Final answer:
The after-tax Weighted Average Cost of Capital (WACC) for Styles Corporation is calculated by combining the proportions of equity and debt, the expected return to shareholders, the interest rate on long-term bonds, and the effect of the corporate tax rate.
Step-by-step explanation:
To calculate the after-tax Weighted Average Cost of Capital (WACC) for Styles Corporation, we need to take into account the cost of equity, the cost of debt, the market value of equity, the market value of debt, and the corporate tax rate.
The market value of equity is found by multiplying the number of shares outstanding (10 million) by the current share price ($55), which gives us $550 million. The cost of equity is given as 12%. The market value of debt is $200 million, and the cost of debt before taxes is 7%. We apply the corporate tax rate of 21% to the cost of debt to find the after-tax cost of debt.
Now, we calculate the proportion of equity as $550 million / ($550 million + $200 million) and the proportion of debt as $200 million / ($550 million + $200 million). With these proportions, we can calculate the WACC using the formula:
WACC = (E/V) * Re + (D/V) * Rd * (1-Tc), where E is the market value of equity, V is the total market value (E + D), Re is the cost of equity, D is the market value of debt, Rd is the cost of debt, and Tc is the tax rate.
WACC = ($550 million / $750 million) * 12% + ($200 million / $750 million) * 7% * (1-21%)
After performing the calculations, we obtain the WACC as a percentage. This is the firm's average cost of capital after accounting for both the cost of debt and the cost of equity while factoring in the tax shield benefits of debt.