The equity beta of a levered firm is 1.6. The corporate tax rate is 30%. The firm’s (market value) debt to equity ratio is 0.4. The firm’s debt is considered riskless. What is the asset beta?A.1.20B.1.03C.1.25D.1.49
Question
The equity beta of a levered firm is 1.6. The corporate tax rate is 30%. The firm’s (market value) debt to equity ratio is 0.4. The firm’s debt is considered riskless. What is the asset beta?A.1.20B.1.03C.1.25D.1.49
Solution
The asset beta (βA) can be calculated using the formula:
βA = βE * [E / (E + D * (1 - Tc))]
where: βE = equity beta = 1.6 E = equity portion = 1 (since debt to equity ratio is 0.4, equity portion is 1) D = debt portion = 0.4 (debt to equity ratio) Tc = corporate tax rate = 0.3
Substituting these values into the formula gives:
βA = 1.6 * [1 / (1 + 0.4 * (1 - 0.3))]
Solving the equation gives:
βA = 1.6 * [1 / (1 + 0.4 * 0.7)] βA = 1.6 * [1 / 1.28] βA = 1.25
Therefore, the asset beta is 1.25, so the correct answer is C. 1.25.
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