# Question

Assume a firm’s debt is risk-free, so that the cost of debt equals the risk-free rate, Rf . Define βA as the firm’s asset beta, that is, the systematic risk of the firm’s assets. Define βS to be the beta of the firm’s equity. Use the capital asset pricing model, CAPM, along with MM Proposition II to show that βS = βA × (1 + B / S ), where B / S is the debt-equity ratio. Assume the tax rate is zero.

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