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FIN516 WEEK 2 - HOMEWORK PROBLEM 14-11 BASED ON CHAPTER 14: WACC AND MODIGLIANI & MILLER EXTENSION MODELS WITH GROWTH ASSUMPTIONS Consider the entrepreneur described in Section 14.1 (and referenced in Tables 14.1- 14.3). Suppose she funds the project by borrowing $750 rather than $500. a. According to MM Proposition I, what is the value of the equity? What are its cash flows if the economy is strong? What are its cash flows if the economy is weak? Equity value: $1000 - $750 = $250 Cash flow (Strong economy): $1400 - 750 (1.05) = $1400 - $787.5 = $612.5 Cash flow (Weak economy): $900 - 750 (1.05) = $900 - $787.5 = $112.5 b. What is the return of the equity in each case? What is its expected return? Return of Equity (Strong economy): ($612.5 / $250) - 1 = 2.45 - 1 = 1.45 or 145% Return of Equity (Weak economy): ($112.5 / $250) - 1 = 0.45 - 1 = -0.55 or -55% Expected return of equity: (145% / 2) + (-55% / 2) = 72.5% + (-27.5%) = 45% c. What is the risk premium of equity in each case? What is the sensitivity of the levered equity return to systematic risk? How does its sensitivity compare to that of unlevered equity? How does its risk premium compare to that of unlevered equity? Risk premium of equity: 45% - 5% = 40% Sensitivity of levered equity return to systematic risk: 145% - (-55%) = 200% *Sensitivity of levered equity is higher than the unlevered equity (200% > 50%) *Risk premium is higher than the unlevered equity (40% > 10%) d. What is the debt-equity ratio of the firm in this case? Debt equity ratio: $750 / $250 = 3 e. What is the firm's WACC in this case? WACC: (0.25 * 0.45) + (0.75 * 0.05) = 0.1125 + 0.0375 = 0.15 or 15% FIN516 WEEK 2 - HOMEWORK PROBLEM 14-18 BASED ON CHAPTER 14: WACC AND MODIGLIANI & MILLER EXTENSION MODELS WITH GROWTH ASSUMPTIONS In mid-2012, AOL Inc. had $100 million in debt, total equity capitalization of $3.1 billion, and an equity beta of 0.90 (as reported on Yahoo! Finance). Included in AOL's assets was $1.5 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 3% and the market risk premium is 4%. a. What is AOL's enterprise value? AOL Enterprise value (In billions): ($3.1 billion + 0.1 billion) - $1.5 billion = $1.7 billion b. What is the beta of AOL's business assets? Beta of AOL assets: ($3.1 billion / $1.7 billion) * (0.90) = 1.824 * 0.90 = 1.641 c. What is AOL's WACC? AOL WACC: 3% + (1.641 * 4%) = 3% + 6.564% = 9.564% FIN516 WEEK 2 - HOMEWORK PROBLEM 15-15 BASED ON CHAPTER 15:DEBT and TAXES Acme Storage has a market capitalization of $100 million and debt outstanding of $40 million. Acme plans to maintain this same debt-equity ratio in the future. The firm pays an interest rate of 7.5% on its debt and has a corporate tax rate of 35%. a. If Acme's free cash flow is expected to be $7 million next year and is expected to grow at a rate of 3% per year, what is Acme's WACC? Acme firm value (Levered): $100 + $40 = $140 million WACC: $7 million + ($140 million * 0.03) / $140 million = $11.2 million / $140 million = 0.08 or 8% b. What is the value of Acme's interest tax shield? WACC before tax: 0.08 + ([40 / 140] * 0.075 * 0.35) = 0.08 + 0.0075 = 0.0875 or 8.75% Acme firm value (Unlevered): $7 million / 0.0875 - 0.03 = $7 million / 0.0575 = $121.74 million Acme's Interest tax shield: $140 million - $121.74 million = $18.26 million