Question

SA company is trying to estimate its optimal capital structure. Right now, it has a capital structure that consists of 20% debt and 80% equity, based on market values (its debt to equity D/S ratio is 0.25). The risk-free rate (rRF) is 6% and the market risk premium (rM – rRF) is 5%. Currently the company’s cost of equity, which is based on the CAPM, is 12% and its tax rate is 40%. Find the firm’s current leveraged beta using the CAPM

1.0

1.2

1.4

1.6

Use info above to find the firm’s unleveraged beta using the Hamada Equation

1.0 |
||

1.04 |
||

1.08 |
||

1.2 |

Use the information for above two question to find, what would be Simon’s new leveraged beta if it were to change its capital structure to 50% debt and 50% equity using the Hamada Equation?

1.0 |
||

1.04 |
||

1.2 |
||

1.67 |

Lastly, use the question and work above to find what would be Simon’s new cost of equity if it were to change its capital structure to 50% debt and 50% equity using the CAPM?

12.8% |
||

13.6% |
||

14.3% |
||

15.8% |

Answer #1

a). According to CAPM,

Cost of Equity = rRF + [Beta * Market Risk Premium]

12% = 6% + [Beta * 5%]

12% - 6% = Beta * 5%

Beta = 6%/5% = 1.20

So, 2nd option is correct.

b). Unlevered Beta = Levered Beta / [1 + {(D/E)*(1-t)]

= 1.20/[1+{0.25*(1-0.4)}]

= 1.20/[1+0.15] = 1.20 / 1.15 = 1.04

So, 2nd option is correct.

c). Levered Beta = Unlevered Beta * [1 + {(D/E)*(1-t)]

= 1.04*[1+{1*(1-0.4)}]

= 1.04*[1+0.6] = 1.04 * 1.6 = 1.67

So, 4th option is correct.

d). According to CAPM,

Cost of Equity = rRF + [Beta * Market Risk Premium]

= 6% + [1.67 * 5%]

= 6% + 8.3% = 14.3%

So, 3rd option is correct.

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