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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 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.

Such options to expand do not show up in the assets that the company lists in its balance sheet, but investors are very aware of their existence. If a company has valuable real options that can allow it to invest in new profitable projects, its market value will be higher than the value of its physical assets now in place.

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’s 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 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 don’t 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.17

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 really exist only 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. 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 doesn’t sell, this equipment will be worthless.

17The abandonment option was first analyzed by A. A. Robichek and J. C. Van Horne, “Abandonment Value in Capital Budgeting,” Journal of Finance 22 (December 1967), pp. 577–590.

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 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 technology B’s flexibility if you are unsure about whether the new outboard will sink or swim in the marketplace.

We can make the value of this flexibility concrete by expressing it as a real option. Just for simplicity, assume that the initial capital outlays for technologies A and B are the same. Technology A, with its low-cost customized machinery, will provide a payoff of $18.5 million if the outboard is popular with boat owners and $8.5 million if it is not. Think of these payoffs as the project’s cash flow in its first year of production plus the present value of all subsequent cash flows. The corresponding payoffs to technology B are $18 million and $8 million.

Payoffs from Producing

Outboard ($ millions)

If you are obliged to continue in production regardless of how unprofitable the project turns out to be, then technology A is clearly the superior choice. But remember that at year-end you can bail out of technology B for $10 million. If the outboard is not a success in the market, you are better off selling the plant and equipment for $10 million than continuing with a project that has a present value of only $8 million.

Figure 10.7 summarizes this example 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:

Technology B provides an insurance policy: If the outboard’s sales are disappointing, you can abandon the project and recover $10 million. You can think of this abandonment option as an option to sell the assets for $10 million. The total value of the project using technology B is its DCF value, assuming that the company does not abandon, plus the value of the abandonment option. When you value this option, you are placing a value on flexibility.

Two Other Real Options

These are not the only real options. For example, companies with positive-NPV projects are not obliged to undertake them right away. If the outlook is uncertain, you may be able to avoid a costly mistake by waiting a bit. Such options to postpone investment are called timing options.

tween burning oil to burning natural gas. We refer to these opportunities as production options.

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 close 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.18 Decision trees can help to understand 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.

An Example: Magna Charter

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 percent chance that demand in the first year will be low. If it is low, there is a 60 percent chance that it will remain low in subsequent years. On the other hand, if the initial demand is high, there is an 80 percent 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 and customer appeal. 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.

That gives Ms. Magna an idea: Why not start out with one piston plane and buy another if demand is still high? It will cost only $150,000 to expand. If demand is low, Magna Charter can sit tight with one small, relatively inexpensive aircraft.

Figure 10.8 displays these choices. The square on the left marks the company’s initial decision to purchase a turboprop for $550,000 or a piston aircraft for $250,000. After the company has made its decision, fate decides on the first year’s demand. You can see in parentheses the probability that demand will be high or low, and you can see the expected cash flow for each combination of aircraft and demand level. At the end of the year the company has a second decision to make if it has a piston-engine aircraft: It can either expand or sit tight. This decision point is marked by the second square. Finally fate takes over again and selects the level of demand for year 2. Again you can see in parentheses the probability of high or low demand. Notice that the probabilities for the second year depend on the firstperiod outcomes. For example, if demand is high in the first period, then there is an 80 percent chance that it will also be high in the second. The chance of high

18The 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.

tomorrow’s decisions, they help the financial manager to find the strategy with the highest net present value.

The trouble with decision trees is that they get so _____ complex so _____

quickly (insert your own expletives). What will Magna Charter do if demand is neither high nor low but just middling? In that event Ms. Magna might sell the turboprop and buy a piston-engine plane, or she might defer expansion and abandonment decisions until year 2. Perhaps middling demand requires a decision about a price cut or an intensified sales campaign.

We could draw a new decision tree covering this expanded set of events and decisions. Try it if you like: You’ll see how fast the circles, squares, and branches accumulate.

Life is complex, 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 10.8, 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.

Decision trees can help identify the future choices available to the manager and can give a clearer view of the cash flows and risks of a project. However, our analysis of the Magna Charter project begged an important question. The option to expand enlarged the spread of possible outcomes and therefore increased the risk of investing in a piston aircraft. Conversely, the option to bail out would narrow the spread of possible outcomes, reducing the risk of investment. We should have used different discount rates to recognize these changes in risk, but decision trees do not tell us how to do this. But the situation is not hopeless. Modern techniques of option pricing can value these investment options. We will describe these techniques in Chapters 20 and 21, and turn again to real options in Chapter 22.

Decision Trees and Monte Carlo Simulation

We have said that any cash-flow forecast rests on assumptions about future investment and operating strategy. Think back to the Monte Carlo simulation model that we constructed for Otobai’s electric scooter project. What strategy was that based on? We don’t know. Inevitably Otobai will face decisions about pricing, production, expansion, and abandonment, but the model builder’s assumptions about these decisions are buried in the model’s equations. The model builder may have implicitly identified a future strategy for Otobai, but it is clearly not the optimal one. There will be some runs of the model when nearly everything goes wrong and when in real life Otobai would abandon to cut its losses. Yet the model goes on period after period, heedless of the drain on Otobai’s cash resources. The most unfavorable outcomes reported by the simulation model would never be encountered in real life.

On the other hand, the simulation model probably understates the project’s potential value if nearly everything goes right: There is no provision for expanding to take advantage of good luck.

Most simulation models incorporate a business-as-usual strategy, which is fine as long as there are no major surprises. The greater the divergence from expected levels of market growth, market share, cost, etc., the less realistic is the simulation. Therefore the extreme high and low simulated values—the “tails” of the simulated distributions—should be treated with extreme caution. Don’t take the area under the tails as realistic probabilities of disaster or bonanza.

SUMMARY There is more to capital budgeting than grinding out calculations of net present value. If you can identify the major uncertainties, you may find that it is worth un-

dertaking some additional preliminary research that will confirm whether the project is worthwhile. And even if you decide that you have done all you can to resolve the uncertainties, you still want to be aware of the potential problems. You do not want to be caught by surprise if things go wrong: You want to be ready to take cor-

rective action.

There are three ways in which companies try to identify the principal threats to a project’s success. The simplest is sensitivity analysis. In this case the manager considers in turn each of the determinants of the project’s success and recalculates NPV at very optimistic and very pessimistic levels of that variable. This establishes a range of possible values. The project is “sensitive to” the variable if the range is wide, especially on the pessimistic side.

Sensitivity analysis of this kind is easy, but it is not always helpful. Variables do not usually change one at a time. If costs are higher than you expect, it is a good bet that prices will be higher also. And if prices are higher, it is a good bet that sales volume will be lower. If you don’t allow for the dependencies between the swings and the merry-go-rounds, you may get a false idea of the hazards of the fairground business. Many companies try to cope with this problem by examining the effect on the project of alternative plausible combinations of variables. In other words, they will estimate the net present value of the project under different scenarios and compare these estimates with the base case.

In a sensitivity analysis you change variables one at a time: When you analyze scenarios, you look at a limited number of alternative combinations of variables. If you want to go whole hog and look at all possible combinations of variables, then you will probably use Monte Carlo simulation to cope with the complexity. In that case you must construct a complete model of the project and specify the probability distribution of each of the determinants of cash flow. You can then ask the computer to select a random number for each of these determinants and work out the cash flows that would result. After the computer has repeated this process a few thousand times, you should have a fair idea of the expected cash flow in each year and the spread of possible cash flows.

Simulation can be a very useful tool. The discipline of building a model of the project can in itself lead you to a deeper understanding of the project. And once you have constructed your model, it is a simple matter to see how the outcomes would be affected by altering the scope of the project or the distribution of 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 mod-