Question

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

		2.0
		1.5
		2.6
		1.9

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

		1.95
		1.0
		1.18
		1.29

Based on the information from Question, 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

Based on the information from Questions, 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%

Answer 1

According to CAPM,

Cost of Equity = Risk free rate + Beta*(Market risk premium)

Leveraged Beta is calculated using the above equation as

13.5 = 3.5 + Beta*(5)

13.5-3.5 = 5Beta

10 = 5Beta

10/5 = Beta

Beta = 2

Correct option is therefore 2.

Unleveraged Beta is calculated using the following Hamada equation

Unleveraged Beta = Leveraged Beta*[1/(1+(1-tax rate)*D/E)]

Where, D/E is debt to equity ratio

Unleveraged Beta = 2*[1/(1+(1-0.30)*1)]

= 2*(1/1.70)

= 1.176 or 1.18(rounded to two decimal places)

Correct option is therefore = 1.18

Leveraged Beta with D/E ratio of 1.5

Leveraged Beta = Unleveraged Beta*(1+(1-tax rate)*D/E)

= 1.176*(1+(1-0.30)*1.5

= 2.41

Therefore, the correct option is 2.41

Cost of Equity using new D/E ratio and therefore new leveraged Beta:

Cost of Equity = Risk free rate + Beta*(Market risk premium)

= 3.5 + 2.41*5

= 15.6%

Therefore, the correct option is 15.6%