Question

RSR Metal currently has no debt and an equity cost of capital of 14%. Suppose that RSR decides to increase its leverage and maintain a market debt-to-value ratio of 1/2. Suppose RSR's debt cost of capital is 8% and its corporate tax rate is 21%. Assuming that RSR's pre-tax WACC remains constant, then with the addition of leverage its effective after-tax WACC will be closest to:

A) 10.8%.
B) 12.4%.
C) 12.8%.
D) 13.6%.

Answer 1

The effective after-tax WACC for RSR Metal with the introduction of leverage is calculated using the formula that factors in the equity and debt cost of capital alongside the corporate tax rate. By applying the given figures, the after-tax WACC comes out to approximately 10.8%, with option A) being the closest answer.

Step-by-step explanation:

The student is asking how to calculate the effective after-tax Weighted Average Cost of Capital (WACC) for a company with the introduction of leverage. To calculate the after-tax WACC, we use the formula: WACC = E/V * Re + D/V * Rd * (1 - Tc), where E is the market value of the equity, D is the market value of the debt, V is the total value (E + D), Re is the cost of equity, Rd is the cost of debt, and Tc is the corporate tax rate.

In this case, the equity cost of capital is 14%, the debt cost of capital is 8%, and the corporate tax rate is 21%. We are given that the market debt-to-value ratio is 1/2, which means that E/V = 1/2 and that D/V also equals 1/2. Substituting in these values:

After-tax WACC = (1/2)*0.14 + (1/2)*0.08*(1 - 0.21)

Simplifying, we get:

After-tax WACC = 0.07 + 0.05 * 0.79 = 0.07 + 0.0395 = 0.1095 or 10.95%, which rounds to 10.8%.

Therefore, the closest answer to the effective after-tax WACC with the addition of leverage is 10.8%, which is option A).