Q 17.37. You expect your firm to be worth $50, $100, or $120 with probabilities
ID: 1169925 • Letter: Q
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Q 17.37. You expect your firm to be worth $50, $100, or $120 with probabilities 1/10, 6/10 and 3/10, respectively You can raise $75 in debt proceeds today if you promise an interest rate of 10%. If this is how you finance your firm, then your cost of equity capital is 20%. 1. What is the expected payoff of your firm? 2. What is the promised value of the debt? 3. What is the cost of capital of this debt? 4. What is the value of your equity? 5. What is the value of your firm? 6. What is your firm's WACC? 7. If you raise $50 in debt proceeds today, your friendly investment banker tells you that you can get away promising an interest rate of 3%. What is your debt cost of capital in this case? 8. How much would then be financed through equity 9. What would be the debt-to-capital ratio of this firm 10. What would be the cost-of-equity-capital for this firm 11. Is the $75 debt-financing scenario cost-of-debt capital (in the $50-debt financing scenario)? in the $50-debt financing scenario)? (in the $50-debt financing scenario)? higher, or is the $50 debt-financing scenario cost-of- debt capital higher? What does this mean for the relative risk of the two types of debt? 12. Is the $75 debt-financing scenario cost-of-equity cap- ital higher, or is the $50 debt-financing scenario cost- of-equity capital higher? What does this mean for the relative risk of the two types of equity? 13. Is the $75 debt-financing scenario cost-of-firm capital higher, or is the $50 debt-financing scenario cost-of- firm capital higher?Explanation / Answer
1) Expected payoff = Sum Sigma( Probability x value) - obligation
= 50 x (1/10) x 100 x (6/100) x 120 x (3/10) - 75x (1.1) = 18.5
Firm's value = 50 x (1/10) x 100 x (6/100) x 120 x (3/10)
Obligation = Debt payment with interest = 75 x 1.1 = 82.5
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2) Promised value of Debt after 1 year = 75 x ( 1 + interest rate) = 75 x 1.1 = 82.5
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3) Cost of capital for this debt is 10% since cost of debt is the rate at which debt is borrowed which means the interest cost .
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4) Value of Equity = Firm's value - debt = 101 - 75 = 26
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