Chapter 18: Derivatives and Risk Management
Learning Objectives
485
Chapter 18
Derivatives and Risk Management
Learning Objectives
After reading this chapter, students should be able to:
◆ Identify the circumstances in which it makes sense for companies to manage risk.
◆ Describe the various types of derivatives and explain how they can be used to manage risk.
◆ Value options using the Binomial and Black-Scholes Option Pricing Models.
◆ Discuss the various elements of risk management and the different processes that firms use to manage
risks.
486
Lecture Suggestions
Chapter 18: Derivatives and Risk Management
Lecture Suggestions
This chapter provides information on derivatives and how they are used in risk management. We begin by
identifying the reasons why risk should be managed. Then, we give a brief background on derivatives. We
illustrate a riskless hedge and present the Binomial Option Pricing Model. Next, we present the Black-
Scholes Option Pricing Model to discuss the various factors that affect a call option’s value. We specifically
DAYS ON CHAPTER: 2 OF 56 DAYS (50-minute periods)
Chapter 18: Derivatives and Risk Management
Answers and Solutions
487
Answers to End-of-Chapter Questions
18-1 Risk management may increase the value of a firm because it allows corporations to (1) increase
their use of debt; (2) maintain their optimal capital budget over time; (3) avoid costs associated
18-2 The market value of an option is typically higher than its exercise value due to the speculative
18-3 There are several ways to reduce a firm’s risk exposure. First, a firm can transfer its risk to an
insurance company, which requires periodic premium payments established by the insurance
company based on its perception of the firm’s risk exposure. Second, the firm can transfer risk–
18-4 The futures market can be used to guard against interest rate and input price risk through the use
of hedging. If the firm is concerned that interest rates will rise, it would use a short hedge, or sell
18-5 Swaps allow firms to reduce their financial risk by exchanging their debt for another party’s debt,
18-6 If the elimination of volatile cash flows through risk management techniques does not significantly
488
Answers and Solutions
Chapter 18: Derivatives and Risk Management
Solutions to End-of–Chapter Problems
a. Exercise value = Current stock price – Exercise price
Chapter 18: Derivatives and Risk Management
Answers and Solutions
489
18-4 P = $15; X = $15; t = 0.5; rRF = 0.10; 2 = 0.12; d1 = 0.32660; d2 = 0.08165; N(d1) = 0.62795;
N(d2) = 0.53252; V = ?
18-5 Futures contract settled at 10016/32% of $100,000 contract value, so PV = 1.005 $1,000 = $1,005
18-6 a. In this situation, the firm would be hurt if interest rates were to rise by March 2015, so it would
490
Answers and Solutions
Chapter 18: Derivatives and Risk Management
c. In a perfect hedge, the gains on futures contracts exactly offset losses due to rising interest
b. Remember, that the options will be exercised only if they yield a positive payoff. In this case,
c. In this case, the call option will not be exercised. The returns under each of the scenarios are
summarized below:
e. Recall, that the stock price is expected to be either $50 or $70, with equal probability. If
Chapter 18: Derivatives and Risk Management
Answers and Solutions
491
b. Ending Price 0.80 = Ending Stock Value Ending Option Value
18-9
Range of values
Time until expiration
$50.00
Current stock price
492
Answers and Solutions
Chapter 18: Derivatives and Risk Management
c. and d.
Chapter 18: Derivatives and Risk Management
Comprehensive/Spreadsheet Problem
493
Comprehensive/Spreadsheet Problem
Note to Instructors:
The solution to part a of this problem is provided at the back of the text; however, the
solutions to parts b, c, d, and e are not. Instructors can access the
Excel
file on the textbook’s
website.
18–10 a. Assume you have been given the following information on Purcell Industries:
b.
Current Intrinsic B-S formula
Exercise stock Value Value Option
Price price $0 $1.82 Premium
$15.00 $1.00 $0.00 $0.00 $0.00
Option Value
494
Comprehensive/Spreadsheet Problem
Chapter 18: Derivatives and Risk Management
$15
Option Value
Intrinsic–vs–Market Value of Options
c.
XCALL = $15
if P= … Call
$1 -$1.82
Chapter 18: Derivatives and Risk Management
Comprehensive/Spreadsheet Problem
495
e.
Step 1:
Step 2:
Calculate the present value of the riskless portfolio today.
Calculate the cost of the stock in the portfolio.
Future Portfolio Value
(1 + rRF)t
PV =
496
Integrated Case
Chapter 18: Derivatives and Risk Management
Integrated Case
18-11
Tropical Sweets Inc.
Derivatives and Corporate Risk Management
Assume that you have just been hired as a financial analyst by Tropical Sweets
Inc., a midsized California company that specializes in creating exotic candies
from tropical fruits such as mangoes, papayas, and dates. The firm’s CEO,
George Yamaguchi, recently returned from an industry corporate executive
conference in San Francisco. One of the sessions he attended was on the
pressing need for smaller companies to institute corporate risk management
programs. As no one at Tropical Sweets is familiar with the basics of
derivatives and corporate risk management, Yamaguchi has asked you to
prepare a brief report that the firm’s executives can use to gain at least a
cursory understanding of the topics.
To begin, you gather some outside materials on derivatives and corporate
risk management and use those 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 must develop the answers.
A. Why might stockholders be indifferent to whether a firm reduces
the volatility of its cash flows?
Answer: [Show S18-1 and S18-2 here.] If volatility in cash flows is not
caused by systematic risk, then stockholders can eliminate the risk
Chapter 18: Derivatives and Risk Management
Integrated Case
497
B. What are seven reasons risk management might increase the value
of a corporation?
Answer: [Show S18-3 here.] There are no studies proving that risk
management either does or does not add value. However, there are
C. What is an option? What is the single most important characteristic
of an option?
Answer: [Show S18-4 here.] An option is a contract that gives its holder the