017 - 17 The Options Approach to Corporate Securities...

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167 Answers to Questions and Problems 1. Explain why common stock is itself like a call option. In the option analysis of common stock, what plays the role of the exercise price and what plays the role of the underlying stock? Common stock is like a call option on the entire firm. To see how this can be the case, consider a firm with a single bond issue outstanding and assume that the bond is a pure discount bond. When the bond matures, the common stockholders have a choice: They can pay the bondholders the promised payment, or they can surrender the firm to the bondholders. If the firm is worth more than the amount due to the bondholders, the stock owners will pay the bondholders and keep the excess. If the firm is worth less than the amount due to the bondholders, the stock owners will abandon the firm to the bond owners. In this situation, the amount due to the bond owners plays the role of the exercise price. The maturity date of the bond is the expiration date of the call option represented by the common stock. The common stock is like a call option. At expiration, the stock owners can exercise their call option by paying the claim of the bond- holders (the exercise price). Upon exercising, the stockholders receive the underlying asset (the entire firm). 2. Consider a firm that issues a pure discount bond that matures in one year and has a face value of $1,000,000. Analyze the payoffs that the bondholders will receive in option pricing terms, assuming the only other secu- rity in the firm is common stock. When the bond matures, the stock owners decide whether to pay the bonds or surrender the firm to the bondholders in lieu of payment. If the value of the firm exceeds the amount owed to the bond owners, $1,000,000, the bondholders receive full payment and the stock owners retain the excess. If the firm’s value is less than the promised payment, the stock owners abandon the firm and the bondholders receive a pay- ment equal to the value of the entire firm. However, by hypothesis, this is less than the promised payment of $1,000,000. This pattern of payment is like the payments on a short put position with an exercise price that equals the face value of the bond. However, a short position in a put can give a payoff at expiration that is negative. This is not true of a bond. The worst payoff for the bond is zero. Therefore, the payoff has the same pattern as a short position in a put with an exercise price that equals the face value of the bond plus a long position in a riskless bond. 3. Consider a firm with common stock and a pure discount bond as its financing. The total value of the firm is $1,000,000. There are 10,000 shares of common stock priced at $70 per share. The bond matures in ten years 17 The Options Approach to Corporate Securities
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and has a total face value of $500,000. What is the interest rate on the bond, assuming annual compounding? Would the interest rate become higher or lower if the volatility of the firm’s cash flows increases?
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This homework help was uploaded on 04/07/2008 for the course BA 4825 taught by Professor Danısoglu during the Spring '08 term at Middle East Technical University.

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017 - 17 The Options Approach to Corporate Securities...

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