The weighted average cost of capital for firm X is currently 10%.Firm X is considering a new project but must raise new debt to finance the project.Debt represents 25% of the capital structure.If the after tax cost of debt will rise from 7% to 8%,what is the marginal cost of capital?

Question

Quizplus · Accepted Answer

To calculate the marginal cost of capital, we need to first calculate the new weighted average cost of capital (WACC) after considering the increase in the after-tax cost of debt.

WACC = E/V * Re + D/V * Rd * (1-Tc)

Where:
E = value of equity
V = total value of the company (E + D)
Re = cost of equity
D = value of debt
Rd = cost of debt
Tc = corporate tax rate

Given:
WACC = 10%
D/V = 25%
Rd1 = 7%
Rd2 = 8%
Tc = unknown

We can solve for Tc using the following equation:

WACC = (E/V * Re) + (D/V * Rd * (1-Tc))
10% = (E/V * Re) + (0.25 * 0.07 * (1-Tc))
10% = (E/V * Re) + (0.0175 - 0.0175Tc)
0.0175Tc = 0.0175 - (E/V * Re)
Tc = (0.0175 - (E/V * Re)) / 0.0175

We don't have enough information to determine the value of E/V or Re, so we can't solve for Tc. However, we know that the marginal cost of capital is equal to the increase in the WACC resulting from the increase in the after-tax cost of debt.

So, the marginal cost of capital = (D/V * Rd2 * (1-Tc2)) - (D/V * Rd1 * (1-Tc1))
= (0.25 * 0.08 * (1-Tc2)) - (0.25 * 0.07 * (1-Tc1))

Assuming a corporate tax rate of 35%, we get:

Marginal cost of capital = (0.25 * 0.08 * (1-0.35)) - (0.25 * 0.07 * (1-0.35)) = 0.01025 or 10.25%

Therefore, the best choice is B.

The Weighted Average Cost of Capital for Firm X Is