CHAPTER 13 Other Topics in Capital Budgeting

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CHAPTER 13Other Topics in Capital Budgeting

• Evaluating projects with unequal lives
• Evaluating projects with embedded options
• Valuing real options in projects

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S and L are mutually exclusive and will be
repeated. k 10. Which is better?
Expected Net CFs
Year
Project S
Project L
(100,000)
0
(100,000)
59,000
1
33,500
59,000
2
33,500
--
3
33,500
--
4
33,500
3
S
L
CF0
-100,000
-100,000
CF1
59,000
33,500
Nj
2
4
I
10
10
NPV
2,397
6,190
Q. NPVL gt NPVS. Is L better? A. Cant say.
Need replacement chain analysis.
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• Note that Project S could be repeated after 2
  years to generate additional profits.
• Use replacement chain to calculate extended NPVS
  to a common life.
• Since S has a 2-year life and L has a 4-year
  life, the common life is 4 years.

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L
0
1
2
3
4
10
33,500
33,500
33,500
33,500
-100,000
NPVL 6,190 (already to Year 4)
S
0
1
2
3
4
10
59,000
59,000
59,000
59,000
-100,000
-100,000
-41,000
NPVS 4,377 (on extended basis)
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What is real option analysis?

• Real options exist when managers can influence
  the size and riskiness of a projects cash flows
  by taking different actions during the projects
  life.
• Real option analysis incorporates typical NPV
  budgeting analysis with an analysis for
  opportunities resulting from managers decisions.

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What are some examples of real options?

• Investment timing options
• Abandonment/shutdown options
• Growth/expansion options
• Flexibility options

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An Illustration of Investment Timing Options

• If we proceed with Project L, its NPV is 6,190.
  (Recall the up-front cost was 100,000 and the
  subsequent CFs were 33,500 a year for four
  years).
• However, if we wait one year, we will find out
  some additional information regarding output
  prices and the cash flows from Project L.

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Investment Timing (Continued)

• If we wait, there is a 50 chance the subsequent
  CFs will be 43,500 a year, and a 50 chance the
  subsequent CFs will be 23,500 a year.
• If we wait, the up-front cost will remain at
  100,000.

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Investment Timing Decision Tree
-100,000 43,500 43,500 43,500
43,500
50 prob.
-100,000 23,500 23,500 23,500
23,500
50 prob.
0 1 2 3 4
5
Years
At k 10, the NPV at t 1 is 37,889, if CFs
are 43,500 per year, or -25,508, if CFs are
23,500 per year, in which case the firm would
not proceed with the project.
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Should we wait or proceed?

• If we proceed today, NPV 6,190.
• If we wait one year, Expected NPV at t 1 is
  0.5(37,889) 0.5(0) 18,944.58, which is
  worth 18,944.58/(1.10) 17,222.34 in todays
  dollars (assuming a 10 discount rate).
• Therefore, it makes sense to wait.

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Issues to Consider

• Whats the appropriate discount rate?
• Note that increased volatility makes the option
  to delay more attractive.
• If instead, there was a 50 chance the subsequent
  CFs will be 53,500 a year, and a 50 chance the
  subse-quent CFs will be 13,500 a year, expected
  NPV next year (if we delay) would be

0.5(69,588) 0.5(0) 34,794 gt 18,944.57.
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Factors to Consider When Deciding When to Invest

• Delaying the project means that cash flows come
  later rather than sooner.
• It might make sense to proceed today if there are
  important advantages to being the first
  competitor to enter a market.
• Waiting may allow you to take advantage of
  changing conditions.

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Abandonment/Shutdown Option

• Project Y has an initial, up-front cost of
  200,000, at t 0. The project is expected to
  produce after-tax net cash flows of 80,000 for
  the next three years.
• At a 10 discount rate, what is Project Ys NPV?

0 1 2 3
k 10
-200,000 80,000 80,000 80,000
NPV -1,051.84
(More)
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Abandonment/Shutdown (continued)

• Project Ys A-T net cash flows depend critically
  upon customer acceptance of the product.
• There is a 60probability that the product will
  be wildly successful and produce A-T net cash
  flows of 150,000, and a 40 chance it will
  produce annual A-T cash flow of -25,000.

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Abandonment/Shutdown Decision Tree
150,000 150,000 150,000
k 10
60 prob.
-200,000
-25,000 -25,000 -25,000
40 prob.
0
1 2 3
Years
If the customer uses the product, NPV is
173,027.80. If the customer does not use the
product, NPV is -262,171.30. E(NPV)
0.6(173,027) 0.4(-262,171) -1,051.84.
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Abandonment/Shutdown (continued)

• Company does not have the option to delay the
  project.
• Company may abandon the project after a year, if
  the customer has not adopted the product.
• If the project is abandoned, there will be no
  operating costs incurred nor cash inflows
  received after the first year.

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NPV with the Abandonment Option
150,000 150,000 150,000
k 10
60 prob.
-200,000
-25,000
40 prob.
0
1 2 3
Years
If the customer uses the product, NPV is
173,027.80. If the customer does not use the
product, NPV is -222,727.27. E(NPV)
0.6(173,027) 0.4(-222,727) 14,725.77.
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Is it reasonable to assume that the abandonment
option does not affect the cost of capital?
No, it is not reasonable to assume that the
abandonment option has no effect on the cost of
capital. The abandonment option reduces risk,
and therefore reduces the cost of capital.
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Growth Option

• Project Z has an initial up-front cost of
  500,000.
• The project is expected to produce A-T cash
  inflows of 100,000 at the end of each of the
  next five years. Since the project carries a 12
  cost of capital, it clearly has a negative NPV.
• There is a 10 chance the project will lead to
  subsequent opportunities that have an NPV of
  3,000,000 at t 5, and a 90 chance of an NPV
  of -1,000,000 at t 5.

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NPV with the Growth Option
3,000,000
100,000 100,000 100,000 100,000
100,000
10 prob.
-1,000,000
-500,000
100,000 100,000 100,000 100,000
100,000
90 prob.
1 2 3 4 5
0
Years
At k 12, NPV of top branch (w / 10 prob.)
1,562,758.19. NPV of bottom branch (w / 90
prob.) - 139,522.38.
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NPV with the Growth Option (contd)

• If it turns out that the project has future
  opportunities with a negative NPV, the company
  would choose not to pursue them.
• Therefore, the NPV of the bottom branch should
  include only the -500,000 initial outlay and
  the 100,000 annual cash flows, which lead to an
  NPV of -139,522.38.

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NPV with the Growth Option (contd)

• Thus, the expected value of this project should
  be
• NPV 0.1(1,562,758) 0.9(-139,522)
• 30,706.

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Flexibility Options
Flexibility options exist when its worth
spending money today, which enables you to
maintain flexibility down the road.