ifying 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 the financial manager to identify real options and their impacts on project risks and cash flows. The options may increase or decrease project risk. 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.
For an excellent case study of break-even analysis, see:
U. E. Reinhardt: “Break-Even Analysis for Lockheed’s TriStar: An Application of Financial Theory,” Journal of Finance, 28:821–838 (September 1973).
Hax and Wiig discuss how Monte Carlo simulation and decision trees were used in an actual capital budgeting decision:
A. C. Hax and K. M. Wiig: “The Use of Decision Analysis in Capital Investment Problems,”
Sloan Management Review, 17:19–48 (Winter 1976).
Merck’s use of Monte Carlo simulation is discussed in:
N. A. Nichols: “Scientific Management at Merck: An Interview with Judy Lewent,” Harvard Business Review, 72:89–99 (January–February 1994).
Three not-too-technical references on real options are listed below. Additional references follow Chapter 22.
M. Amram and N. Kulatilaka: Real Options: Managing Strategic Investments in an Uncertain World, Harvard Business School Press, Boston, 1999.
A. Dixit and R. Pindyck: “The Options Approach to Capital Investment,” Harvard Business Review, 73:105–115 (May–June 1995).
W. C. Kester: “Today’s Options for Tomorrow’s Growth,” Harvard Business Review, 62:153–160 (March–April 1984).
FURTHER READING
1. Define and briefly explain each of the following terms or procedures:
QUIZ
a.Sensitivity analysis
b.Scenario analysis
c.Break-even analysis
d.Monte Carlo simulation
e.Decision tree
f.Real option
g.Abandonment value
h.Expansion value
2.True or false?
a.Sensitivity analysis is unnecessary for projects with asset betas that are equal to zero.
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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.Monte Carlo simulation can be used to help forecast cash flows.
f.Monte Carlo simulation eliminates the need to estimate a project’s opportunity cost of capital.
3.What are the advantages of scenario analysis compared to sensitivity analysis?
4.How should Monte Carlo simulation be used to help determine a project’s NPV?
5.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.
6.What are the four chief categories of real options?
7.True or false?
a.Decision trees can help identify and describe real options.
b.The option to expand increases NPV
c.High abandonment value decreases NPV.
d.If a project has positive NPV, the firm should always invest immediately.
8.Give an example of why flexible production facilities are valuable.
PRACTICE
1. What is the NPV of the electric scooter project under the following scenario?
QUESTIONS
Market size
1.1 million
Market share
.1
EXCEL
Unit price
¥400,000
Unit variable cost
¥360,000
Fixed cost
¥2 billion
2. Otobai’s staff has come up with the following revised estimates for the electric scooter
project:
Pessimistic
Expected
Optimistic
Market size
.8 million
1.0 million
1.2 million
Market share
.04
.1
.16
Unit price
¥300,000
¥375,000
¥400,000
Unit variable cost
¥350,000
¥300,000
¥275,000
Fixed cost
¥5 billion
¥3 billion
¥1 billion
Conduct a sensitivity analysis. What are the principal uncertainties in the project?
3.Otobai is considering still another production method for its electric scooter. It would require an additional investment of ¥15 billion but would reduce variable costs by ¥40,000 per unit. Other assumptions follow Table 10.1.
a.What is the NPV of this alternative scheme?
b.Draw break-even charts for this alternative scheme along the lines of Figure 10.1.
c.Explain how you would interpret the break-even figure.
Now suppose Otobai’s management would like to know the figure for variable cost per unit at which the electric scooter project in Section 10.1 would break even. Calculate the
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level of costs at which the project would earn zero profit and at which it would have zero NPV.
4.The Rustic Welt Company is proposing to replace its old welt-making machinery with more modern equipment. The new equipment costs $10 million and the company expects to sell its old equipment for $1 million. 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
.4
.5
.7
Manufacturing cost with new
machinery, dollars per welt
6
4
3
Economic life of new
machinery, years
7
10
13
Conduct a sensitivity analysis of the replacement decision, assuming a discount rate of 12 percent. Rustic Welt does not pay taxes.
5.Rustic Welt could commission engineering tests to determine the actual improvement in manufacturing costs generated by the proposed new welt machines. (See problem 4 above.) The study would cost $450,000. Would you advise the company to go ahead with the study?
6.Summarize the problems that a manager would encounter in interpreting a standard sensitivity analysis, such as the one shown in Table 10.2. Which of these problems are alleviated by examining the project under alternative scenarios?
7.Operating leverage is often measured as the percentage increase in profits after depre-
ciation for a 1 percent increase in sales.
EXCEL
a.Calculate the operating leverage for the electric scooter project assuming unit sales are 100,000 (see Section 10.1).
b.Now show that this figure is equal to 1 (fixed costs/profits) including depreciation, divided by profits.
c.Would operating leverage be higher or lower if sales were 200,000 scooters?
8.For what kinds of capital investment projects do you think Monte Carlo simulation would be most useful? For example, can you think of some industries in which this technique would be particularly attractive? Would it be more useful for large-scale investments than small ones? Discuss.
9.Look back at the Vegetron electric mop project in Section 9.6. 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.
10.Describe the real option in each of the following cases:
a.Deutsche Metall postpones a major plant expansion. 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
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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.
e.The British–French treaty giving a concession to build a railroad link under the English Channel also required the concessionaire to propose by the year 2000 to build a “drive-through link” if “technical and economic conditions permit . . . and the decrease in traffic shall justify it without undermining the expected return
on the first [rail] link.” Other companies will not be permitted to build a link before the year 2020.
11.An auto plant that costs $100 million to build can produce a new line of cars that will generate 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 percent.
a.Would you build the plant?
b.Suppose that the plant can be sold for $90 million to another automaker if the line is not successful. Now would you build the plant?
c.Illustrate this option to abandon using a decision tree.
12.Agnes Magna has found some errors in her data (see Section 10.3). The corrected figures are as follows:
Price of turbo, year 0
$350,000
Price of piston, year 0
$180,000
Discount rate
8 percent
Redraw the decision tree with the changed data. Calculate the value of the option to expand. Which plane should Ms. Magna buy?
13.Ms. Magna has thought of another possibility. She could abandon the venture entirely by selling the plane at the end of the first year. Suppose that the piston-engine plane can be sold for $150,000 and the turboprop can be sold for $500,000.
a.In what circumstances would it pay for Ms. Magna to sell either plane?
b.Redraw the decision tree in Figure 10.8 to recognize that there will be circumstances in which Ms. Magna will choose to take the money and bail out.
c.Recalculate the value of the project recognizing the abandonment option.
d.How much does the option to abandon add to the value of the piston-engine project? How much does it add to the value of the turboprop project?
14.How can decision trees help the financial manager to “open up the black box” and understand a capital investment project better? Why are decision trees not complete solutions to the valuation of real options?
CHALLENGE QUESTIONS
1.You own an unused gold mine that will cost $100,000 to reopen. If you open the mine, you expect to be able to extract 1,000 ounces of gold a year for each of three years. After that, the deposit will be exhausted. The gold price is currently $500 an ounce, and each year the price is equally likely to rise or fall by $50 from its level at the start of the year. The extraction cost is $460 an ounce and the discount rate is 10 percent.
a.Should you open the mine now or delay one year in the hope of a rise in the gold price?
b.What difference would it make to your decision if you could costlessly (but irreversibly) shut down the mine at any stage?
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2.You are considering starting a company to provide a new Internet access service. There is a 60 percent chance the demand will be high in the first year. If it is high, there is an 80 percent chance that it will continue high indefinitely. If demand is low in the first year, there is a 60 percent chance that it will continue low indefinitely.
If demand is high, forecasted revenue is $900,000 a year; if demand is low, forecasted revenue is $700,000 a year. You can cease to offer the service at any point, in which case, revenues are zero. Costs other than computing and telecommunications are forecasted at $500,000 a year regardless of demand. These costs also can be terminated at any point.
You have a choice on computing and telecommunications. One possibility is to buy your own computers and software and to set up your own network and systems. This involves an initial outlay of $2,000,000 and no subsequent expenditure. The resulting system would have an economic life of 10 years and no salvage value. The alternative is to rent computer and telecommunications services as you need them from AT&T or one of the other major telecommunications companies. They propose to charge you 40 percent of your revenues.
Assume that a decision to buy your own system cannot be reversed (i.e., if you buy a computer, you cannot resell it; if you do not buy it today, you cannot do so later). There are no taxes, and the opportunity cost of capital is 10 percent.
Draw a decision tree showing your choices. Is it better to construct your own system or to rent it? State clearly any additional assumptions that you need to make.
3.Explain why real options are most valuable when forecasts of future cash flows are most uncertain.
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 Probit 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 percent 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 real estate taxes were all likely to rise in line with inflation, which was forecasted at 2 percent a year. The company’s tax rate was 35 percent and the cost of capital was 9 percent in nominal terms.
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Year
0
1
2
3
4
5–17
Investment:
Land
30
Construction
20
30
10
Operations:
Rentals
12
12
12
Share of retail sales
24
24
24
Operating and maintenance costs
2
4
4
10
10
10
Real estate taxes
2
2
3
4
4
4
T A B L E 1 0 . 7
Projected revenues and costs in real terms for the Downeast Tourist Mall (figures in $ millions).
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 percent 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 longterm inflation rate, but George also wondered what would happen if inflation jumped to, say, 10 percent.
A third concern was possible construction cost overruns and delays due to required zoning changes and environmental approvals. George had seen cases of 25 percent 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?
C H A P T E R E L E V E N
WHERE POSITIVE
N E T P R E S E N T V A L U E S C O M E F R O M
286
WHY IS AN M.B.A. student who has learned about DCF like a baby with a hammer? Answer: Because to a baby with a hammer, everything looks like a nail.
Our point is that you should not focus on the arithmetic of DCF and thereby ignore the forecasts that are the basis of every investment decision. Senior managers are continuously bombarded with requests for funds for capital expenditures. All these requests are supported with detailed DCF analyses showing that the projects have positive NPVs.1 How, then, can managers distinguish the NPVs that are truly positive from those that are merely the result of forecasting errors? We suggest that they should ask some probing questions about the possible sources of economic gain.
The first section in this chapter reviews certain common pitfalls in capital budgeting, notably the tendency to apply DCF when market values are already available and no DCF calculations are needed. The second section covers the economic rents that underlie all positive-NPV investments. The third section presents a case study describing how Marvin Enterprises, the gargle blaster company, analyzed the introduction of a radically new product.
11.1 LOOK FIRST TO MARKET VALUES
Let us suppose that you have persuaded all your project sponsors to give honest forecasts. Although those forecasts are unbiased, they are still likely to contain errors, some positive and others negative. The average error will be zero, but that is little consolation because you want to accept only projects with truly superior profitability.
Think, for example, of what would happen if you were to jot down your estimates of the cash flows from operating various lines of business. You would probably find that about half appeared to have positive NPVs. This may not be because you personally possess any superior skill in operating jumbo jets or running a chain of laundromats but because you have inadvertently introduced large errors into your estimates of the cash flows. The more projects you contemplate, the more likely you are to uncover projects that appear to be extremely worthwhile. Indeed, if you were to extend your activities to making cash-flow estimates for various companies, you would also find a number of apparently attractive takeover candidates. In some of these cases you might have genuine information and the proposed investment really might have a positive NPV. But in many other cases the investment would look good only because you made a forecasting error.
What can you do to prevent forecast errors from swamping genuine information? We suggest that you begin by looking at market values.
The Cadillac and the Movie Star
The following parable should help to illustrate what we mean. Your local Cadillac dealer is announcing a special offer. For $45,001 you get not only a brand new Cadillac but also the chance to shake hands with your favorite movie star. You wonder how much you are paying for that handshake.
There are two possible approaches to the problem. You could evaluate the worth of the Cadillac’s power steering, disappearing windshield wipers, and other features and conclude that the Cadillac is worth $46,000. This would seem to suggest that the dealership is willing to pay $999 to have a movie star shake hands with
1Here is another riddle. Are projects proposed because they have positive NPVs, or do they have positive NPVs because they are proposed? No prizes for the correct answer.
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you. Alternatively, you might note that the market price for Cadillacs is $45,000, so that you are paying $1 for the handshake. As long as there is a competitive market for Cadillacs, the latter approach is more appropriate.
Security analysts face a similar problem whenever they value a company’s stock. They must consider the information that is already known to the market about a company, and they must evaluate the information that is known only to them. The information that is known to the market is the Cadillac; the private information is the handshake with the movie star. Investors have already evaluated the information that is generally known. Security analysts do not need to evaluate this information again. They can start with the market price of the stock and concentrate on valuing their private information.
While lesser mortals would instinctively accept the Cadillac’s market value of $45,000, the financial manager is trained to enumerate and value all the costs and benefits from an investment and is therefore tempted to substitute his or her own opinion for the market’s. Unfortunately this approach increases the chance of error. Many capital assets are traded in a competitive market, so it makes sense to start with the market price and then ask why these assets should earn more in your hands than in your rivals’.
Example: Investing in a New Department Store
We encountered a department store chain that estimated the present value of the expected cash flows from each proposed store, including the price at which it could eventually sell the store. Although the firm took considerable care with these estimates, it was disturbed to find that its conclusions were heavily influenced by the forecasted selling price of each store. Management disclaimed any particular real estate expertise, but it discovered that its investment decisions were unintentionally dominated by its assumptions about future real estate prices.
Once the financial managers realized this, they always checked the decision to open a new store by asking the following question: “Let us assume that the property is fairly priced. What is the evidence that it is best suited to one of our department stores rather than to some other use? In other words, if an asset is worth more to others than it is to you, then beware of bidding for the asset against them.
Let us take the department store problem a little further. Suppose that the new store costs $100 million.2 You forecast that it will generate after-tax cash flow of $8 million a year for 10 years. Real estate prices are estimated to grow by 3 percent a year, so the expected value of the real estate at the end of 10 years is 100 (1.03)10$134 million. At a discount rate of 10 percent, your proposed department store has an NPV of $1 million:
NPV 100
8
8
…
8 134
$1 million
1.10
11.1022
11.10210
Notice how sensitive this NPV is to the ending value of the real estate. For example, an ending value of $120 million implies an NPV of $5 million.
It is helpful to imagine such a business as divided into two parts—a real estate subsidiary which buys the building and a retailing subsidiary which rents and operates it. Then figure out how much rent the real estate subsidiary would have to charge, and ask whether the retailing subsidiary could afford to pay the rent.
2For simplicity we assume the $100 million goes entirely to real estate. In real life there would also be substantial investments in fixtures, information systems, training, and start-up costs.
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In some cases a fair market rental can be estimated from real estate transactions. For example, we might observe that similar retail space recently rented for $10 million a year. In that case we would conclude that our department store was an unattractive use for the site. Once the site had been acquired, it would be better to rent it out at $10 million than to use it for a store generating only $8 million.
Suppose, on the other hand, that the property could be rented for only $7 million per year. The department store could pay this amount to the real estate subsidiary and still earn a net operating cash flow of 8 7 $1 million. It is therefore the best current use for the real estate.3
Will it also be the best future use? Maybe not, depending on whether retail profits keep pace with any rent increases. Suppose that real estate prices and rents are expected to increase by 3 percent per year. The real estate subsidiary must charge 7 1.03 $7.21 million in year 2, 7.21 1.03 $7.43 million in year 3, and so on.4 Figure 11.1 shows that the store’s income fails to cover the rental after year 5.
If these forecasts are right, the store has only a five-year economic life; from that point on the real estate is more valuable in some other use. If you stubbornly believe that the department store is the best long-term use for the site, you must be ignoring potential growth in income from the store.5
There is a general point here. Whenever you make a capital investment decision, think what bets you are placing. Our department store example involved at least two bets—one on real estate prices and another on the firm’s ability to run a successful department store. But that suggests some alternative strategies. For instance, it would be foolish to make a lousy department store investment just because you are optimistic about real estate prices. You would do better to buy real estate and rent it out to the highest bidders. The converse is also true. You shouldn’t be deterred from going ahead with a profitable department store because you are pessimistic about real estate prices. You would do better to sell the real estate and rent it back for the department store. We suggest that you separate the two bets by first asking, “Should we open a department store on this site, assuming that the real estate is fairly priced?” and then deciding whether you also want to go into the real estate business.
Another Example: Opening a Gold Mine
Here is another example of how market prices can help you make better decisions. Kingsley Solomon is considering a proposal to open a new gold mine. He estimates that the mine will cost $200 million to develop and that in each of the next 10 years it will produce .1 million ounces of gold at a cost, after mining and refining, of $200 an ounce. Although the extraction costs can be predicted with reasonable accuracy, Mr. Solomon is much less confident about future gold prices. His best guess is that
3The fair market rent equals the profit generated by the real estate’s second-best use.
4This rental stream yields a 10 percent rate of return to the real estate subsidiary. Each year it gets a 7 percent “dividend” and 3 percent capital gain. Growth at 3 percent would bring the value of the property to $134 million by year 10.
The present value (at r .10) of the growing stream of rents is
7
7
PV r g
.10 .03
$100 million
This PV is the initial market value of the property.
5Another possibility is that real estate rents and values are expected to grow at less than 3 percent a year. But in that case the real estate subsidiary would have to charge more than $7 million rent in year 1 to justify its $100 million real estate investment (see footnote 4 above). That would make the department store even less attractive.
