Finance management cengage 2013 chapter 013

Chapter 13

Real Options and Other Topics in
Capital Budgeting
Identifying Embedded Options
Valuing Real Options in Projects

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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 or at the end of a project’s
life.

•

Real option analysis incorporates typical NPV capital
budgeting analysis with an analysis of opportunities
resulting from managers’ responses to changing
circumstances that can influence a project’s
outcome.

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What are some examples of real options?

•
•
•
•

Growth/expansion options
Abandonment/shutdown options
Investment timing options
Flexibility options

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Investment Timing Option

•

Project X has an up-front cost of $100,000. The
project is expected to produce 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 information about market conditions and
the impact on the project’s expected cash flows.

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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?
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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

2

3

4

5

1

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.

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Should we wait or proceed?

•
•

If we proceed today, NPV = $6,190.

•

Therefore, it makes sense to wait.

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).

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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:

t = 1: 0.5($69,588) + 0.5(0) = $34,794 > $18,945
t = 0: $34,794/1.10 = $31,631 > $17,222
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Factors to Consider In Decision of 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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Abandonment/Shutdown Option

•

Project Y has an initial, up-front cost of $200,000, at
t = 0. The project is expected to produce 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
80,000

2
80,000

3
80,000

NPV = -$1,051.84

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Abandonment Option

•

Project Y’s cash flows depend critically upon
customer acceptance of the product.

•

There is a 60% probability that the product will be
wildly successful and produce CFs of $150,000, and
a 40% chance it will produce annual CFs of
−$25,000.

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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

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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.

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NPV with Abandonment Option

60% prob.
-$200,000
40% prob.
0

•
•

150,000

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 and it can be
abandoned after Year 1, NPV is −$222,727.27.

E(NPV) = 0.6($173,027.8) + 0.4(−$222,727.27)
= $14 ,725.77

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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.

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Growth Option

•
•

Project Z has an initial cost of $500,000.

•

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.

The project is expected to produce cash flows 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.

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NPV with the Growth Option

100,000 100,000

10% prob.
-$500,000
90% prob.

•

0

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
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NPV with the Growth Option

•

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 NPV of this project is:
NPV = 0.1($1,562,758) + 0.9(-$139,522)
= $30,706.
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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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