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# Important WACC problems on Chapter 9.docx

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BUS 330a: Corporate Finance I SPRING 2012, AUBG Additional Problems (Chapter 9) Chapter 9/ Problem 1 Tyler Manufacturing has 9.5 million shares of common stock outstanding. The current share price is \$53, and the book value per share is \$5. Tyler Manufacturing also has two bond issues outstanding. The first bond issue has a face value of \$75 million and an 8% coupon and sells for 93% of par. The second issue has a face value of \$60 million and a 7.5% coupon and sells for 96.5% of par. The first issue matures in 10 years, the second in 6 years. a. What are Tyler’s capital structure weights on a book value basis? b. What are Tyler’s capital structure weights on a market value basis? c. Which is more relevant, the book or market value weights? Why? Solution a. The book value of equity is the book value per share times the number of shares, and the book value of debt is the face value of the company’s debt, so: BVE = 9.5M(\$5) = \$47.5M BVD = \$75M + 60M = \$135M So, the total value of the company is: V = \$47.5M + 135M = \$182.5M And the book value weights of equity and debt are: E/V = \$47.5/\$182.5 = .2603 D/V = 1 – E/V = .7397 b. The market value of equity is the share price times the number of shares, so: MVE = 9.5M(\$53) = \$503.5M Using the relationship that the total market value of debt is the price quote times the par value of the bond, we find the market value of debt is: MVD = .93(\$75M) + .965(\$60M) = \$127.65M This makes the total market value of the company: V = \$503.5M + 127.65M = \$631.15M And the market value weights of equity and debt are: E/V = \$503.5/\$631.15 = .7978 D/V = 1 – E/V = .2022 c. The market value weights are more relevant. Chapter 9/ Problem 2 In the previous problem, suppose the company’s stock has a beta of 1.5. The risk-free rate is 5.2%, and the market risk premium is 9%. Assume that the overall cost of debt is the weighted average implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 35%. What is the company’s WACC? Solution First, we will find the cost of equity for the company. The information provided allows us to solve for the cost of equity using the CAPM, so: RE = .052 + 1.2(.09) = .1600 or 16.00% Next, we need to find the YTM on both bond issues. Doing so, we find: P1 = \$930 = \$40(PVIFAR%,20) + \$1,000(PVIFR%,20) R = 4.54%; YTM = 4.54% × 2 = 9.08% P2 = \$965 = \$37.5(PVIFAR%,12) + \$1,000(PVIFR%,12) R = 4.13%; YTM = 4.13% × 2 = 8.25% To find the weighted average after-tax cost of debt, we need the weight of each bond as a percentage of the total debt. We find: wD1 = .93(\$75M)/\$127.65M = .546 wD2 = .965(\$60M)/\$127.65M = .454 Now we can multiply the weighted average cost of debt times one minus the tax rate to find the weighted average aftertax cost of debt. This gives us: RD = (1 – .35)[(.546)(.0908) + (.454)(.0825)] = .0566 or 5.66% Using these costs and the weight of debt we calculated earlier, the WACC is: WACC = .7978(.1600) + .2022(.0566) = .1391 or 13.91% Chapter 9/ Problem 3 ABB Corporation has 9 million shares of common stock outstanding and 120,000 8.5% semiannual bonds outstanding, par value \$1,000 each. The common stock currently sells for \$34 per share and has a beta of 1.2, and the bonds have 15 years to maturity and sell for 93% of par. The market risk premium is 10%, T-bills are yielding 5%, and ABB’s tax rate is 35%. a. What is the firm’s market value capital structure? b. If ABB is evaluating a new investment project that has the same risk as the firm’s typical project, what rate should the firm use to discount the project’s cash flows? Solution a. We will begin by finding the market value of each type of financing. We find: MVD
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