Chapter 13
Real Options and Other
Topics in Capital Budgeting
 Identifying Embedded Options
 Valuing Real Options in Projects
13-1
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.
13-2
What are some examples of real
options?




Growth/expansion options
Abandonment/shutdown options
Investment timing options
Flexibility options
13-3
Investment Timing Option



Project X has an up-front cost of $100,000.
The project is expected to produce after-tax
cash flows of $33,500 at the end of each of
the next four years (t = 1, 2, 3, and 4). The
project has a WACC=10%.
The project’s NPV is $6,190. Therefore, it
appears that the company should go ahead
with the project.
However, if the company waits a year they will
find out more about the project’s expected
cash flows.
13-4
Investment Timing Option

If they wait a year:
 There is a 50% chance the market will be strong



and the expected cash flows will be $43,500 a year
for four years.
There is a 50% chance the market will be weak
and the expected cash flows will be $23,500 a year
for four years.
The project’s initial cost will remain $100,000, but
it will be incurred at t = 1 only if it makes sense at
that time to proceed with the project.
Should the company go ahead with the project
today or wait for more information?
13-5
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
3
4
5
Years
At WACC = 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.
13-6
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% WACC).
Therefore, it makes sense to wait.
13-7
Issues to Consider with Investment
Timing Options


What is 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 > $18,945
13-8
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.
13-9
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% WACC, what is Project Y’s NPV?
0
10%
-$200,000
1
2
3
80,000
80,000
80,000
NPV = -$1,051.84
13-10
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.
13-11
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
13-12
Issues with Abandonment Options
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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.
13-13
NPV with Abandonment Option
150,000


60% prob.
-$200,000
40% prob.
0
150,000
150,000
2
3
-25,000
1
If the customer uses the product, NPV is
$173,027.80.
If the customer does not use the product,
NPV is -$222,727.27.
Years
E(NPV)  0.6($173,027.8)  0.4(-$222,727.27)
 $14,725.77
13-14
Should an abandonment option affect a
project’s WACC?


Yes, an abandonment option should have an
effect on the WACC.
The abandonment option reduces risk, and
therefore reduces the WACC.
13-15
Growth Option



Project Z has an initial 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, and has a WACC of 12%. 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.
13-16
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
3
4
5 Years
At WACC = 12%,
 NPV of top branch (10% prob) = $1,562,758.19
 NPV of lower branch (90% prob) = -$139,522.38
13-17
NPV with the Growth Option
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If the project’s future opportunities have a
negative NPV, the company would choose not
to pursue them.
The bottom branch only has the -$500,000
initial outlay and the $100,000 annual cash
flows, which lead to an NPV of -$139,522.
The expected value of this project should be:
NPV= 0.1($1,562,758) + 0.9(-$139,522)
= $30,706.
13-18
Flexibility Options

Flexibility options exist when it’s worth
spending money today, which enables you
to maintain flexibility down the road.
13-19