project NPV equal zero?
9. Sensitivity analysis* A project currently generates sales of $10 million, variable costs equal 50% of sales, and fixed costs are $2 million. The firm’s tax rate is 21%. What are the effects of the following changes on cash flow?
a. Sales increase from $10 million to $11 million.
b. Variable costs increase to 65% of sales.
10. Scenario analysis What is the NPV of the electric scooter project under the following scenario?
Unit sales are 20% below expectations.
Unit price is 10% below expectations.
Unit variable cost remains at 50% of revenue.
Fixed costs increase by 5%.
Investment in plant and equipment and in working capital are unchanged.
11. Scenario analysis You are considering a proposal to produce and market a new sluffing machine. The most likely outcomes for the project are as follows:
Expected sales: 30,000 units per year
Unit price: $50
Variable cost: $30
Fixed cost: $300,000
The project will last for 10 years and requires an initial investment of $1 million, which will be depreciated straight-line over the project life to a final value of zero. The firm’s tax rate is 30%, and the required rate of return is 12%.
However, you recognize that some of these estimates are subject to error. Sales could fall 30% below expectations for the life of the project and, if that happens, the unit price would probably be only $40. The good news is that fixed costs could be as low as $200,000, and variable costs would decline in proportion to sales.
a. What is project NPV if all variables are as expected?
b. What is NPV in the worst-case scenario?
12. Break-even analysis Break-even calculations are most often concerned with the effect of a shortfall in sales, but they could equally well focus on any other component of cash flow. Dog Days is considering a proposal to produce and market a caviar-flavored dog food. It will involve an initial investment of $90,000 that can be depreciated for tax straight-line over 10 years. In each of years 1 to 10, the project is forecast to produce sales of $100,000 and to incur variable costs of 50% of sales and fixed costs of $30,000. The corporate tax rate is 30%, and the cost of capital is 10%.
a. Calculate the NPV and accounting break-even levels of fixed costs.
b. Suppose that you are worried that the corporate tax rate will be increased immediately after you commit to the project. Calculate the break-even rate of taxes.
c. How would a rise in the tax rate affect the accounting break-even point?
13. Break-even analysis Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $100. The materials cost for a synthetic diamond is $40. The fixed costs incurred each year for factory upkeep and administrative expenses are $200,000. The machinery costs $1 million and is depreciated straight-line over 10 years to a salvage value of zero.
a. What is the accounting break-even level of sales in terms of number of diamonds sold?
b. What is the NPV break-even level of sales assuming a tax rate of 35%, a 10-year project life, and a discount rate of 12%?
14. Break-even analysis Modern Artifacts can produce keepsakes that will be sold for $80 each. Nondepreciation fixed costs are $1,000 per year, and variable costs are $60 per unit. The initial investment of $3,000 will be depreciated straight-line over its useful life of five years to a final value of zero, and the discount rate is 10%.
a. What is the accounting break-even level of sales if the firm pays no taxes?
b. What is the NPV break-even level of sales if the firm pays no taxes?
c. What is the accounting break-even level of sales if the firm’s tax rate is 20%?
d. What is the NPV break-even level of sales if the firm’s tax rate is 20%?
15. Break-even analysis Define the cash-flow break-even point as the sales volume (in dollars) at which cash flow equals zero.
a. Is the cash-flow break-even level of sales higher or lower than the zero-profit (accounting) break-even point?
b. If a project operates at cash-flow break-even [see part (a)] for all future years, is its NPV positive or negative?
16. Break-even analysis A financial analyst has computed both accounting and NPV break-even sales levels for a project using straight-line depreciation over a six-year period. The project manager wants to know what will happen to these estimates if the firm can write off the entire investment in the year that it is made. The firm is in a 21% tax bracket.
a. Would the accounting break-even level of sales in the first years of the project increase or decrease?
b. Would the NPV break-even level of sales in the first years of the project increase or decrease?
c. If you were advising the analyst, would the answer to part (a) or (b) be important to you? Specifically, would you say that the switch to immediate expensing makes the project more or less attractive?
17. Fixed and variable costs In a slow year, Deutsche Burgers will produce 2 million hamburgers at a total cost of $3.5 million. In a good year, it can produce 4 million hamburgers at a total cost of $4.5 million.
a. What are the fixed costs of hamburger production?
b. What are the variable costs?
c. What is the average cost per burger when the firm produces 1 million hamburgers?
d. What is the average cost when the firm produces 2 million hamburgers?
e. Why is the average cost lower when more burgers are produced?
18. Operating leverage You estimate that your cattle farm will generate $1 million of profits on sales of $4 million under normal economic conditions and that the degree of operating leverage is 8.
a. What will profits be if sales turn out to be $3.5 million?
b. What if they are $4.5 million?
19. Operating leverage Look again at Modern Artifacts in Problem 12.
a. What is the degree of operating leverage of Modern Artifacts when sales are $7,000?
b. What is the degree of operating leverage when sales are $12,000?
c. Why is operating leverage different at these two levels of sales?
20. Operating leverage What is the lowest possible value for the degree of operating leverage for a profitable firm? Show with a numerical example that if Modern Artifacts (see Problem 12) has zero fixed costs and zero depreciation, then DOL = 1 and, in fact, sales and profits are directly proportional, so a 1% change in sales results in a 1% change in profits.
21. Operating leverage* A project has fixed costs of $1,000 per year, depreciation charges of $500 a year, annual revenue of $6,000, and variable costs equal to two-thirds of revenues.
a. If sales increase by 10%, what will be the increase in pretax profits?
b. What is the degree of operating leverage of this project?
22. Monte Carlo simulation Suppose a manager has already estimated a project’s cash flows, calculated its NPV, and done a sensitivity analysis like the one shown in Table 10.2. List the additional steps required to carry out a Monte Carlo simulation of project cash flows.
23. Real options Explain why options to expand or contract production are most valuable when forecasts about future business conditions are most uncertain.
24. Real options Describe the real option in each of the following cases:
a. Moda di Milano postpones a major investment. The expansion has positive NPV on a discounted cash-flow basis, but top management wants to get a better fix on product demand before proceeding.
b. Western Telecom commits to production of digital switching equipment specially designed for the European market. The project has a negative NPV, but it is justified on strategic grounds by the need for a strong market position in the rapidly growing, and potentially very profitable, market.
c. Western Telecom vetoes a fully integrated, automated production line for the new digital switches. It relies on standard, less-expensive equipment. The automated production line is more efficient overall, according to a discounted cash-flow calculation.
d. Mount Fuji Airways buys a jumbo jet with special equipment that allows the plane to be switched quickly from freight to passenger use or vice versa.
25. Real options True or false?
a. Decision trees can help identify and describe real options.
b. The option to expand increases PV.
c. High abandonment value decreases PV.
d. If a project has positive NPV, the firm should always invest immediately.
26. Real options* A silver mine can yield 10,000 ounces of silver at a variable cost of $32 per ounce. The fixed costs of owning the mine are $40,000 per year regardless of whether the mine is open or closed. In half the years, silver can be sold for $48 per ounce; in the other years, silver can be sold for only $24 per ounce. Ignore taxes.
a. What is the average cash flow you will receive from the mine if it is always kept in operation and the silver always is sold in the year it is mined?
b. Now suppose you can costlessly shut down the mine in years of low silver prices. What happens to the average cash flow from the mine?
27. Real options An auto plant that costs $100 million to build can produce a line of flex-fuel cars. The investment will produce cash flows with a present value of $140 million if the line is successful but only $50 million if it is unsuccessful. You believe that the probability of success is only about 50%. You will learn whether the line is successful immediately after building the plant.
a. Would you build the plant?
b. Suppose that the plant can be sold for $95 million to another automaker if the auto line is not successful. Now would you build the plant?
c. Illustrate the option to abandon in part (b) using a decision tree.
28. Decision trees Look back at the Vegetron electric mop project in Section 9-4. Assume that if tests fail and Vegetron continues to go ahead with the project, the $1 million investment would generate only $75,000 a year. Display Vegetron’s problem as a decision tree.
29. Decision trees* Your midrange guess as to the amount of oil in a prospective field is 10 million barrels, but there is a 50% chance that the amount of oil is 15 million barrels and a 50% chance of 5 million barrels. If the actual amount of oil is 15 million barrels, the present value of the cash flows from drilling will be $8 million. If the amount is only 5 million barrels, the present value will be only $2 million. It costs $3 million to drill the well. Suppose that a seismic test costing $100,000 can immediately verify the amount of oil under the ground. Is it worth paying for the test? Use a decision tree to justify your answer.
30. Decision trees Look again at the decision tree in Figure 10.4. Expand the possible outcomes as follows:
· Blockbuster: PV = $1.5 billion with 5% probability.
· Above average: PV = $700 million with 20% probability.
· Average: PV = $300 million with 40% probability.
· Below average: PV = $100 million with 25% probability.
· “Dog”: PV = $40 million with 10% probability.
Redraw the decision tree. Is the $18 million investment in phase II trials still positive NPV?
31. Decision trees Look again at the example in Figure 10.4. The R&D team has put forward a proposal to invest an extra $20 million in expanded phase II trials. The object is to prove that the drug can be administered by a simple inhaler rather than as a liquid. If successful, the scope of use is broadened and the upside PV increases to $1 billion. The probabilities of success are unchanged. Go to the Beyond the Page Excel spreadsheet version of Figure 10.4. Is the extra $20 million investment worthwhile? Would your answer change if the probability of success in the phase III trials falls to 75%?
CHALLENGE
30. Project analysis New Energy is evaluating a new biofuel facility. The plant would cost $4,000 million to build and has the potential to produce up to 40 million barrels of synthetic oil a year. The product is a close substitute for conventional oil and would sell for the same price. The market price of oil currently is fluctuating around $100 per barrel, but there is considerable uncertainty about future prices. Variable costs for the organic inputs to the production process are estimated at $82 per barrel and are expected to be stable. In addition, annual upkeep and maintenance expenses on the facility will be $100 million regardless of the production level. The plant has an expected life of 15 years, and it will be depreciated straight-line over 10 years. Salvage value net of clean-up costs is expected to be negligible. Demand for the product is difficult to forecast. Depending on consumer acceptance, sales might range from 25 million to 35 million barrels annually. The discount rate is 12% and New Energy’s tax bracket is 25%.
a. Find the project NPV for the following combinations of oil price and sales volume. Which source of uncertainty seems most important to the success of the project?
|
Oil Price |
|||
|
Annual Sales (millions of barrels) |
$80/Barrel |
$100/Barrel |
$120/Barrel |
|
25 |
|||
|
30 |
|||
|
35 |
|||
b. At an oil price of $100, what level of annual sales, maintained over the life of the plant, is necessary for NPV break-even? (This will require trial and error unless you are familiar with more advanced features of Excel such as the Goal Seek command.)
c. At an oil price of $100, what is the accounting break-even level of sales in each year? Why does it change each year? Does this notion of break-even seem reasonable to you?
d. If each of the scenarios in the table in part (a) is equally likely, what is the NPV of the facility?
e. Why might the facility be worth building despite your answer to part (d)? (Hint: What real option may the firm have to avoid losses in low-oil-price scenarios?)
31. Monte Carlo simulation Look back at the guano project in Section 6-3. Use the Crystal Ball™ software to simulate how uncertainty about inflation could affect the project’s cash flows.
32. Decision trees Magna Charter is a new corporation formed by Agnes Magna to provide an executive flying service for the southeastern United States. The founder thinks there will be a ready demand from businesses that cannot justify a full-time company plane but nevertheless need one from time to time. However, the venture is not a sure thing. There is a 40% chance that demand in the first year will be low. If it is low, there is a 60% chance that it will remain low in subsequent years. On the other hand, if the initial demand is high, there is an 80% chance that it will stay high. The immediate problem is to decide what kind of plane to buy. A turboprop costs $550,000. A piston-engine plane costs only $250,000 but has less capacity. Moreover, the piston-engine plane is an old design and likely to depreciate rapidly. Ms. Magna thinks that next year secondhand piston aircraft will be available for only $150,000.
Table 10.6 shows how the payoffs in years 1 and 2 from both planes depend on the pattern of demand. You can see, for example, that if demand is high in both years 1 and 2, the turbo will provide a payoff of $960,000 in year 2. If demand is high in year 1 but low in year 2, the turbo’s payoff in the second year is only $220,000. Think of the payoffs in the second year as the cash flow that year plus the year-2 value of any subsequent cash flows. Also think of these cash flows as certainty equivalents, which can therefore be discounted at the risk-free interest rate of 10%.
Ms. Magna now has an idea: Why not start out with one piston-engine plane? If demand is low in the first year, Magna Charter can sit tight with this one relatively inexpensive aircraft. On the other hand, if demand is high in the first year she can buy a second piston-engine plane for only $150,000. In this case, if demand continues to be high, the payoff in year 2 from the two piston planes will be $800,000. However, if demand in year 2 were to decline, the payoff would be only $100,000.
a. Draw a decision tree setting out Magna Charter’s choices.
b. If Magna Charter buys a piston plane, should it expand if demand turns out to be high in the first year?
c. Given your answer to part (b), would you recommend that Ms. Magna buy the turboprop or the piston-engine plane today?
d. What would be the NPV of an investment in a piston plane if there were no option to expand? How much extra value is contributed by the option to expand?
TABLE 10.6 The possible payoffs from Ms. Magna’s flying service. (All figures are in thousands. Probabilities are in parentheses.)
MINI-CASE 
Waldo County
Waldo County, the well-known real estate developer, worked long hours, and he expected his staff to do the same. So George Chavez was not surprised to receive a call from the boss just as George was about to leave for a long summer’s weekend.
Mr. County’s success had been built on a remarkable instinct for a good site. He would exclaim “Location! Location! Location!” at some point in every planning meeting. Yet finance was not his strong suit. On this occasion, he wanted George to go over the figures for a new $90 million outlet mall designed to intercept tourists heading downeast toward Maine. “First thing Monday will do just fine,” he said as he handed George the file. “I’ll be in my house in Bar Harbor if you need me.”
George’s first task was to draw up a summary of the projected revenues and costs. The results are shown in Table 10.7. Note that the mall’s revenues would come from two sources: The company would charge retailers an annual rent for the space they occupied and, in addition, it would receive 5% of each store’s gross sales.
Construction of the mall was likely to take three years. The construction costs could be depreciated straight-line over 15 years starting in year 3. As in the case of the company’s other developments, the mall would be built to the highest specifications and would not need to be rebuilt until year 17. The land was expected to retain its value, but could not be depreciated for tax purposes.
Construction costs, revenues, operating and maintenance costs, and local real estate taxes were all likely to rise in line with inflation, which was forecasted at 2% a year. Local real estate taxes are deductible for corporate tax. The company’s corporate tax rate was 25% and the cost of capital was 9% in nominal terms.
George decided first to check that the project made financial sense. He then proposed to look at some of the things that might go wrong. His boss certainly had a nose for a good retail project, but he was not infallible. The Salome project had been a disaster because store sales had turned out to be 40% below forecast. What if that happened here? George wondered just how far sales could fall short of forecast before the project would be underwater.
Inflation was another source of uncertainty. Some people were talking about a zero long-term inflation rate, but George also wondered what would happen if inflation jumped to, say, 10%.
TABLE 10.7 Projected revenues and costs in real terms for the Downeast Tourist Mall (figures in $ millions)
A third concern was possible construction cost overruns and delays due to required zoning changes and environmental approvals. George had seen cases of 25% construction cost overruns and delays up to 12 months between purchase of the land and the start of construction. He decided that he should examine the effect that this scenario would have on the project’s profitability.
“Hey, this might be fun,” George exclaimed to Mr. Waldo’s secretary, Fifi, who was heading for Old Orchard Beach for the weekend. “I might even try Monte Carlo.”
“Waldo went to Monte Carlo once,” Fifi replied. “Lost a bundle at the roulette table. I wouldn’t remind him. Just show him the bottom line. Will it make money or lose money? That’s the bottom line.”
“OK, no Monte Carlo,” George agreed. But he realized that building a spreadsheet and running scenarios was not enough. He had to figure out how to summarize and present his results to Mr. County.
QUESTIONS
1. What is the project’s NPV, given the projections in Table 10.7?
2. Conduct a sensitivity and a scenario analysis of the project. What do these analyses reveal about the project’s risks and potential value?
1Notice that the term “fixed costs” does not imply that they are certain or cannot change from year to year. It indicates that the costs are not related to the level of sales.
2If you doubt this, try some simple experiments. Ask the person who repairs your dishwasher to state a numerical probability that it will work for at least one more year. Or construct your own subjective probability distribution of the number of telephone calls you will receive next week. That ought to be easy. Try it. We will also refer in Chapter 11 to evidence that people tend to be overconfident in their forecasts and to understate the possible errors.
3Notice that because fixed costs change from year to year, so does the break-even level of sales.
4In Chapter 9, we developed a measure of operating leverage that was expressed in terms of cash flows and their present values. We used this measure to show how beta depends on leverage.
5This formula for DOL can be derived as follows. If sales increase by 1%, then variable costs will also increase by 1%, and profits will increase by .01 × (sales – variable costs) = .01 × (pretax profits + fixed costs). Now recall the definition of DOL:
6Suppose “near certainty” means “99% of the time.” If forecast errors are normally distributed, this degree of certainty requires a range of plus or minus three standard deviations. Other distributions could, of course, be used. For example, the marketing department may view any level of sales of 15% either side of forecast as equally likely. In that case, the simulation would require a uniform (rectangular) distribution of forecast errors.
7Some simulation models do recognize the possibility of changing policy. For example, when a pharmaceutical company uses simulation to analyze its R&D decisions, it allows for the possibility that the company can abandon the development at each phase.
8The website of the Tufts Center for the Study of Drug Development (http://csdd.tufts.edu) provides a wealth of information about the costs and risks of pharmaceutical R&D.
9The most likely case is not the average outcome because PVs in the pharmaceutical business are skewed to the upside. The average PV is .25 × 700 + .5 × 300 + .25 × 100 = $350 million.
10The market risk attached to the PVs at launch is recognized in the 9.6% discount rate.