The beta of an all-equity firm is 1.2. Suppose the firm changes its capital structure to 50 percent debt and 50 percent equity using 8 percent debt financing. What is the equity beta of the levered firm? The beta of debt is 0.2. (Assume no taxes.)

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Quizplus · Accepted Answer

The equity beta of a levered firm ($\beta_{L}$) can be calculated using the formula: $\beta_{L} = \beta_{U} + (\beta_{U} - \beta_{D}) \times (D/E)$, where $\beta_{U}$ is the unlevered beta (beta of the firm with no debt), $\beta_{D}$ is the beta of debt, and $D/E$ is the debt-to-equity ratio. Given that $\beta_{U} = 1.2$, $\beta_{D} = 0.2$, and the firm moves to a 50% debt and 50% equity structure, $D/E = 1$. Plugging these values into the formula gives: $\beta_{L} = 1.2 + (1.2 - 0.2) \times 1 = 2.2$.

The Beta of an All-Equity Firm Is 1