## The option pricing model has many uses. This question demonstrates its application in calculating the market value of a company ’ s debt capital. Assume that a company has risky zero-coupon 65 bonds with a market value B (the debt ’ s face value is D ), which are guaranteed by the company ’ s assets.

The option pricing model has many uses. This question demonstrates its application in calculating the market value of a company ’ s debt capital. Assume that a company has risky zero-coupon 65 bonds with a market value B (the debt ’ s face value is D ), which are guaranteed by the company ’ s assets. The debt (including interest payments) is paid at the end of period T , and so bankruptcy claims can be made only at the end of the period. As discussed in chapter 14, if the market value of the company ’ s shares is S , then the company ’ s market value is V = S + B . In question 10 of chapter 18, we demonstrated that buying a share S (or for our present purposes, any risky asset) and a put option on that share (or that risky asset), and selling a call option on that share (or risky asset), where both options have the same exercise time T and where the exercise price is equal to the share price S = X , we will obtain the same result as holding a risk-free zero-coupon bond D where S + P − C = D . Using the end-of-period payment schedule for shareholders and bondholders, and for scenarios where asset values at the end of the period are either higher or lower than the debt V ≤ D ; V > D , demonstrate that the following: a. A leveraged company ’ s shares can be considered an option on that company ’ s value (Black and Scholes 1973). In other words, the share price S is actually a call option on the company ’ s assets V left over at the end of the period (after payment of the company ’ s debt). b. Using part (a) above and the equation S + P − C = D , demonstrate that the risky debt ’ s value B is equivalent to the risk-free debt ’ s value D plus the sale of a put option on the company ’ s assets

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