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
3. Interest rate increases are good for calls and bad for puts. The reason is that if a call is exercised in
4. If you buy a put option on a stock that you already own, you guarantee that you can sell the stock for
5. The intrinsic value of a call is Max[S – E, 0]. The intrinsic value of a put is Max[E – S, 0]. The
6. The time value of both a call option and a put option is the difference between the price of the option
7. Since you have a large number of stock options in the company, you have an incentive to accept the
8. Rearranging the put-call parity formula, we get: S – PV(E) = C – P. Since we know that the stock
9. Rearranging the put-call parity formula, we get: S – PV(E) = C – P. If the call and the put have the
10. A stock can be replicated using a long call (to capture the upside gains), a short put (to reflect the
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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
1. With continuous compounding, the FV is:
2. With continuous compounding, the PV is:
3. Using put-call parity and solving for the put price, we get:
S + P = Ee–Rt + C
4. Using put-call parity and solving for the call price we get:
S + P = Ee–Rt + C
5. Using put-call parity and solving for the stock price we get:
S + P = Ee–Rt + C
6. Using put-call parity, we can solve for the risk-free rate as follows:
S + P = Ee–Rt + C
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7. Using the Black-Scholes option pricing model to find the price of the call option, we find:
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10. Using the call price we found in the previous problem and put-call parity, you would need to pay:
11. Using the Black-Scholes option pricing model to find the price of the call option, we find:
(6/12 )
Putting these values into the Black-Scholes model, we find the call price is:
Using put-call parity, we find the put price is:
a. The intrinsic value of each option is:
b. The option value consists of time value and intrinsic value, so:
Call option value = Intrinsic value + Time value
Put option value = Intrinsic value + Time value
12. Using put-call parity, the price of the put option is:
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Intermediate
14. If the standard deviation is zero, d1 and d2 go to +∞, so N(d1) and N(d2) go to 1. This is the no-risk
call option formula we discussed in an earlier chapter, so:
15. If the standard deviation is infinite, d1 goes to positive infinity so N(d1) goes to 1, and d2 goes to
16. We can use the Black-Scholes model to value the equity of a firm. Using the asset value of $16,200
Putting these values into the Black-Scholes model, we find the equity value is:
The value of the debt is the firm value minus the value of the equity, so:
17. a. We can use the Black-Scholes model to value the equity of a firm. Using the asset value of
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Putting these values into the Black-Scholes model, we find the equity value is:
The value of the debt is the firm value minus the value of the equity, so:
The asset value if the firm takes Project B is $19,000 (= $17,100 + 2,800), so the value of equity
will be:
Putting these values into the Black-Scholes model, we find the equity value is:
The value of the debt is the firm value minus the value of the equity, so:
b. Although the NPV of Project B is higher, the equity value with Project A is higher. While NPV
c. Yes. If the same group of investors have equal stakes in the firm as bondholders and stockholders,
d. Stockholders may have an incentive to take on more risky, less profitable projects if the firm is
18. We can use the Black-Scholes model to value the equity of a firm. Using the asset value of $26,200
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Putting these values into the Black-Scholes model, we find the equity value is:
The value of the debt is the firm value minus the value of the equity, so:
The return on the company’s debt is:
19. a. The combined value of equity and debt of the two firms is:
b. For the new firm, the combined market value of assets is $42,400, and the combined face value of
Putting these values into the Black-Scholes model, we find the equity value is:
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The value of the debt is the firm value minus the value of the equity, so:
c. The change in the value of the firm’s equity is:
The change in the value of the firm’s debt is:
d. In a purely financial merger, when the standard deviation of the assets declines, the value of the
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