# HW6sol - Solution to Problem Set 6 - FINA 4200 Spring 2010...

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Solution to Problem Set 6 - FINA 4200 Spring 2010 I. Multiple Choices 1. b 2. a 3. b 4. b 5. a 6. a 7. e 8. e 9. b 10. a 11. d 12. d 13. b 14. e 15. c 16. c 17. d 18. a 19. a 20. c 21. e 22. a 23. a Explanations to multiple choice questions 8. Step 1: Find the new WACC: WACC = w e r s + w d (1-T)r d = (0.8(0.11)) + (0.2(1-0.4)0.10) = 0.10. Step 2: Find the free cash flow. Because there is no growth, there is no investment in capital, hence FCF is equal to NOPAT: FCF = NOPAT – Investment in capital = EBIT(1-T) –0 = \$800(1-.4) = \$480 million. Step 3: Find the new value of the firm: V = FCF/(WACC-g) = \$480/0.10 = \$4,800 million. 9. Step 1. Find the new value of the firm after the recapitalization. Because growth is zero, free cash flow is equal to NOPAT: V = FCF/WACC = NOPAT/WACC = EBIT(1-t)/WACC = \$20(1- 0.4)/0.1 = \$120 million. Step 2. Find the new value of equity and debt after the recapitalization: S = w e V = 0.6(\$120) = \$72 million. D = w d V = 0.4(\$120) = \$48 million. Step 3. Find the new price per share after the recapitalization: P = [S + (D-D 0 )]/n 0 = [\$72 + (\$48 – 0)]/2.5 = \$48. 10. Facts given: r s = 12%; D/E = 0.25; r RF = 6%; RP M = 5%; T = 40%. 1

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Step 1: Find the firm’s current levered beta using the CAPM: r s = r RF + RP M (b) 12% = 6% + 5%(b) b = 1.2. Step 2: Find the firm’s unlevered beta using the Hamada equation: b = b U [1 + (1 - T)(D/E)] 1.2 = b U [1 + (0.6)(0.25)] 1.2 = 1.15b U 1.0435 = b U . Step 3: Find the new levered beta given the new capital structure using the Hamada equation: b = b U [1 + (1 - T)(D/E)] b = 1.0435[1 + (0.6)(1)] b = 1.6696. Step 4: Find the firm’s new cost of equity given its new beta and the CAPM: r s = r RF + R PM (b) r s = 6% + 5%(1.6696) r s = 14.35%. 11. r RF = 5%; r M - r RF = 6%. r s = r RF + (r M - r RF )b. WACC = r d × w d × (1 - T) + r s × w c . You need to use the D/E ratio given for each capital structure to find the levered beta using the Hamada equation. Then, use each of these betas with the CAPM to find the r s for that capital structure. Use this r s and r d for each capital structure to find the WACC. The optimal capital structure is the one that minimizes the WACC. (D/E) b = b U [1 + (1-T)(D/E)] r s = r RF + (r M - r RF )b w c r d w d WACC 0.11 1.0667 11.4005% 0.9 7.0% 0.1 10.68% 0.25 1.1500 11.9000 0.8 7.2 0.2 10.38 0.43 1.2571 12.5429 0.7 8.0 0.3 10.22 0.67 1.4000 13.4000 0.6 8.8 0.4 10.15 1.00 1.6000 14.6000 0.5 9.6 0.5 10.18 For example, if the D/E is 0.11: b = 1.0[1 + (1 - T)(D/E)] = 1.0[1 + (1 - 0.4)(0.1111)] = 1.0667. 2
r s = r RF + (r M - r RF )b = 5% + 6%(1.0667) = 11.40%. The weights are given at 0.9 and 0.1 for equity and debt, respectively, and the r d for that capital structure is given as 7 percent. WACC= r

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## HW6sol - Solution to Problem Set 6 - FINA 4200 Spring 2010...

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