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Chapter 13: Real Options
Learning Objectives
353
Chapter 13
Real Options and Other Topics in Capital Budgeting
Learning Objectives
After reading this chapter, the student should be able to:
◆ Explain what real options are, how they influence capital budgeting, and how they can be analyzed.
354
Lecture Suggestions
Chapter 13: Real Options
Lecture Suggestions
This chapter covers some important but relatively technical topics. Note too that this chapter is more
modular than most, i.e., the major sections are discrete, hence they can be omitted without loss of
continuity. Therefore, if you are experiencing a time crunch, you could skip sections or even the entire
chapter.
DAYS ON CHAPTER: 2 OF 56 DAYS (50-MINUTE PERIODS)
Chapter 13: Real Options
Answers and Solutions
355
Answers to End-of-Chapter Questions
13-1 a. An abandonment option is the option to stop a project if operating cash flows turn out to be
b. An investment timing option occurs when a firm has the option of delaying the start of a
c. Growth options exist if an investment creates the opportunity to make other potentially
13-3 It might be necessary for the firm to arrange things so that it has the possibility of abandonment
when it is making the initial decision. This might require contractual arrangements with suppliers,
13-4 For large, mature firms with good track records we can assume that all of its profitable projects can
be financed, but this assumption is harder to make for smaller firms, new firms, and firms with
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Answers and Solutions
Chapter 13: Real Options
13-5 The post-audit is a comparison of actual versus expected results for a given capital project. The
post-audit has two main purposes: (1) improve forecasts and (2) improve operations.
Chapter 13: Real Options
Answers and Solutions
357
Solutions to End-of-Chapter Problems
13-1 a. WACC = 11%; cash flows shown in millions.
0 1 2 3 NPV @ Yr. 0
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Answers and Solutions
Chapter 13: Real Options
13-4 a. NPV of abandonment after Year t:
Using a financial calculator, input the following: CF0 = -22500, CF1 = 23750, and I/YR = 10 to
13-5 a. WACC = 12.5%.
Chapter 13: Real Options
Answers and Solutions
359
b. Wait 2 years:
c. The investment timing option has a value of $0. Since the difference between the project with
13-7 a. Cash flows if tax imposed:
b. Cash flows if tax not imposed:
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Answers and Solutions
Chapter 13: Real Options
d. Since the project’s NPV with the tax is negative, if the tax were imposed the firm would
abandon the project. Thus, the decision tree looks like this:
e. 0 1 NPV @ Yr. 0
12%
Chapter 13: Real Options
Comprehensive/Spreadsheet Problems
361
Comprehensive/Spreadsheet Problems
Note to Instructors:
The solutions to these problems are not provided to students at the back of their text.
Instructors can access the
Excel
files on the textbook’s website.
13-8 See problem 13-7 on the preceding two pages.
13-9 a. Without abandonment (Cost @ t = 0 = -$10 million):
1 2 3 NPV @ Yr. 0
30% Prob. | | |
Good 9.0 9.0 9.0 $11.62
12%
362
Comprehensive/Spreadsheet Problems
Chapter 13: Real Options
b.
c. Without abandonment, with growth (Cost @ t = 0 = -$10 million)
1 2 3 NPV @ Yr. 0
30% Prob. | | |
Good 9.0 9.0 20.6 $19.88
d. Without abandonment, with investment timing (Cost @ t = 0 = -$10 million)
2 3 4 NPV @Yr. 1
30% Prob. | | |
Good 9.0 9.0 9.0 $11.62
12%
12%
$2.01 63% 72% 81% 90% 99% 108% 117%
8.4% $2.26 $2.43 $2.59 $2.76 $2.93 $3.09 $3.26
9.6% $2.01 $2.17 $2.34 $2.50 $2.67 $2.83 $2.99
% of Book Value the Assets are sold at
Chapter 13: Real Options
Integrated Case
363
Integrated Case
13-10
21st Century Educational Products
Other Topics in Capital Budgeting
21st Century Educational Products (21st Century) is a rapidly growing software
company; and consistent with its growth, it has a relatively large capital budget.
While most of the company’s projects are fairly easy to evaluate, a handful of
projects involve more complex evaluations.
John Keller, a senior member of the company’s finance staff, coordinates the
evaluation of these more complex projects. His group brings their
recommendations directly to the company’s CFO and CEO, Kristin Riley and Bob
Stevens, respectively.
A. In recent months, Keller’s group has focused on real option analysis.
(1) What is real option analysis?
Answer: [Show S13-1 and S13-2 here.] Real options exist when managers can
influence the size and riskiness of a project’s cash flows by taking
A. (2) What are some examples of projects with real options?
Answer: [Show S13-3 here.] A project may contain one or more different types
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Integrated Case
Chapter 13: Real Options
B. Considering real options, one of Keller’s colleagues, Barbara Hudson,
has suggested that instead of investing in Project X today, it might
make sense to wait one year because 21st Century would learn more
about market conditions and would improve its forecast of the
project's cash flows. Right now 21st Century forecasts that Project X
will generate expected cash flows of $33,500 for 4 years. However, if
the company waits one year, it will learn more about market
conditions. There is a 50% chance that the market will be strong and
a 50% chance that it will be weak. If the market is strong, the annual
cash flows will be $43,500. If the market is weak, the annual cash
flows will be only $23,500. If 21st Century chooses to wait one year,
the initial investment will remain $100,000 and cash flows will
continue for 4 years after the initial investment is made. Assume that
all cash flows are discounted at 10%. Should 21st Century invest in
Project X today, or should it wait a year before deciding whether to
invest in the project?
Answer: [Show S13-4 through S13-7 here.]
0 1 2 3 4 5 NPV @ t = 1
50% Prob. | | | | | |
Strong Mkt. 0 -100,000 43,500 43,500 43,500 43,500 $37,889.15
10%
Chapter 13: Real Options
Integrated Case
365
C. Now assume that there is more uncertainty about the future cash
flows. More specifically, assume that the annual cash flows are
$53,500 if the market is strong and $13,500 if the market is weak.
Assume that the upfront cost is still $100,000 and that the WACC is
still 10%. Will this increased uncertainty make the firm more or less
willing to invest in the project today? Explain.
Answer: [Show S13-8 and S13-9 here.]
0 1 2 3 4 5 NPV @ t = 1
50% Prob. | | | | | |
Strong Mkt. 0 -100,000 53,500 53,500 53,500 53,500 $69,587.80
10%
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Integrated Case
Chapter 13: Real Options
D. 21st Century is considering another project, Project Y. Project Y has
an upfront cost of $200,000 and an economic life of three years. If
the company develops the project, its after-tax operating costs will
be $100,000 a year; however, the project is expected to produce
after-tax cash inflows of $180,000 a year. Thus, the project’s
estimated cash flows are as follows:
Estimated Project
Year Cash Outflows Cash Inflows Cash Flows
0 ($200,000) $ 0 ($200,000)
1 (100,000) 180,000 80,000
2 (100,000) 180,000 80,000
3 (100,000) 180,000 80,000
(1) The project has an estimated WACC of 10%. What is the project’s
NPV?
Answer: [Show S13-10 here.]
0 1 2 3
| | | |
-200,000 80,000 80,000 80,000
10%
Chapter 13: Real Options
Integrated Case
367
D. (2) Although the project’s operating costs are fairly certain at $100,000
per year, the estimated cash inflows depend critically on whether
21st Century's largest customer uses the product. Keller estimates
that there is a 60% chance the customer will use the product, in
which case the project will produce after-tax cash inflows of
$250,000. Thus, its estimated project cash flows will be $150,000
per year. However, there is a 40% chance that the customer will
not use the product, in which case the project will produce after-tax
cash inflows of only $75,000. Thus, its estimated project cash flows
will be -$25,000. Write out the estimated cash flows and calculate
the project’s expected NPV under each of the two scenarios.
Answer: [Show S13-11 and S13-12 here.]
Customer uses product (60% probability)
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Integrated Case
Chapter 13: Real Options
D. (3) Although 21st Century does not have the option to delay the project,
it will know one year from now whether the key customer has
selected the product. If the customer chooses not to adopt the
product, 21st Century has the option to abandon the project. If 21st
Century abandons the project, it will not receive any cash flows after
Year 1 and it will not incur any operating costs after Year 1. Thus, if
the company chooses to abandon the project, its estimated cash flows
will be as follows:
0 1 2 3
| | | |
60% Prob. -200,000 150,000 150,000 150,000
| | | |
40% Prob. -200,000 -25,000
Again, assuming a WACC of 10%, what is the project’s expected NPV
if it abandons the project? Should 21st Century invest in Project Y
today, realizing it has the option to abandon the project at t = 1?
Answer: [Show S13-13 and S13-14 here.]
D. (4) Up until now, we have assumed that the abandonment option has
not affected the project’s WACC. Is this assumption reasonable?
How might the abandonment option affect the WACC?
Chapter 13: Real Options
Integrated Case
369
Answer: [Show S13-15 here.] It is not reasonable to assume that the
E. Finally, 21st Century is also considering Project Z. Project Z has an
upfront cost of $500,000, and it is expected to produce cash flows
of $100,000 at the end of each of the next five years
(t = 1, 2, 3, 4, and 5). Because Project Z has a WACC of 12%, it
clearly has a negative NPV. However, Keller and his group
recognize that if 21st Century goes ahead with Project Z today,
there is a 10% chance that this will lead to subsequent
opportunities that have an expected net present value at t = 5
equal to $3,000,000. At the same time, there is a 90% chance that
the subsequent opportunities will have an expected negative net
present value (-$1,000,000) at t = 5. On the basis of their
knowledge of real options, Keller and his group understand that the
company will choose to develop these subsequent opportunities
only if they appear to be profitable at t = 5. Given this information,
should 21st Century invest in Project Z today? Explain your
answer.
Answer: [Show S13-16 through S13-19 here.]
10% 0 1 2 3 4 5 NPV @ t = 0
Prob. | | | | | |
12%
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Integrated Case
Chapter 13: Real Options
