Question

Wentworth's five and dime store has a cost of equity of 11.2 percent. the company has an after tax cost of debt of 4.8 percent, and the tax rate is 23 percent. if the company's debt-equity ratio is .72, what is the weighted average cost of capital?

a. 6.97%
b. 6.84%
c. 8.06%
d. 8.52%
e. 6.39%

Answer 1

The weighted average cost of capital (WACC) for Wentworth's five and dime store can be calculated using the given cost of equity, after-tax cost of debt, the corporate tax rate, and the debt-equity ratio. After converting the debt-equity ratio to equity and debt proportions of total financing, the WACC computes to approximately 8.06%. Therefore, the correct option is C.

Step-by-step explanation:

To calculate the weighted average cost of capital (WACC) for Wentworth's five and dime store, we use the formula:

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

Where:

• E = Market value of the equity
• D = Market value of the debt
• V = E + D = Total market value of the financing (equity + debt)
• Re = Cost of equity
• Rd = Cost of debt (after-tax)
• Tc = Corporate tax rate

From the information provided:

• Cost of equity (Re) = 11.2%
• After-tax cost of debt (Rd) = 4.8%
• Tax rate (Tc) = 23%
• Debt-equity ratio (D/E) = 0.72

First, we need to convert the debt-equity ratio into the debt and equity proportions of total financing:

V = E + D

E/V = 1 / (1 + D/E)

D/V = D/E / (1 + D/E)

Substituting D/E = 0.72:

E/V = 1 / (1 + 0.72) = 1 / 1.72 ≈ 0.5814

D/V = 0.72 / 1.72 ≈ 0.4186

Now, we substitute these values into the WACC formula, including the cost of equity and the after-tax cost of debt:

WACC = (0.5814 * 0.112) + (0.4186 * 0.048) * (1 - 0.23)

WACC ≈ 0.0653 + 0.0153

WACC ≈ 0.0806 or 8.06%