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The book value of Charcoal Corporation’s common equity is $10 million, and it has 1 million shares outstanding. The book value as well as market value of its risk-free debt is $10 million. The stock is currently trading at $20 per share. The beta of the company’s common stock is 1, and the market risk premium is 8%. If the risk-free Treasury bill rate is 4%, and the corporate tax rate is 0%, what is the company's (after-tax) weighted-average cost of capital?Group of answer choices8%None of the above10.5%9.5%9.33

Question

The book value of Charcoal Corporation’s common equity is 10million,andithas1millionsharesoutstanding.Thebookvalueaswellasmarketvalueofitsriskfreedebtis10 million, and it has 1 million shares outstanding. The book value as well as market value of its risk-free debt is 10 million. The stock is currently trading at $20 per share. The beta of the company’s common stock is 1, and the market risk premium is 8%. If the risk-free Treasury bill rate is 4%, and the corporate tax rate is 0%, what is the company's (after-tax) weighted-average cost of capital?Group of answer choices8%None of the above10.5%9.5%9.33

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Solution

The Weighted Average Cost of Capital (WACC) is calculated by multiplying the cost of each capital component by its proportional weight and then summing:

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

Where: Re = cost of equity Rd = cost of debt E = market value of the firm's equity D = market value of the firm's debt V = E + D = total market value of the firm’s equity and debt Tc = corporate tax rate

Given: E (market value of equity) = 1 million shares * 20/share=20/share = 20 million D (market value of debt) = 10millionV(totalmarketvalueofthefirmsequityanddebt)=E+D=10 million V (total market value of the firm’s equity and debt) = E + D = 20 million + 10million=10 million = 30 million Tc (corporate tax rate) = 0% Beta = 1 Risk-free rate = 4% Market risk premium = 8%

We can calculate Re using the Capital Asset Pricing Model (CAPM): Re = Risk-free rate + Beta * Market risk premium Re = 4% + 1 * 8% = 12%

Since the company's debt is risk-free, Rd = risk-free rate = 4%.

Now we can substitute all the values into the WACC formula: WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc) WACC = (20million/20 million/30 million) * 12% + (10million/10 million/30 million) * 4% * (1 - 0) WACC = 0.67 * 12% + 0.33 * 4% WACC = 8% + 1.32% = 9.32%

So, the company's after-tax weighted-average cost of capital is approximately 9.32%. The closest answer choice is 9.33%.

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