ch12 other topics capital budgeting
CHAPTER 12
Other Topics in Capital
Budgeting
Evaluating projects with unequal
lives
Identifying embedded options
Valuing real options in projects
12-1
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
4
33,500
12-2
Solving for NPV,
with no repetition
Enter CFs into calculator CFLO register
for both projects, and enter I/YR =
10%.
NPV = $2,397
S
NPVL = $6,190
Is Project L better?
Need replacement chain analysis.
12-3
Replacement chain
Use the replacement chain to calculate an
extended NPVS to 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
10%
-100,000
1
59,000
2
3
59,000
59,000
-100,000
-41,000
NPVS = $4,377 (on extended basis)
4
59,000
12-4
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.
12-5
What are some examples
of
real
options?
Investment timing options
Abandonment/shutdown
options
Growth/expansion options
Flexibility options
12-6
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
subsequent CFs will be $43,500 a year, and
a 50% chance the subsequent CFs will be
$23,500 a year.
12-7
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.
12-8
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).
Therefore, it makes sense to wait.
12-9
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:
0.5($69,588) + 0.5(0) = $34,794 >
$18,944.57
12-10
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.
12-11
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
0
1
2
3
Project
Y’s NPV?
k = 10%
-$200,000
80,000
80,000
80,000
NPV = -$1,051.84
12-12
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
$150,000, and a 40% chance it will
produce annual A-T net CFs of $25,000.
12-13
Abandonment decision
tree
60% prob.
-$200,000
40% prob.
0
150,000
150,000
150,000
-25,000
-25,000
-25,000
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(173,027.8) + 0.4(-262,171.3)
= -1,051.84
12-14
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.
If the project is abandoned, there
will be no operating costs incurred
nor cash inflows received after the
first year.
12-15
NPV with abandonment
option
150,000
60% prob.
-$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(173,027.8) + 0.4(-222,727.27)
= 14,725.77
12-16
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.
12-17
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.
12-18
NPV with the growth
option
100,000
10% prob.
-$500,000
90% prob.
0
100,000
100,000
100,000
1
2
100,000
$3,000,000
100,000
100,000
100,000
-$1,000,000
100,000
100,000
Years
3
4
5
At k = 12%,
NPV of top branch (10% prob) =
$1,562,758.19
NPV of lower branch (90% prob) = $139,522.38
12-19
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:
NPV = 0.1($1,562,758) + 0.9(-$139,522)
= $30,706.
12-20
Flexibility options
Flexibility options exist when it’s
worth spending money today,
which enables you to maintain
flexibility down the road.
12-21
Other Topics in Capital
Budgeting
Evaluating projects with unequal
lives
Identifying embedded options
Valuing real options in projects
12-1
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
4
33,500
12-2
Solving for NPV,
with no repetition
Enter CFs into calculator CFLO register
for both projects, and enter I/YR =
10%.
NPV = $2,397
S
NPVL = $6,190
Is Project L better?
Need replacement chain analysis.
12-3
Replacement chain
Use the replacement chain to calculate an
extended NPVS to 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
10%
-100,000
1
59,000
2
3
59,000
59,000
-100,000
-41,000
NPVS = $4,377 (on extended basis)
4
59,000
12-4
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.
12-5
What are some examples
of
real
options?
Investment timing options
Abandonment/shutdown
options
Growth/expansion options
Flexibility options
12-6
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
subsequent CFs will be $43,500 a year, and
a 50% chance the subsequent CFs will be
$23,500 a year.
12-7
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.
12-8
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).
Therefore, it makes sense to wait.
12-9
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:
0.5($69,588) + 0.5(0) = $34,794 >
$18,944.57
12-10
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.
12-11
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
0
1
2
3
Project
Y’s NPV?
k = 10%
-$200,000
80,000
80,000
80,000
NPV = -$1,051.84
12-12
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
$150,000, and a 40% chance it will
produce annual A-T net CFs of $25,000.
12-13
Abandonment decision
tree
60% prob.
-$200,000
40% prob.
0
150,000
150,000
150,000
-25,000
-25,000
-25,000
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(173,027.8) + 0.4(-262,171.3)
= -1,051.84
12-14
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.
If the project is abandoned, there
will be no operating costs incurred
nor cash inflows received after the
first year.
12-15
NPV with abandonment
option
150,000
60% prob.
-$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(173,027.8) + 0.4(-222,727.27)
= 14,725.77
12-16
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.
12-17
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.
12-18
NPV with the growth
option
100,000
10% prob.
-$500,000
90% prob.
0
100,000
100,000
100,000
1
2
100,000
$3,000,000
100,000
100,000
100,000
-$1,000,000
100,000
100,000
Years
3
4
5
At k = 12%,
NPV of top branch (10% prob) =
$1,562,758.19
NPV of lower branch (90% prob) = $139,522.38
12-19
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:
NPV = 0.1($1,562,758) + 0.9(-$139,522)
= $30,706.
12-20
Flexibility options
Flexibility options exist when it’s
worth spending money today,
which enables you to maintain
flexibility down the road.
12-21