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CHAPTER 13
Other Topics in Capital Budgeting
Evaluating projects with unequal
lives
Evaluating projects with embedded
options
Valuing real options in projects
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13 - 2
S and L are mutually exclusive and will
be repeated. k = 10%. Which is better?
Expected Net CFs
Year
0
1
2
3
4
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Project S
($100,000)
59,000
59,000
---
Project L
($100,000)
33,500
33,500
33,500
33,500
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CF0
CF1
Nj
I
NPV
S
-100,000
59,000
2
10
2,397
L
-100,000
33,500
4
10
6,190
Q. NPVL > NPVS. Is L better?
A. Can’t say. Need replacement chain
analysis.
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13 - 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.
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13 - 5
L:
0
1
2
3
4
33,500
33,500
33,500
33,500
10%
-100,000
NPVL = $6,190 (already to Year 4)
S:
0
10%
-100,000
1
2
3
4
59,000
59,000
59,000 59,000
-100,000
-41,000
NPVS = $4,377 (on extended basis)
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13 - 6
What is real option analysis?
Real options exist when managers
can influence the size and riskiness
of a project’s cash flows by taking
different actions during the project’s
life.
Real option analysis incorporates
typical NPV budgeting analysis with
an analysis for opportunities
resulting from managers’ decisions.
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13 - 7
What are some examples of
real options?
Investment timing options
Abandonment/shutdown options
Growth/expansion options
Flexibility options
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13 - 8
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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13 - 9
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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13 - 10
Investment Timing Decision Tree
50% prob.
50% prob.
0
-$100,000
43,500
43,500
43,500
43,500
-$100,000
23,500
23,500
23,500
23,500
1
2
Years
3
4
5
At k = 10%, the NPV at t = 1 is:
$37,889, if CF’s are $43,500 per year, or
-$25,508, if CF’s are $23,500 per year, in
which case the firm would not proceed
with the project.
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13 - 11
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
today’s dollars (assuming a 10%
discount rate).
Therefore, it makes sense to wait.
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13 - 12
Issues to Consider
What’s 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 subsequent 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 > $18,944.57.
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13 - 13
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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13 - 14
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
Y’s NPV?
0 k = 10%
-$200,000
1
80,000
NPV = -$1,051.84
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2
80,000
3
80,000
(More…)
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13 - 15
Abandonment/Shutdown (continued)
Project Y’s A-T net cash flows
depend critically upon customer
acceptance of the product.
There is a 60%probability 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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13 - 16
Abandonment/Shutdown Decision Tree
150,000
150,000
150,000
-25,000
-25,000
-25,000
1
2
3
k = 10%
60% prob.
-$200,000
40% prob.
0
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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13 - 17
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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13 - 18
NPV with the Abandonment Option
60% prob.
150,000
k = 10%
-$200,000
40% prob.
0
150,000
150,000
2
3
-25,000
1
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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13 - 19
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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13 - 20
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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13 - 21
NPV with the Growth Option
100,000
10% prob.
-$500,000
90% prob.
0
100,000
100,000
100,000
1
2
At k = 12%,
NPV of top branch
(w / 10% prob.)
NPV of bottom branch
(w / 90% prob.)
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100,000
$3,000,000
100,000
100,000
100,000
-$1,000,000
100,000
100,000
3
4
5
Years
= $1,562,758.19.
= -$ 139,522.38.
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13 - 22
NPV with the Growth Option (cont’d)
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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13 - 23
NPV with the Growth Option (cont’d)
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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13 - 24
Flexibility Options
Flexibility options exist when it’s
worth spending money today,
which enables you to maintain
flexibility down the road.
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