Consider the following two statements: (i) The beta of levered equity must be greater than the beta of the unlevered ﬁrm
(ii) Leverage increases the equity beta more rapidly under corporate taxes.

Question

Quizplus · Accepted Answer

Statement (i) is correct as the beta of levered equity is a function of the beta of unlevered firm and the amount of debt in the capital structure. Since debt is a less risky investment compared to equity, adding debt to the capital structure will lower the overall risk of the firm, which will lead to a lower beta for the firm. However, since debt has a fixed return, the increase in the equity portion of the capital structure will lead to a higher risk and a higher beta for equity. Therefore, the beta of levered equity must be greater than the beta of the unlevered firm.

Statement (ii) is incorrect, as leverage increases the equity beta more rapidly under personal taxes, not corporate taxes. This is because interest payments on debt are tax-deductible, which reduces the tax liability of the firm. Therefore, adding debt to the capital structure under personal taxes will lead to a higher after-tax return on equity, which will incentivize investors to demand more equity for the same amount of risk. This will increase the equity beta more rapidly compared to when there are no taxes.

Consider the Following Two Statements: (I) the Beta of Levered