A company\'s debt is given by a bond that will mature in two years. After two ye

Question

A company's debt is given by a bond that will mature in two years. After
two years the company will terminate all activity. The company unlevered
equity value in two years can be $17 millions with a 50% probability, or $14
millions with probability 50%. The bond is a zero-coupon bond with face value
$16 millions. The market risk premium is 5% the risk-free rate is 3%. The
bankruptcy costs are $4 millions. The market price of the bond is 70% of the
face value. Assume perfect capital markets and no taxation.
What is the beta of the company's debt?

Explanation / Answer

A company's debt is given by a bond that will mature in two years. After
two years the company will terminate all activity. The company unlevered
equity value in two years can be $17 millions with a 50% probability, or $14
millions with probability 50%. The bond is a zero-coupon bond with face value
$16 millions. The market risk premium is 5% the risk-free rate is 3%. The
bankruptcy costs are $4 millions. The market price of the bond is 70% of the
face value. Assume perfect capital markets and no taxation.
What is the beta of the company's debt?

Market Value of Bond = 70%*16 = 11.20 Million

Cost of Company debt = (16/11.20)^(1/2) - 1

Cost of Company debt = 19.52%

Beta of Companys Debt = (Cost of Company debt -  risk-free rate)/market risk premium

Beta of Companys Debt = ( 19.52 - 3)/5

Beta of Companys Debt = 3.30

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