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248 PART II Risk

d. Burlington’s cost of debt was 6 percent and its debt-to-value ratio, D/V, was .40. What was Burlington’s company cost of capital? Use the industry average beta.

9. Amalgamated Products has three operating divisions:

EXCEL

To estimate the cost of capital for each division, Amalgamated has identified the following three principal competitors:

Assume these betas are accurate estimates and that the CAPM is correct.

a.Assuming that the debt of these firms is risk-free, estimate the asset beta for each of Amalgamated’s divisions.

b.Amalgamated’s ratio of debt to debt plus equity is .4. If your estimates of divisional betas are right, what is Amalgamated’s equity beta?

c.Assume that the risk-free interest rate is 7 percent and that the expected return on the market index is 15 percent. Estimate the cost of capital for each of Amalgamated’s divisions.

d.How much would your estimates of each division’s cost of capital change if you assumed that debt has a beta of .2?

10.Look at Table 9.2. What would the four countries’ betas be if the correlation coefficient for each was 0.5? Do the calculation and explain.

11.“Investors’ home country bias is diminishing rapidly. Sooner or later most investors will hold the world market portfolio, or a close approximation to it.” Suppose that statement is correct. What are the implications for evaluating foreign capital investment projects?

12.Consider the beta estimates for the country indexes shown in Table 9.2. Could this information be helpful to a U.S. company considering capital investment projects in these countries? Would a German company find this information useful? Explain.

13.Mom and Pop Groceries has just dispatched a year’s supply of groceries to the government of the Central Antarctic Republic. Payment of $250,000 will be made one year hence after the shipment arrives by snow train. Unfortunately there is a good chance of a coup d’état, in which case the new government will not pay. Mom and Pop’s controller therefore decides to discount the payment at 40 percent, rather than at the company’s 12 percent cost of capital.

a.What’s wrong with using a 40 percent rate to offset political risk?

b.How much is the $250,000 payment really worth if the odds of a coup d’état are 25 percent?

14.An oil company is drilling a series of new wells on the perimeter of a producing oil field. About 20 percent of the new wells will be dry holes. Even if a new well strikes oil, there is still uncertainty about the amount of oil produced: 40 percent of new wells which strike oil produce only 1,000 barrels a day; 60 percent produce 5,000 barrels per day.

a.Forecast the annual cash revenues from a new perimeter well. Use a future oil price of $15 per barrel.

c.The German company can also buy shares of U.S. pharmaceutical companies. Suppose the expected rate of return in these shares is 13 percent, reflecting their beta of about 1.0 with respect to the U.S. market. Should the German company demand a 13 percent rate of return on investments in the United States?

3.An oil company executive is considering investing $10 million in one or both of two wells: Well 1 is expected to produce oil worth $3 million a year for 10 years; well 2 is expected to produce $2 million for 15 years. These are real (inflation-adjusted) cash flows.

The beta for producing wells is .9. The market risk premium is 8 percent, the nominal risk-free interest rate is 6 percent, and expected inflation is 4 percent.

The two wells are intended to develop a previously discovered oil field. Unfortunately there is still a 20 percent chance of a dry hole in each case. A dry hole means zero cash flows and a complete loss of the $10 million investment.

Ignore taxes and make further assumptions as necessary.

a.What is the correct real discount rate for cash flows from developed wells?

b.The oil company executive proposes to add 20 percentage points to the real discount rate to offset the risk of a dry hole. Calculate the NPV of each well with this adjusted discount rate.

c.What do you say the NPVs of the two wells are?

d.Is there any single fudge factor that could be added to the discount rate for developed wells that would yield the correct NPV for both wells? Explain.

4.If you have access to “Data Analysis Tools” in Excel, use the “regression” functions to investigate the reliability of the betas estimated in Practice Questions 3 and 5 and the industry cost of capital calculated in question 6.

a.What are the standard errors of the betas from questions 3(a) and 3(c)? Given the standard errors, do you regard the different beta estimates obtained for each company as signficantly different? (Perhaps the differences are just “noise.”) What would you propose as the most reliable forecast of beta for each company?

b.How reliable are the beta estimates from question 5(a)?

c.Compare the standard error of the industry beta from question 5(b) to the standard errors for individual-company betas. Given these standard errors, would you change or amend your answer to question 6(e)?

MINI-CASE

Holiport Corporation

Holiport Corporation is a diversified company with three operating divisions:

•The construction division manages infrastructure projects such as roads and bridge construction.

•The food products division produces a range of confectionery and cookies.

•The pharmaceutical division develops and produces anti-infective drugs and animal healthcare products.

These divisions are largely autonomous. Holiport’s small head-office financial staff is principally concerned with applying financial controls and allocating capital between the divisions. Table 9.3 summarizes each division’s assets, revenues, and profits. Holiport has always been regarded as a conservative—some would say “stodgy”—company. Its bonds are highly rated and yield 7 percent, only 1.5 percent more than comparable government bonds.

Holiport’s previous CFO, Sir Reginald Holiport-Bentley, retired last year after an autocratic 12-year reign. He insisted on a hurdle rate of 12 percent for all capital expenditures for all three divisions. This rate never changed, despite wide fluctuations in interest rates and inflation. However, the new CFO, Miss Florence Holiport-Bentley-Smythe (Sir Reginald’s niece) had brought a breath of fresh air into the head office. She was determined to set dif-

T A B L E 1 0 . 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.

It would reduce the NPV of your project by

putting the NPV of the scooter project underwater at 3.43 6.14 ¥2.71 billion. Suppose further that a ¥10 million pretest of the machine will reveal whether it will work or not and allow you to clear up the problem. It clearly pays to invest ¥10 million to avoid a 10 percent probability of a ¥6.14 billion fall in NPV. You are

ahead by 10 .10 6,140 ¥604 million.

On the other hand, the value of additional information about market size is small. Because the project is acceptable even under pessimistic assumptions about market size, you are unlikely to be in trouble if you have misestimated that variable.

Limits to Sensitivity Analysis

Sensitivity analysis boils down to expressing cash flows in terms of key project 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 confused or inappropriate forecasts.

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 the production department’s; but what you may discover 10 years hence is no help now. One solution is to ask the two departments for a complete description of the various odds. However, it is far from easy to extract a forecaster’s subjective notion of the complete probability distribution of possible outcomes.1

Another problem with sensitivity analysis is that the underlying variables are likely to be interrelated. What sense does it make to look at the effect in isolation of an increase in market size? If market size exceeds expectations, it is likely that

1If you doubt this, try some simple experiments. Ask the person who repairs your television to state a numerical probability that your set will work for at least one more year. Or construct your own subjective probability distribution of the number of telephone calls you will receive next week. That ought to be easy. Try it.

T A B L E 1 0 . 3

How the NPV of the electric scooter project would be affected by higher oil prices and a world recession.

demand will be stronger than you anticipated and unit prices will be higher. And why look in isolation at the effect of an increase in price? If inflation pushes prices to the upper end of your range, it is quite probable that costs will also be inflated.

Sometimes the analyst can get around these problems by defining underlying variables so that they are roughly independent. But you cannot push one-at-a-time sensitivity analysis too far. It is impossible to obtain expected, optimistic, and pessimistic values for total project cash flows from the information in Table 10.2.

Scenario Analysis

If the variables are interrelated, it may help to consider some alternative plausible scenarios. For example, perhaps the company economist is worried about the possibility of another sharp rise in world oil prices. The direct effect of this would be to encourage the use of electrically powered transportation. The popularity of compact cars after the oil price increases in the 1970s leads you to estimate that an immediate 20 percent price rise in oil would enable you to capture an extra 3 percent of the scooter market. On the other hand, the economist also believes that higher oil prices would prompt a world recession and at the same time stimulate inflation. In that case, market size might be in the region of .8 million scooters and both prices and cost might be 15 percent higher than your initial estimates. Table 10.3 shows that this scenario of higher oil prices and recession would on balance help your new venture. Its NPV would increase to ¥6.5 billion.

Managers often find scenario analysis helpful. It allows them to look at different but consistent combinations of variables. Forecasters generally prefer to give an