a) Beta(Levered) = Beta(Unlevered) + (Beta(Unlevered) - Beta(Debt) Debt/Equity T

Question

a) Beta(Levered) = Beta(Unlevered) + (Beta(Unlevered) - Beta(Debt) Debt/Equity The Unlevered equity betas of the three firms are;

EMN 1.79 = Bu + (Bu - 0.3)*0.3077; 1.79 = Bu + 0.3077Bu - 0.09231; 1.88231 = 1.3077Bu Therefore, Beta unlevered = 1.44 CE 1.98 = Bu + (Bu - 0.3)*0.2355; 1.98 + Bu +0.2355Bu - 0.07065; 2.05065 = 1.2355Bu Therefore, Beta Unlevered = 1.66

DOW 1.71 = Bu + (Bu - 0.30)*0.216; 1.71 =Bu +0.216Bu - 0.0648; 1.7748 = 1.216Bu Therefore, Beta Unlevered = 1.46 b) The average of the unlevered betas of the three firms can be used. =(1.44+1.66+1.45)/3 = 1.52 Sterling's levered equity beta will be B Levered = Bu + (Bu - Bd)*0.2 = 1.52 + (1.52 - 0.3)*0.2 = 1.52 + 0.24 = 1.76

can someone provide a step by step calculation thank you

Explanation / Answer

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

In this problem we assumed tax rate as 30%

The Unlevered equity betas of the three firms are :

1) For the firm EMN :

1.79 = Bu *(1+ (1 - 0.3)*0.3077)

1.79 = Bu *(1+(0.7)*0.3077)

1.79 = Bu*(1.21539)

Therefore, Beta unlevered = 1.48 (rounded)

2) For the firm CE :

1.98 = Bu*(1+((1 - 0.3)*0.2355))

1.98 = Bu * (1+(0.7*0.2355))

1.98 = Bu * 1.16485

Therefore, Beta Unlevered = 1.70 (rounded)

3) For the firm DOW :

1.71 = Bu * (1+ ((1 - 0.30)*0.216))

1.71 = Bu * (1+((0.7*0.216))

1.71 = Bu * 1.1512

Therefore, Beta Unlevered = 1.49 (rounded)

b) The average of the unlevered betas of the three firms can be used. = (1.48+1.70+1.49) / 3 = 1.56 (rounded)

c) Sterling's levered equity beta will be

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

Beta(Levered) = 1.56 * (1+(1-0.3)0.2))

Beta(Levered) = 1.78 (rounded).

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