Math Problem Statement

An unlevered firm has a cost of capital of 12.46 percent and a tax rate of 35 percent. The firm is considering a new capital structure with 35 percent debt. The interest rate on the debt would be 6.68 percent. What would be the firm's levered cost of capital if they undertake this new capital structure?

Multiple Choice

13.94%

14.27%

14.48%

14.78%

13.90%

Solution

To calculate the firm's levered cost of capital (also known as the WACC or weighted average cost of capital), we can use the Modigliani-Miller Proposition II with Taxes, which states:

rL=rU+DE×(rUrD)×(1TC)r_L = r_U + \frac{D}{E} \times (r_U - r_D) \times (1 - T_C)

Where:

  • rLr_L = Levered cost of capital (WACC)
  • rUr_U = Unlevered cost of capital (12.46%)
  • rDr_D = Cost of debt (6.68%)
  • D/ED/E = Debt-to-equity ratio (based on 35% debt, so D/E = 0.35 / 0.65)
  • TCT_C = Tax rate (35%)

First, we calculate the Debt-to-Equity ratio DE\frac{D}{E}:

DE=0.350.65=0.5385\frac{D}{E} = \frac{0.35}{0.65} = 0.5385

Now, applying the values to the formula for the levered cost of capital:

rL=12.46%+0.5385×(12.46%6.68%)×(10.35)r_L = 12.46\% + 0.5385 \times (12.46\% - 6.68\%) \times (1 - 0.35)

Let's solve for rLr_L.The firm's levered cost of capital (WACC) is 14.48%. Thus, the correct answer is:

14.48%.

Would you like any further details or explanations?

Here are some related questions for further exploration:

  1. How does the tax shield benefit impact the WACC in this scenario?
  2. How would a higher debt percentage affect the levered cost of capital?
  3. What would happen to the WACC if the cost of debt increased?
  4. How would the WACC change if there were no taxes?
  5. How does the Modigliani-Miller theorem relate to the firm's capital structure?

Tip: Increasing debt can lower the cost of capital due to the tax shield, but only to a certain extent before the cost of financial distress outweighs the benefits.

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Math Problem Analysis

Mathematical Concepts

Corporate Finance
Capital Structure
Weighted Average Cost of Capital (WACC)
Modigliani-Miller Proposition II

Formulas

Levered cost of capital (WACC) formula: r_L = r_U + (D/E) * (r_U - r_D) * (1 - T_C)
Debt-to-equity ratio formula: D/E = Debt % / (1 - Debt %)

Theorems

Modigliani-Miller Proposition II with Taxes

Suitable Grade Level

Undergraduate Finance or MBA Level