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Chapter 8
Financial Options and Applications in Corporate Finance
ANSWERS TO END-OF-CHAPTER QUESTIONS
8-1 a. An option is a contract which gives its holder the right to buy or sell an asset at some
b. A simple measure of an option’s value is its exercise value. The exercise value is
equal to the current price of the stock (underlying the option) less the striking price of
c. The Black-Scholes Option Pricing Model is widely used by option traders to value
options. It is derived from the concept of a riskless hedge. By buying shares of a
8-2 The market value of an option is typically higher than its exercise value due to the
speculative nature of the investment. Options allow investors to gain a high degree of
8-3 (1) An increase in stock price causes an increase in the value of a call option. (2) An
increase in strike price causes a decrease in the value of a call option. (3) An increase in
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
8-1 Exercise value = Current stock price – strike price
Answers and Solutions: 8 - 1
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
Time value = Option price – Exercise value
8-2 Option’s strike price = $15; Exercise value = $22; Time value = $5;
V = ? P0 = ?
Time Value = Market price of option - Exercise value
Exercise value = P0 - Strike price
Using the Black-Scholes Option Pricing Model, you calculate the option’s value as:
V = P[N(d1)] -
tr
RF
Xe
[N(d2)]
8-4 Put = V – P + X exp(-rRF t)
Answers and Solutions: 8 - 2
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
8-5
.3319.0
33333.05.0
)333333.0)](2/25.0(05.0[)35/$30($ln
tσ
)]t2/
2
(σ
RF
[r(P/X)ln
1
d
V = P[N(d1)] -
tr
RF
Xe
[N(d2)]
8-6 The stock’s range of payoffs in one year is $26 - $16 = $10. At expiration, the option will
Equalize the range to find the number of shares of stock: Option range / Stock range =
With 0.5 shares, the stock’s payoff will be either $13 or $8. The portfolio’s payoff will be
The present value of $8 at the daily compounded risk-free rate is: PV = $8 / (1+
The option price is the current value of the stock in the portfolio minus the PV of the
payoff:
Answers and Solutions: 8 - 3
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
8-7 The stock’s range of payoffs in six months is $18 - $13 = $5. At expiration, the option
range of payoffs for the stock option is $4 – 0 = $5.
Equalize the range to find the number of shares of stock: Option range / Stock range =
The present value of $10.40 at the daily compounded risk-free rate is: PV = $10.40 / (1+
The option price is the current value of the stock in the portfolio minus the PV of the
payoff:
SOLUTION TO SPREADSHEET PROBLEMS
8-8 The detailed solution for the problem is available in the file Ch08 P08 Build a Model
Solution.xlsx at the textbook’s web site.
Answers and Solutions: 8 - 4
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
MINI CASE
Assume that you have just been hired as a financial analyst by Triple Play Inc., a mid-sized
California company that specializes in creating high-fashion clothing. Since no one at
Triple Play is familiar with the basics of financial options, you have been asked to prepare a
brief report that the firm's executives could use to gain at least a cursory understanding of
the topic.
To begin, you gathered some outside materials the subject and used these materials to
draft a list of pertinent questions that need to be answered. In fact, one possible approach
to the paper is to use a question-and-answer format. Now that the questions have been
drafted, you have to develop the answers.
a. What is a financial option? What is the single most important characteristic of
an option?
Answer: A financial option is a contract which gives its holder the right to buy (or sell) an
b. Options have a unique set of terminology. Define the following terms: (1) call
option; (2) put option; (3) strike price; (4) expiration date; (5) exercise value (6)
option price; (7) time value; (8) covered option; (9) naked option; (10)
in-the-money call; (11) out-of-the-money call; and (12) LEAPS.
Answer: 1. A call option is an option to buy a specified number of shares of a security
within some future period.
Answers and Solutions: 8 - 5
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
7. The time value is the difference between the option price and the exercise value.
8. For every new option, there is an investor who “writes” the option. A writer
Answers and Solutions: 8 - 6
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
c. Consider Triple Play’s call option with a $25 strike price. The following table
contains historical values for this option at different stock prices:
Stock Price Call Option Price
$25 $ 3.00
30 7.50
35 12.00
40 16.50
45 21.00
50 25.50
1. Create a table which shows (a) stock price, (b) strike price, (c) exercise value, (d)
option price, and (e) the time value, which is the option’s price less its exercise
value.
Answer: Price Of Strike Exercise Value Market Price Time Value
Stock Price Of Option Of Option (D) - (C) =
(A) (B) (A) - (B) = (C) (D) (E)
$25.00 $25.00 $ 0.00 $ 3.00 $3.00
30.00 25.00 5.00 7.50 2.50
c. 2. What happens to the option’s time value as the stock price rises? Why?
Answer: As the table shows, the option’s time value declines as the stock price increases. This
Answers and Solutions: 8 - 7
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
d. Consider a stock with a current price of P = $27. Suppose that over the next 6
months the stock price will either go up by a factor of 1.41 or down by a factor of
0.71. Consider a call option on the stock with a strike price of $25 which expires
in 6 months. The risk-free rate is 6%.
1. Using the binomial model, what are the ending values of the stock price? What
are the payoffs of the call option?
Answer: The assumptions which underlie the OPM are as follows:
Strike price: X = $25.00
Current stock price: P = $27.00
Ending "up" stock price = P (u) = $38.07
Answers and Solutions: 8 - 8
© 2017 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or
in part.
