Title: CHAPTER 13 Other Topics in Capital Budgeting
1CHAPTER 13Other Topics in Capital Budgeting
- Evaluating projects with unequal lives
- Evaluating projects with embedded options
- Valuing real options in projects
2S 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
3S
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.
4- 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.
5L
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)
6What 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.
7What are some examples of real options?
- Investment timing options
- Abandonment/shutdown options
- Growth/expansion options
- Flexibility options
8An 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.
9Investment 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.
10Investment 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.
11Should 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.
12Issues 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.
13Factors 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.
14Abandonment/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)
15Abandonment/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.
16Abandonment/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.
17Abandonment/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.
18NPV 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.
19Is 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.
20Growth 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.
21NPV 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.
22NPV 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.
23NPV 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.
24Flexibility Options
Flexibility options exist when its worth
spending money today, which enables you to
maintain flexibility down the road.