Question

Simon Software Co. is trying to estimate its optimal capital structure. Right now, Simon has a capital structure that consists of 20 percent debt and 80 percent equity, based on market values. (Its D/S ratio is 0.25.) The risk-free rate is 6 percent and the market risk premium, rM – rRF, is 5 percent. Currently the company’s cost of equity, which is based on the CAPM, is 12 percent and its tax rate is 40 percent.

**Find the new levered beta given the new capital
structure (if it were to change its capital structure to 50 percent
debt and 50 percent equity) using the Hamada equation.**

0.81 |

1.00 |

1.22 |

1.45 |

1.67 |

Answer #1

**Step 1: Calculation
of current Beta**

We have

**Cost of Equity Ke = Rf + b (
Rm – Rf )**

Where,

Rf – Risk free return

b – Beta

Rm – Expected return on market portfolio

Cost of Equity Ke = Rf + b ( Rm – Rf )

12 = 6 + b * 5

5b = 12-6 = 6

**beta = 6 / 5 =
1.20**

**Step 2: Calculation
of unlevered Beta (Aseet beta)**

**Asset Beta = Equity Beta /
[(1+(1-tax rate)*(debt/equity)]**

**=** 1.20 /
[(1+.6*.2/.8]

= 1.2 / (1+.15)

**Asset Beta =
1.0435**

**Step 3: Calculation
of levered beta at 50% debt**

**levered beta = unlevered beta
* (1+ (1-tax rate) (Debt/Equity))**

= 1.0435* ( 1+ .6*.5/.5))

= 1.0435* (1+.6)

=1.0435 * 1.6

= 1.6696

**?levered beta
=1.67**

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