Question

# 40. A company is estimating its optimal capital structure. Now the company has a capital structure...

40. A company is estimating its optimal capital structure. Now the company has a capital structure that consists of 50% debt and 50% equity, based on market values (debt to equity D/S ratio is 1.0). The risk-free rate (rRF) is 3.5% and the market risk premium (rM – rRF) is 5%. Currently the company’s cost of equity, which is based on the CAPM, is 13.5% and its tax rate is 30%. Find the firm’s current leveraged beta using the CAPM

 2 1.5 2.6 1.9

41. Based on the information from Question 40, find the firm’s unleveraged beta using the Hamada Equation

 1.95 1 1.18 1.29

42. Based on the information from Question 40 and 41, what would be the company’s new leveraged beta if it were to change its capital structure to 60% debt and 40% equity (D/S=1.5) using the Hamada Equation?

 1.65 1.95 2.16 2.41

43. Based on the information from Questions 40 ~ 42, what would be the company’s new cost of equity if it were to change its capital structure to 60% debt and 40% equity (D/S =1.5) using the CAPM?

 13.8% 15.6% 16.8% 18.5%

Solution:

40.Calculation of firm’s current leveraged beta using the CAPM

Cost of equity=Risk free rate+Beta*Market risk premium

13.5%=3.5%+Beta*5%

Beta=10.00%/5%

=2

41.Calculation of firm’s unleveraged beta using the Hamada Equation

unleveraged beta=Leveraged beta/1+(1-tax rate)*debt/equity

=2/1+(1-0.30)*1

=1.176 or 1.18

42.Calculation of company’s new leveraged beta sing the Hamada Equation

New leveraged beta=UnLevarged beta[1+(1-tax rate)*Debt/equity]

=1.18[1+(1-0.30)*1.5]

=2.419 or 2.41

43.Calculation of company’s new cost of equity

New Cost of equity=Risk free rate+Beta*Market risk premium

=3.5%+2.41*5%

=15.55 or 15.60%

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