Question

1. You are calculating an equity required rate of return for Kings Corporation (KC) using the CAPM. Rather than relying on the published beta for KC or calculating one yourself, you are going to base you required rate of return on the betas of two comparable companies: ABL and NBL. The debt-TA ratio of KC is 0.75 and the corporate tax rate is 0.21. The appropriate risk-free rate of return is 2.75 percent and the appropriate equity risk premium is 5.5 percent. Given the information below, calculate the required return on RR equity using the average unlevered beta for the comparable firms, re-levered to reflect KC’s capital structure. Show all your work!

Company	Published Beta	Debt/TA	Tax Rate
ABL	0.75	0.25	0.20
NBL	1.25	0.50	0.15

Answer 1

1. Unlevered Beta of ABL = Levered beta / (1 + (1 - Tax) * DE ratio)

Unlevered Beta of ABL = 0.75 / (1 + (1 - 0.20) * 0.25/0.75)

Unlevered Beta of ABL = 0.75 / (1 + 0.80*0.33)

Unlevered Beta of ABL = 0.59

2. Unlevered Beta of NBL = Levered beta / (1 + (1 - Tax) * DE ratio)

Unlevered Beta of NBL = 1.25 / (1 + (1 - 0.15) * 0.50/0.50)

Unlevered Beta of NBL = 1.25 / (1 + 0.85*1)

Unlevered Beta of NBL = 0.68

3. levered Beta of KC = Average of unlevered betas * (1 + (1 - Tax) * DE ratio)

levered Beta of KC = 0.63 * (1 + (1 - 0.21) * 0.75/0.25)

levered Beta of KC = 0.63 * (1 + 0.79*3)

levered Beta of KC = 2.14

4. Return on RR equity = Risk free rate + beta * risk premium

Return on RR equity = 2.75% + 2.14 * 5.50%

Return on RR equity = 14.50%

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