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

ID: 2749351 • Letter: A

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% and the expected market risk premium is 6%.

It has identified 3 pure play firms with the following equity betas and debt-to-equity rations:

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

A ............... 1.8 ............ 0.6

B ............... 1.2 ............ 0.4

C .............. 2.1 ............ 0.8 .

What is the firm's estimated equity beta (levered beta)? .

A. 1.60

B. 1.40

C. 1.21

D. 1.70

E. 1.51

Unlevered Beta A = Levered Beta / (1 + ((1 – Tax Rate) x (Debt/Equity)))

= 1.8/(1+(1-0.35)*(0.6))) = 1.2949

Unlevered Beta B = Levered Beta / (1 + ((1 – Tax Rate) x (Debt/Equity)))

= 1.2/(1+(1-0.35)*(0.4))) = .95238

Unlevered Beta C = Levered Beta / (1 + ((1 – Tax Rate) x (Debt/Equity)))

= 2.1/(1+(1-0.35)*(0.8))) = 1.38147

Average unlevered beta for the industry = (Unlevered Beta A+Unlevered Beta B+Unlevered Beta C)/3

= (1.38147+.95238+1.2949)/3 = 1.2096

Firms levered beta =

Unlevered Beta x (1 + ((1 – Tax Rate) x (Debt/Equity)))

=1.2096*(1+(1-0.35)*(.5)) = 1.602

cost of equity = risk-free rate + beta * (market risk premium) = 4+1.602*6 = 13.612%

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