Question

A firm is currently all equity. It has a cost of equity (unlevered) of 10%. The firm decided to transform 80% of the financing to debt, with a cost of debt at 6%. The tax rate is 15%. What's the firm's new levered cost of equity?

A. 23.6%
B. 12.5%
C. 9%

Answer 1

The new levered cost of equity for the firm after changing its financing structure to 80% debt is calculated using the Modigliani-Miller Proposition II with taxes. The calculated cost is 23.6%, which matches option A.

Step-by-step explanation:

To calculate the new levered cost of equity for the firm after it has transformed 80% of its financing to debt, we can use the Modigliani-Miller Proposition II with taxes. This proposition provides us with a formula to determine the cost of equity in a leveraged firm (Re):

Re = Ra + (Ra - Rd)(1 - Tc)(D/E)

Where:

• Re is the levered cost of equity
• Ra is the cost of equity if the firm was all equity (unlevered cost of equity)
• Rd is the cost of debt
• Tc is the corporate tax rate
• D/E is the debt-to-equity ratio

Given the values:

• Ra (unlevered cost of equity) = 10%
• 80% debt financing implies D/E = 4 (since 80/20 = 4)
• Rd (cost of debt) = 6%
• Tc (tax rate) = 15%

Substituting these into our formula gives:

Re = 10% + (10% - 6%) * (1 - 0.15) * 4

Re = 10% + 4% * 0.85 * 4

Re = 10% + 13.6%

Re = 23.6%

Therefore, the firm's new levered cost of equity would be 23.6%, which corresponds to option A.