1. The total market value of the common stock of the Okefenokee Real Estate Company is $6 million, and the total value of its debt is $4 million. The treasurer estimates that the beta of the stock is currently 1.5 and that the expected risk premium on the market is 6 percent. The Treasury bill rate is 4 percent. Assume for simplicity that Okefenokee debt is risk-free and the company does not pay tax. a. What is the required return on Okefenokee stock? b. Estimate the company cost of capital. c. What is the discount rate for an expansion of the company’s present business? d. Suppose the company wants to diversify into the manufacture of rose-colored spectacles. The beta of unleveraged optical manufacturers is 1.2. Estimate the required return on Okefenokee’s new venture. 1. a. requity = rf + (rm – rf) = 0.04 + (1.5 0.06) = 0.13 = 13% b. rassets D E $4million $6million rdebt requity 0.04 0.13 V V $10million $10million rassets = 0.094 = 9.4% c. The cost of capital depends on the risk of the project being evaluated. If the risk of the project is similar to the risk of the other assets of the company, then the appropriate rate of return is the company cost of capital. Here, the appropriate discount rate is 9.4%. d. requity = rf + (rm – rf) = 0.04 + (1.2 0.06) = 0.112 = 11.2% rassets D E $4million $6million rdebt requity 0.04 0.112 V V $10million $10million rassets = 0.0832 = 8.32% 7. You are given the following information for Golden Fleece Financial. Long-term debt outstanding: $300,000 Current yield to maturity (rdebt): 8% Number of shares of common stock: 10,000 Price per share: $50 Book value per share: $25 Expected rate of return on stock (requity): 15% Calculate Golden Fleece’s company cost of capital. Ignore taxes. The total market value of outstanding debt is $300,000. The cost of debt capital is 8 percent. For the common stock, the outstanding market value is: $50 10,000 = $500,000. The cost of equity capital is 15 percent. Thus, Lorelei’s weighted-average cost of capital is: 300,000 500,000 0.08 (0.15 ) rassets 300,000 500,000 300,000 500,000 rassets = 0.124 = 12.4% 8. Look again at Table 9.1. This time we will concentrate on Burlington Northern. a. Calculate Burlington’s cost of equity from the CAPM using its own beta estimate and the industry beta estimate. How different are your answers? Assume a risk-free rate of 3.5 percent and a market risk premium of 8 percent. b. Can you be confident that Burlington’s true beta is not the industry average? c. Under what circumstances might you advise Burlington to calculate its cost of equity based on its own beta estimate? a. rBN = rf + BN (rm – rf) = 0.035 + (0.53 0.08) = 0.0774 = 7.74% rIND = rf + IND (rm – rf) = 0.035 + (0.49 0.08) = 0.0742 = 7.42% No, we can not be confident that Burlington’s true beta is not the industry average. The difference between BN and IND (0.04) is less than one standard error (0.20), so we cannot reject the hypothesis that BN = IND. c. Burlington’s beta might be different from the industry beta for a variety of reasons. For example, Burlington’s business might be more cyclical than is the case for the typical firm in the industry. Or Burlington might have more fixed operating costs, so that operating leverage is higher. Another possibility is that Burlington has more debt than is typical for the industry so that it has higher financial leverage b. 11. 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 that 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. b. Ageologist proposes to discount the cash flows of the new wells at 30 percent to offset the risk of dry holes. The oil company’s normal cost of capital is 10 percent. Does this proposal make sense? Briefly explain why or why not. a. Expected daily production = (0.2 0) + 0.8 [(0.4 x 1,000) + (0.6 x 5,000)] = 2,720 barrels Expected annual cash revenues = 2,720 x 365 x $15 = $14,892,000 b. The possibility of a dry hole is a diversifiable risk and should not affect the discount rate. This possibility should affect forecasted cash flows, however. See Part (a). Chapter 10 4. 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: If Rustic replaces now rather than in one year, several things happen: i. It incurs the equivalent annual cost of the $9 million capital investment. ii. It reduces manufacturing costs. For example, for the “Expected” case, analyzing “Sales” we have (all dollar figures in millions): i. The economic life of the new machine is expected to be 10 years, so the equivalent annual cost of the new machine is: $9/5.6502 = $1.59 ii. The reduction in manufacturing costs is: 0.5 $4 = $2.00 Thus, the equivalent annual cost savings is: –$1.59 + $2.00 = $0.41 Continuing the analysis for the other cases, we find: Sales Manufacturing Cost Economic Life Equivalent Annual Cost Savings (Millions) Pessimistic Expected Optimistic 0.01 0.41 1.21 -0.59 0.41 0.91 0.03 0.41 0.60