CHAPTER 12
Other Topics in Capital
Budgeting
Evaluating projects with unequal
lives
Evaluating projects with
unequal lives
Projects S and L are mutually exclusive, and will be repeated. If k = 10%, which is better?
Expected Net CFs Year Project S Project L
0 ($100,000) ($100,000)
1 59,000 33,500 2 59,000 33,500 3 - 33,500
Solving for NPV,
with no repetition
Enter CFs into calculator CFLO register
for both projects, and enter I/YR =
10%.
NPV
S
= $2,397
NPV
L
= $6,190
Is Project L better?
-100,000 59,000 59,000 59,000 59,000 -100,000
-41,000
Replacement chain
Use the replacement chain to calculate an
extended NPV
Sto a common life.
Since Project S has a 2-year life and L has a
4-year life, the common life is 4 years.
0 1 2 3
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
What are some examples
of
real options?
Investment timing options
Abandonment/shutdown
options
Growth/expansion options
Illustrating an investment
timing option
If we proceed with Project L, its annual cash
flows are $33,500, and its NPV is $6,190.
However, if we wait one year, we will find
out some additional information regarding output prices and the cash flows from
Project L.
If we wait, the up-front cost will remain at
$100,000 and there is a 50% chance the
Investment timing decision
tree
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.
50% prob.
50% prob.
0 1 2 3 4 5
Years
-$100,000 43,500 43,500 43,500 43,500
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) =
$18,944.57, which is worth
$18,944.57 / (1.10) = $17,222.34
in today’s dollars (assuming a 10%
discount rate).
Issues to consider with
investment timing options
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:
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.
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 1 2 3-$200,000 80,000 80,000 80,000
Abandonment option
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 CFs of
-Abandonment decision
tree
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(173,027.8) + 0.4(-262,171.3) -$200,000
60% prob.
40% prob.
1 2 3
Years 0
150,000 150,000 150,000
Issues with abandonment
options
The company does not have the
option to delay the project.
The company may abandon the
project after a year, if the customer
has not adopted the product.
NPV with abandonment
option
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(173,027.8) + 0.4(-222,727.27) -$200,000
60% prob.
40% prob.
1 2 3
Years 0
150,000 150,000 150,000
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
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.
NPV with the growth
option
100,000 100,000 100,000 100,000 100,000
-$500,000 10% prob.
90% prob.
1 2 3 4 5
Years 0
100,000 100,000 100,000 100,000 100,000
-$1,000,000 $3,000,000
At k = 12%,
NPV of top branch (10% prob) =
NPV with the growth
option
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.
Thus, the expected value of this project
should be:
Flexibility options
Flexibility options exist when it’s
