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# Zero Coupon Bonds: Value of Option to Default on the Bonds

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2. Assume your firm has zero coupon bonds maturing in 10 years with a face value of \$183.75 million.

a) If the assets are worth \$150 million, what is the value of the stocks and the bonds?
b) If the assets are worth \$400 million, what is the value of the stocks and the bonds?
c) If the assets are worth \$400 million, the standard deviation is 0.60 and the risk-free rate is the T-bond rate, what is the value of the option to default on the bonds? What is the value of the stockholders' call option? Use Black and Scholes to get the answer to part c.

Note: For parts a and b, assume the options would be exercised immediately. Be sure to label your answer.

#### Solution Preview

See the attached file.

2. Assume your firm has zero coupon bonds maturing in 10 years with a face value of \$183.75 million.

a) If the assets are worth \$150 million, what is the value of the stocks and the bonds?
Equity is a call option. If this option is exercised today, shareholders will receive their share only when after satisfying the financial claims of the debt holders.
The payoff to equity investors on liquidation are
= V - D if V > D
= 0 if V <D
where,
V = Value of the firm
D = Face Value of the outstanding debt ...

#### Solution Summary

Shows how to calculate the value of the option to default on the bonds, value of the stockholders' call option using Black and Scholes.

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