Question

Mark IV Industries' current debt to equity ratio is 0.4; it has a (levered) equity beta of 1.4, and a cost of equity 15.2%. Risk-free rate is 4%, the market risk premium is 8%, the cost of debt is 4%, and the corporate tax rate is 34%. The firm is in a matured business, ie. it is not growing anymore. It has long-term debt outstanding that is rolled over when it matures, so that the amount of debt outstanding does not change.

Suppose the firm repurchases stock and finances its repurchase with debt, issued at the same cost of debt. As a result, its debt to equity ratio changes to 0.6.

We can derive the WACC under the current capital structure.

WACC (*old*) = (1/1.4)*(15.2%) + (0.4/1.4)*(4%)*(1-34%) =
11.61%

1. What is the firm's equity beta under the new capital structure?

2. What is the firm's new cost of equity?

3. What is the change in the cost of equity due to the change in its business risk?

4. What is the change in the cost of equity due to the change in its financial risk?

5. What is the WACC under the new capital structure?

Answer #1

1) | Unlevered equity beta = Levered equity beta/[1+(1-t)*D/E] | |

= 1.4/(1+66%*0.4) = | 1.11 | |

Equity beta under the new CS - Levered equity beta = Unlevered equity beta*[1+(1-t)*D/E] | ||

= 1.11+0.66*0.6 = | 1.51 | |

2) | New cost of equity per CAPM = 4%+1.51*8% = | 16.08% |

3) | Change in cost of equity due to change in business risk | 0 |

4) | Change in cost of equity due to change in financial risk = (1.51-1.40)*8% = | 0.88% |

or alternatively 16.08%-15.20% = | ||

5) | WACC under the new CS = (1/1.6)*16.08%+(0.6/1.6)*4%*(1-34%) = | 11.04% |

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