Solutions-Chapter12

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Chapter 12: Estimating the Cost of Capital
12-1. Suppose Pepsico’s stock has a beta of 0.57. If the risk-free rate is 3% and the expected return of the market portfolio is 8%, what is Pepsico’s equity cost of capital?
Use the CAPM to get Pepsico’s equity cost of capital: 3% + 0.57 􏰀 (8% – 3%) = 5.85%
12-18. Your firm is planning to invest in an automated packaging plant. Harburtin Industries is an all-equity firm that specializes in this business. Suppose Harburtin’s equity beta is 0.85, the risk-free rate is 4%, and the market risk premium is 5%. If your firm’s project is all equity financed, estimate its cost of capital.
Project beta = 0.85 (using an all-equity comparable)
Thus, cost of capital for the project = 4% + 0.85(5%) = 8.25%
12-19. Consider the setting of Problem 18. You decided to look for other comparables to reduce estimation error in your cost of capital estimate. You find a second firm, Thurbinar Design, which is also engaged in a similar line of business. Thurbinar has a stock price of $20 per share, with 15 million shares outstanding. It also has $100 million in outstanding debt, with a yield on the debt of 4.5%. Thurbinar’s equity beta is 1.00.
a. Assume Thurbinar’s debt has a beta of zero. Estimate Thurbinar’s unlevered beta. Use the unlevered beta and the CAPM to estimate Thurbinar’s unlevered cost of capital.
b. Estimate Thurbinar’s equity cost of capital using the CAPM. Then assume its debt cost of capital equals its yield, and using these results, estimate Thurbinar’s unlevered cost of capital.
c. Explain the difference between your estimate in part (a) and part (b).
d. You decide to average your results in part (a) and part (b), and then average this result with your estimate from Problem 17. What is your estimate for the cost of capital of your firm’s project?
a. E=20􏰀15=300 E + D = 400
βu = 300/400 􏰀 1.00 + 100/400 􏰀 0 = 0.75
ru = 4% + 0.75(5%) = 7.75%
b. re =4%+1.0􏰀5%=9%
ru = 300/400 􏰀 9% + 100/400 􏰀 4.5% = 7.875%
c. In the first case, we assumed that debt had a beta of zero, so rd = rf = 4%.
In the second case, we assumed rd = YTM = 4.5%.
d. Thurbinar’s ru = (7.75 + 7.875)/2 = 7.8125%
Harburtin’s ru = 8.25%
Estimate = (8.25% + 7.8125%)/2 = 8.03%

12-20. IDX Tech is looking to expand its investment in advanced security systems. The project will be financed with equity. You are trying to assess the value of the investment, and must estimate its cost of capital. You find the following data for a publicly traded firm in the same line of business:
What is your estimate of the project’s beta? What assumptions do you need to make?
Assume that i) debt is risk-free and its market value equals its book value ii) comparable assets have the same risk as the project.
βe =1.20,βd =0
E = 15 􏰀 80 = 1200
D = 400
βu = (1200/1600) 􏰀 1.20 + (400/1600) 􏰀 0 = 0.90
12-21. In mid-2015, Cisco Systems had a market capitalization of $130 billion. It had A-rated debt of $25 billion as well as cash and short-term investments of $60 billion, and its estimated equity beta at the time was 1.11.
a. What is Cisco’s enterprise value?
b. Assuming Cisco’s debt has a beta of zero, estimate the beta of Cisco’s underlying business enterprise.
a. Enterprise Value = E + D – C = 130 + 25 – 60 = $95 billion (see class notes for clarification)
b. Net Debt = 25 – 60 = –35
ru = (130/95) 􏰀 1.11 + (–35/95) 􏰀 0 = 1.52
But
12-26. Unida Systems has 40 million shares outstanding trading for $10 per share. In addition, Unida has $100 million in outstanding debt. Suppose Unida’s equity cost of capital is 15%, its debt cost of capital is 8%, and the corporate tax rate is 40%.
a. What is Unida’s unlevered cost of capital?
b. What is Unida’s after-tax debt cost of capital?
c. What is Unida’s weighted average cost of capital?
a. E=40􏰀$10=$400
D = $100
ru = 400/500 􏰀 15% + 100/500 􏰀 8% = 13.6%
b. rd =8%􏰀(1–40%)=4.8%
c. rwacc = 400/500 􏰀 15% + 100/500 􏰀 4.8% = 12.96%