QUESTION 1 Pinder Inc. in the U.S. is examining its capital structure, with the intent of arriving at an optimal debt ratio. It currently has no debt and has a beta of 1.5. The riskless interest rate and the market risk premium are is 9% and 5.5%, respectively. Your research indicates that the debt rating will be as follows at different debt levels: D/(D+E) Rating Interest rate 0% AAA 10% 10% AA 10.5% 20% A 11% 30% BBB 12% 40% BB 13% 50% B 14% 60% CCC 16% 70% CC 18% 80% C 20% 90% D 25% The firm currently has 1 million shares outstanding at $20 per share. Assume corporate tax rate for this firm is 40%. (a) What is the firm's optimal debt ratio (only consider the above 10 choices from 0% to 90%). Please use the cost of capital approach in which you need to check how the cost of debt (using the debt rating above) and the cost of equity (using the equation for levered beta) would change at each debt ratio. (b) What is the current market value of the firm? After the firm restructures its financial structure at the optimal debt level you calculated in (a), what will be the value of the firm? Assume that the firm’s assets are expected to generate a constant annual cash flow forever, which will not be affected by financing policy.
Question
QUESTION 1 Pinder Inc. in the U.S. is examining its capital structure, with the intent of arriving at an optimal debt ratio. It currently has no debt and has a beta of 1.5. The riskless interest rate and the market risk premium are is 9% and 5.5%, respectively. Your research indicates that the debt rating will be as follows at different debt levels: D/(D+E) Rating Interest rate 0% AAA 10% 10% AA 10.5% 20% A 11% 30% BBB 12% 40% BB 13% 50% B 14% 60% CCC 16% 70% CC 18% 80% C 20% 90% D 25% The firm currently has 1 million shares outstanding at $20 per share. Assume corporate tax rate for this firm is 40%. (a) What is the firm's optimal debt ratio (only consider the above 10 choices from 0% to 90%). Please use the cost of capital approach in which you need to check how the cost of debt (using the debt rating above) and the cost of equity (using the equation for levered beta) would change at each debt ratio. (b) What is the current market value of the firm? After the firm restructures its financial structure at the optimal debt level you calculated in (a), what will be the value of the firm? Assume that the firm’s assets are expected to generate a constant annual cash flow forever, which will not be affected by financing policy.
Solution
To answer this question, we need to follow several steps:
(a) To find the optimal debt ratio, we need to calculate the cost of capital at each debt ratio. The cost of capital is the weighted average of the cost of equity and the cost of debt.
The cost of equity can be calculated using the levered beta formula: Levered Beta = Unlevered Beta * (1 + (1 - Tax Rate) * (Debt/Equity)). The cost of equity is then calculated using the Capital Asset Pricing Model (CAPM): Cost of Equity = Risk-Free Rate + Levered Beta * Market Risk Premium.
The cost of debt is given in the table.
We then calculate the weighted average cost of capital (WACC) at each debt ratio: WACC = (Equity/(Debt + Equity)) * Cost of Equity + (Debt/(Debt + Equity)) * Cost of Debt * (1 - Tax Rate).
The optimal debt ratio is the one that minimizes the WACC.
(b) The current market value of the firm is the number of shares outstanding times the price per share, which is 1 million * 20 million.
After the firm restructures its financial structure at the optimal debt level, the value of the firm will be the present value of the firm's future cash flows discounted at the new WACC. Since the cash flows are constant forever, this is a perpetuity and the value of the firm is Cash Flow/WACC.
Please note that the question does not provide information on the firm's cash flows, so we cannot calculate the exact value of the firm after restructuring.
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