Firm's Beta Calculation

Beta Calculation for Firm

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Question

A firm's capital structure has a debt-to-equity ratio of 1.2. The pretax cost of debt is 6.8% and the weighted average cost of capital of the firm equals 9.8%. The risk-free rate in the economy is 6.2% the expected rate of return on the market is 14%. The firm must pay 35% of its gross income in taxes. The beta of the stock equals ________.

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Explanations

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A. B. C. D.

Explanation

Since the debt interest is tax deductible, the after-tax cost of debt equals 6.8%*(1-0.35) = 4.42%. Since the D/E ratio = 1.2, (D+E)/E = 2.2, giving E/(D+E) = 0.455.

Thus, equity forms 45.5% of the capital whiledebt forms 54.5%. The WACC is then equal to 0.455*RE + 0.545*4.42% = 9.8% (given). Solving gives RE = 16.24%.

If B is the beta of the stock, then using CAPM, 16.24% = 6.2% + B*(14% - 6.2%), giving B = 1.29.

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