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%

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