Chapter 9 公司理财 74 CHAPTER 9 Capital Budgeting and Risk Answers to Practice Questions 1. a. requity = rf + (rm rf) = 0.04 + (1.5 0.06) = 0.13 = 13% b. 0.13$10million$6million0.04$10million$4millionrVErVDrequitydebtassets 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% 0.112$10million$6million0.04$10million$4millionrVErVDrequitydebtassets rassets = 0.0832 = 8.32% 2. a. 0.836n$439million$299millio1.20n$439millio$40million0.20n$439million$100millio0VCVPVDcommonpreferreddebtassets b. r = rf + (rm rf) = 0.05 + (0.836 0.06) = 0.10016 = 10.016% 3. Internet exercise; answers will vary. 4. Internet exercise; answers will vary. 74 5. Note: In the first printing of the text, the table for Practice Question #5 incorrectly shows the standard deviations written with decimal points. a. The R2 value for BP was 0.27, which means that 27% of total risk comes from movements in the market (i.e., market risk). Therefore, 73% of total risk is unique risk. The R2 value for British Airways was 0.37, which means that 37% of total risk comes from movements in the market (i.e., market risk). Therefore, 63% of total risk is unique risk. b. The variance of BP is: (25)2 = 625 Market risk for BP: 0.27 625 = 168.75 Unique risk for BP: 0.73 625 = 456.25 c. The t-statistic for BA is: 2.12/0.37 = 5.73 This is significant at the 1% level, so that the confidence level is 99%. d. rBA = rf + BA (rm rf) = 0.05 + 2.12 (0.12 0.05) = 0.1984 = 19.84% e. rBA = rf + BA (rm rf) = 0.05 + 2.12 (0 0.05) = 0.0560 = 5.60% 6. Internet exercise; answers will vary. 7. The total market value of outstanding debt is 100 million. The cost of debt capital is 7.5 percent. For the common stock, the outstanding market value is: 40 2 million = 80 million. The cost of equity capital is 11 percent. Thus, Loreleis weighted-average cost of capital is: 0.1180million100million80million0.07580million100million100millionrassets rassets = 0.0906 = 9.06% 8. 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% b. No, we can not be confident that Burlingtons 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. 74 c. Burlingtons beta might be different from the industry beta for a variety of reasons. For example, Burlingtons 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. 9. a. The threat of a coup dtat means that the expected cash flow is less than $NZ900 million. The threat could also increase the discount rate, but only if it increases market risk. b. If New Zealand Marine proceeds with the construction of the supply submarine and the Republic then fails to make the final $NZ900 million payment, then New Zealand Marine can sell the submarine to another buyer for $NZ600 million. Therefore, the expected cash flow for the year 2 payment is: (0.20 $NZ600 million) + (0.80 $NZ900 million) = $NZ840 million Assume that New Zealand Marines costs are incurred equally in Year 0, Year 1 and Year 2, and that the cash flows are about as risky as the rest of the companys business. Then: PV = 400 + 500 + ( 400/1.10) + ( 400 + 840)/1.102 = +100 or $NZ100 million 10. a. If you agree to the fixed price contract, operating leverage increases. Changes in revenue result in greater than proportionate changes in profit. If all costs are variable, then changes in revenue result in proportionate changes in profit. Business risk, measured by assets, also increases as a result of the fixed price contract. If fixed costs equal zero, then: assets = revenue. However, as PV(fixed cost) increases, assets increases. b. With the fixed price contract: PV(assets) = PV(revenue) PV(fixed cost) PV(variable cost) 9(1.09)(0.09)$10million)6%,10years factorannuity $10million0.09$20millionPV(assets)( PV(assets) = $97,462,710 Without the fixed price contract: PV(assets) = PV(revenue) PV(variable cost) 0.09$10million0.09$20millionPV(assets) = $111,111,111 74 11. 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). 12. Ratio of s Correlation Beta Brazil 6.29 0.5 3.15 Egypt 5.67 0.5 2.84 India 6.10 0.5 3.05 Indonesia 7.29 0.5 3.65 Mexico 3.92 0.5 1.96 Poland 3.21 0.5 1.61 Thailand 6.32 0.5 3.16 South Africa 4.04 0.5 2.02 The betas increase compared to those reported in Table 9.2 because the returns for these markets are now more highly correlated with the U.S. market. Thus, the contribution to overall market risk becomes greater. 13. The information could be helpful to a U.S. company considering international capital investment projects. By examining the beta estimates, such companies can evaluate the contribution to risk of the potential cash flows. A German company would not find this information useful. The relevant risk depends on the beta of the country relative to the portfolio held by investors. German investors do not invest exclusively, or even primarily, in U.S. company stocks. They invest the major portion of their portfolios in German company stocks. 74 14. The opportunity cost of capital is given by: r = rf + (rm rf) = 0.05 + (1.2 0.06) = 0.122 = 12.2% Therefore: CEQ1 = 150(1.05/1.122) = 140.37 CEQ2 = 150(1.05/1.122)2 = 131.37 CEQ3 = 150(1.05/1.122)3 = 122.94 CEQ4 = 150(1.05/1.122)4 = 115.05 CEQ5 = 150(1.05/1.122)5 = 107.67 a1 = 140.37/150 = 0.9358 a2 = 131.37/150 = 0.8758 a3 = 122.94/150 = 0.8196 a4 = 115.05/150 = 0.7670 a5 = 107.67/150 = 0.7178 From this, we can see that the a t values decline by a constant proportion each year: a2/a1 = 0.8758/0.9358 = 0.9358 a3/a2 = 0.8196/0.8758 = 0.9358 a4/a3 = 0.7670/0.8196 = 0.9358 a5/a4 = 0.7178/0.7670 = 0.9358 15. a. Using the Security Market Line, we find the cost of capital: r = 0.07 + 1.5 (0.16 0.07) = 0.205 = 20.5% Therefore: b. CEQ1 = 40(1.07/1.205) = 35.52 CEQ2 = 60(1.07/1.205)2 = 47.31 CEQ3 = 50(1.07/1.205)3 = 35.01 c. a1 = 35.52/40 = 0.8880 a2 = 47.31/60 = 0.7885 a3 = 35.01/50 = 0.7002 d. Using a constant risk-adjusted discount rate is equivalent to assuming that at decreases at a constant compounded rate. 103.091.205501.205601.20540PV32 74 16. At t = 2, there are two possible values for the projects NPV: Therefore, at t = 0: 0)successfulnotistestif(NPV212,500,0000.127,500,00050,000,000)successfulistestif(NPV21,173,4691.40)12,500,000.60(00)(0.405,000,000NPV20 74 Challenge Questions 1. It is correct that, for a high beta project, you should discount all cash flows at a high rate. Thus, the higher the risk of the cash outflows, the less you should worry about them because, the higher the discount rate, the closer the present value of these cash flows is to zero. This result does make sense. It is better to have a series of payments that are high when the market is booming and low when it is slumping (i.e., a high beta) than the reverse. The beta of an investment is independent of the sign of the cash flows. If an investment has a high beta for anyone paying out the cash flows, it must have a high beta for anyone receiving them. If the sign of the cash flows affected the discount rate, each asset would have one value for the buyer and one for the seller, which is clearly an impossible situation. 2. a. Since the risk of a dry hole is unlikely to be market-related, we can use the same discount rate as for producing wells. Thus, using the Security Market Line: rnominal = 0.06 + (0.9 0.08) = 0.132 = 13.2% We know that: (1 + rnominal) = (1 + rreal) (1 + rinflation) Therefore: 8.85% 0.0885 1 1.041.132rreal b. c. Expected income from Well 1: (0.2 0) + (0.8 3 million) = $2.4 million Expected income from Well 2: (0.2 0) + (0.8 2 million) = $1.6 million Discounting at 8.85 percent gives: (3.1914)(3million)million101.28853millionmillion10NPV101tt1$425,800NPV1(3.3888)(2million)10million1.28852millionmillion10NPV151tt2$3,222,300NPV2 74 d. For Well 1, one can certainly find a discount rate (and hence a “fudge factor”) that, when applied to cash flows of $3 million per year for 10 years, will yield the correct NPV of $5,504,600. Similarly, for Well 2, one can find the appropriate discount rate. However, these two “fudge factors” will be different. Specifically, Well 2 will have a smaller “fudge factor” because its cash flows are more distant. With more distant cash flows, a smaller addition to the discount rate has a larger impact on present value. 3. Internet exercise; answers will vary. (6.4602)n)(2.4milliomillion101.08852.4millionmillion10NPV101tt1$5,504,600NPV1(8.1326)n)(1.6millio10million1.08851.6millionmillion10NPV151tt2$3,012,100NPV2