Question

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 (r_RF) is 3.5% and the market risk premium (r_M – r_RF) 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. (answer = 2.0 I believe, check if necessary)

41. based on information in Q.40, find the firms unleveraged beta using the Hamada Equation. (answer = 1.18 I believe, check if necessary)

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? Based on this information what would be new cost of equity using CAPM?

(Need help please).  

Answer 1

Solution:

40.The question is correctly solved by you.However I am showing you the steps;

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

13.5%=3.5%+Beta*5%

Beta=10%/5%

=2%

41.Calculation of unleveraged beta

Unleveraged beta=Leveraged beta/1+(1-tax rate)*Debt/Equity

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

=1.176 or 1.18

42.Calculation of leveraged beta

Leveraged Beta=Unleveraged Beta[1+(1-tax rate)*Debt/Equity]

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

=2.419 or 2.42

New Cost of equity using CAPM

=3.5%+2.42*5%

=15.60%