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CHAPTER 25
OPTION VALUATION
Answers to Concepts Review and Critical Thinking Questions
1. Increasing the time to expiration increases the value of an option. The reason is that the option gives
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Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this solutions
manual, rounding may appear to have occurred. However, the final answer for each problem is found
without rounding during any step in the problem.
Basic
6. Using put-call parity, we can solve for the risk-free rate as follows:
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7. Using the Black-Scholes option pricing model to find the price of the call option, we find:
8. The delta of a call option is N(d1), so:
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10. Using the call price we found in the previous problem and put-call parity, you would need to pay:
b. Option value consists of time value and intrinsic value, so:
12. Using put-call parity, the price of the put option is:
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Intermediate
16. We can use the Black-Scholes model to value the equity of a firm. Using the asset value of $21,600 as
17. a. We can use the Black-Scholes model to value the equity of a firm. Using the asset value of $23,500
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18. We can use the Black-Scholes model to value the equity of a firm. Using the asset value of $33,400 as
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19. a. The combined value of equity and debt of the two firms is:
c. The change in the value of the firm’s equity is:
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20. a. Using the Black-Scholes model to value the equity, we get:
d. Using the Black-Scholes model to value the equity, we get:
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Using the equation for the PV of a continuously compounded lump sum, we get:
Challenge
21. a. Using the equation for the PV of a continuously compounded lump sum, we get:
c. The value of a risky bond is the value of a risk-free bond minus the value of a put option on the
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d. The value of the debt with five years to maturity at the risk-free rate is:
Putting these values into Black-Scholes:
two more years.
22. a. Using the equation for the PV of a continuously compounded lump sum, we get:
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b. Using the Black-Scholes model to value the equity, we get:
c. The value of a risky bond is the value of a risk-free bond minus the value of a put option on the
firm’s equity, so:
d. Using the equation for the PV of a continuously compounded lump sum, we get:
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And using put-call parity, the price of the put option is:
23. a. Going back to the chapter on dividends, the price of the stock will decline by the amount of the
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24. a. Going back to the chapter on dividends, the price of the stock will decline by the amount of the
26. From put-call parity:
27. Based on Black-Scholes, the call option is worth $50! The reason is that present value of the exercise
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