Company’s shares have a market value of €120 million and a beta of 1.5. It curre

Question

Company’s shares have a market value of €120 million and a beta of 1.5. It currently has risk-free debt as well. The firm decides to change its capital structure by issuing €30 million in additional risk-free debt, and then using this €30 million to repurchase stock.

a) With perfect capital markets, what will the beta of the company’s shares be after this transaction? Assume that the beta of debt is zero.
b) Suppose that the company, in addition, uses €10 million from its cash reserves to repurchase shares. What will the new beta of its shares be?

Explanation / Answer

A) The current beta is 1.5, according to MM the beta has to stay the same of after the repurchase. Equity + Debt = 120 (since they don't say a specific amount), where Equity = 120 After repurchase: D/V * Bd + E/V *Be = 1.5 30/120 * 0 + 90/120 *Be = 1.5 90/120 * Be = 1.5 Be = 1.5/(90/120) Be = 2.0 B) The Beta will stay the same because the firm will repurchase 10 million with cash but the value of the remaining shares will increase by 10 million so therefore the beta will stay the same.

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