A privately held corporation wishes to estimate its cost of equity. The firm has

Question

A privately held corporation wishes to estimate its cost of equity. The firm has a target debt-to-equity ratio of 0.5 and the marginal tax rate is 35%. The yield on 10-year U.S. Treasury Securities is 4%. The firm will use a market risk premium of 7% based on historical averages. It will use the pure play firm approach to estimate the firm’s equity beta and use that to estimate the firm’s cost of equity. It has identified 3 pure play firms along with their equity betas and debt-to-equity ratios.

Firm A has a beta of 1.5 and debt-to-equity ratio of 0.3.

Firm B has a beta of 1.3 and a debt-to-equity ratio of 0.4.

Firm C has a beta of 2.0 and a debt-to-equity ratio of 0.6.

What is the cost of equity for the privately held firm?

Explanation / Answer

Beta Unlevered of Firm A = 1.5/(1+(1-35%)*0.5) = 1.13

Beta Unlevered of Firm B = 1.3/(1+0.65* 0.4) = 1.03

Beta Unlevered of Firm C = 2/(1+0.65*0.6) = 1.44

Average Beta = 1.13 + 1.03+1.44/3 = 1.2

Beta Unlevered if firm = 1.2

Beta Levered of firm = 1.2*(1+ 0.65* 0.5) = 1.59

Cost of Equity = 4% + 1.59* 7% = 15.5%

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