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 21%. The yield on 10 year U.S. Treasury securities is 4% and the expected market risk premium is 6%. It has identified 2 pure play firms with the following equity betas and debt-to-equity rations:

.

Firm ......... Beta ........... D/E Ratio

A ............... 1.5 ............ 0.3

B ............... 1.3 ............ 0.4

Estimate the firm's asset beta (unlevered beta) using the pure play firms. Re-lever the asset beta for the firm's target debt-to-equity ratio to estimate the firm's equity beta (levered beta). Use that equity beta to calculate the firm's cost of equity.

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

.

13.2%

15.7%

12.6%

14.4%

11.6%

13.2%

15.7%

12.6%

14.4%

11.6%

Explanation / Answer

Firm ......... Beta ........... D/E Ratio

A ............... 1.5 ............ 0.3

B ............... 1.3 ............ 0.4
Beta unlevered of Firm A = Beta levered /(1+(1-tax rate)*D/E) = 1.5/(1+(1-21%)*0.3) = 1.21
Beta unlevered of Firm B = Beta levered /(1+(1-tax rate)*D/E) = 1.3/(1+(1-21%)*0.4) = 0.99

Target D/E ratio = 0.5
Beta levered with target debt Equity ratio =  Beta unlevered *(1+(1-tax rate)*D/E) = 1.21/(1+(1-21%)*0.5) = 1.69
Beta levered with target debt Equity ratio =  Beta unlevered *(1+(1-tax rate)*D/E) = 0.99/(1+(1-21%)*0.5) = 1.38

Cost of equity using Capm = risk free rate + beta levered * rmarket risk premium
Cost of equity of A = 4% + 1.69 * 6%= 14.14%
Cost of equity of A = 4% + 1.38 * 6% = 12.28%

Cost of Quity for Privately held firms = (14.14% + 12.28%)/2 = 13.2%

Best of Luck. God Bless

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