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Problem on leveraged beta

AB Restaurants has debt/equity ratio .25, and its leveraged beta is 1.5. Its tax rate is 30%, and its cost of equity is 15%. The risk-free rate is 5%. CD Restaurants has debt/equity ratio .4, and tax rate 35%. Find the cost of equity for CD.

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Expert

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AB’s Cost of equity = 15% = 5% + 1.5 (Rm - 5%)
1.5 Rm = 17.5%
Rm = 11.67%
Bu = BL/(1 + (1 – T)(D/E)) = 1.5/(1 + (1 – 0.3)(0.25) = 1.5/1.175 = 1.277

Hence with a D/E ratio of 40%,

BL = BU (1 + (1 – T)(D/E)) = 1.277 (1 + (1 – 0.35)(0.4)) = 1.61

Cost of equity = 5% + 1.61*(11.67% - 5%) = 15.72%

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