Transcript Chapter 10: Basics of capital budgeting

Chapter 8: Strategy and Analysis
Using NPV
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Where are the sources of positive NPV
Introduction to real options and decisions trees
8-1
Introduction to Real Options
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Traditional NPV analysis (Chapters 4, 6, and 7) usually
does not address the decisions that managers have after
a project has been accepted.
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In reality, capital budgeting and project management is
typically dynamic, rather than static in nature.
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 and also incorporates opportunities
resulting from managers’ decisions.
8-2
Real options and decision trees,
an example
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A new proposed project would cost $500 now (t=0) in order to
explore the project’s feasibility.
Next year, it will cost an additional $1500 at t=1 upon final
acceptance, and is expected to produce cash flows in years 2
through 6 (from t=2 to t=6).
Our current (t=0) forecast for cash flows CF2 through CF6 is:
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70% probability of $1000 per year
30% probability of $400 per year
Next year (t=1), we will know cash flows CF2 through CF6 with
certainty; they will be either $1000 or $400 per year.
8-3
Traditional or static NPV
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Calculate the expected cash flows CF2 through CF6
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E(CF) = (0.70)(1000) + (0.30)(400) = $820 per year
A time line of expected cash flows is shown below.
t=0
t=1
t=2
t=3
t=4
t=5
t=6
CF0 = -500
CF1 = -1500
CF2 = 820
CF3 = 820
CF4 = 820
CF5 = 820
CF5 = 820
8-4
Traditional or static NPV
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Now calculate the NPV of the project’s timeline.
This project’s NPV consists of the following items:
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$500 spent today
$1500 spent at t=1
Five expected cash flows of $820 each from t=2 to t=6 (a
n=5 year annuity). The PV annuity formula produces a value
for t=1, which must be discounted by n=1 years from t=1 to
t=0.
 1

1
820

5
0.15


0.15
1

0.15
1500


NP V0  - 500 
1  0.15
1  0.15
NP V0  585.884
8-5
Traditional or static NPV
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This estimated NPV of $585.884 is incomplete. It
assumes the continuation of the project from t=0 to
termination at t=6 if the project is accepted today.
All we have is the NPV of expected future cash flows,
ignoring the option to abandon the project.
In reality, if $500 is spent today, then next year at t=1,
the firm has the option to either spend $1500 to
continue, or abandon the project.
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The decision at t=1 to continue or abandon depends on
whether CF2 to CF6 are then known to be $1000 or $400 per
year. If the project is believed to be negative NPV at t=1,
then it will be cancelled at that time.
8-6
NPV including the option to
abandon
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When the $1500 expenditure is made at t=1, we know
if CF2 through CF6 is either $1000 or $400 per year.
We first calculate the project’s NPV1, for CF1 through
CF6 being $1000 per year. We deem this as the success
NPV.
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From today’s (t=1) perspective, this success NPV has a
p=70% chance of occurring.
 1

1
NP V1  - 1500 1000
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5
0
.
15
0.151  0.15 
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NP V1  - 1500 (1000)(3.3
52155) $1852.155
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NPV including the option to
abandon
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Next we calculate the project’s NPV1, for CF1
through CF6 being $400 per year. We deem this
as the failure NPV.
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From today’s (t=1) perspective, this failure NPV has
a p=30% chance of occurring.
 1

1
NP V1  - 1500 400
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5
0
.
15
0.151  0.15 
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NP V1  - 1500 (400)(3.35
2155) - $159.138
8-8
NPV including the option to
abandon
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What is today’s (t=0) decision, based on this new
scenario analysis of next year’s likelihood of p=70%
success and p=30% failure?
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NPV0 = -500 + (0.7)[success NPV1/(1+r)] + (0.3)[failure
NPV1/(1+r)]
We will not go forward next year with negative NPV1,
therefore the failure NPV1 is ZERO, as the project will
just be cancelled at t=1 if CF2 through CF6 are then
known to be $400 per year.
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PV0 = -500 + (0.7)[1852/(1+0.15)] + (0.3)[0] = $627.399
8-9
NPV including the option to
abandon
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Note that this dynamic NPV=$627.399 is greater than
the earlier static NPV=$585.884. The $41.52
difference is the value of the option to abandon.
A decision tree of the project is shown below.
success,
p=70%
ACCEPT,
NPV1=$1852
conduct
$500 study
failure,
p=30%
REJECT,
NPV1=$0
do nothing
8-10
Second example of incorporating
the option to abandon
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A project has a k=10% cost of capital. If accepted, the project
costs $1100 today at t=0.
Next year, at t=1, we will know whether or not the project is
actually a success or failure. Today at t=0, all we know are the
probabilities of future success or failure.
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Success: probability=50%, and the project will generate cash flows of
$180 per year forever (perpetuity) if a success.
Failure: probability=50%, and the project will generate cash flows of
$30 per year forever (perpetuity) if a failure.
Project X can be abandoned at t=1 for $500 salvage value.
CFs here are perpetuities. The PV of a perpetuity is always
PV=CF/r
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Second example, NPV while
ignoring the option to abandon
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Expected annual CF = (p success)(180) + (p
failure)(30) = (0.5)(180) + (0.5)(30) = $105
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The expected cash flow is $105 per year forever.
NPV0 = -1100 + 105/0.1 = -1100 + 1050 = -$50
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If treated as a project that is allowed to continue
forever after t=0 acceptance, the expected NPV is
negative.
Under this type of analysis (ignoring the
abandonment option), the project should be rejected.
8-12
Second example
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A tree diagram of the project is shown below. There
are really two NPVs for this project; one for success
and one for failure, each with a probability of 50%.
Success,
p=50%
CF = $180/year, forever,
PV0 = 180/0.1 = $1800
Investment costs
$1100 today
Failure,
p=50%
CF = $30/year, forever,
PV0 = 30/0.1 = $300
Or abandon at t=1 for $500
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Second example
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The first timeline shows the project, if successful and, of course, never
abandoned.
The second timeline shows the project, if an eventual failure and not
abandoned.
The third timeline shows the project, if known to be a failure at t=1 and
abandoned at t=1 for $500 (the project’s t=1 cash flow will be earned).
t=0
CF0 = -1100
t=0
CF0 = -1100
t=0
CF0 = -1100
t=1
t=2
CF1 = 180
CF2 = 180
t=1
t=2
CF1 = 30
CF2 = 30
t=1
CF1 = 30
+ 500 salvage
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Second example
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NPV0 (if success) = -1100 + 180/0.1 = -1100 + 1800 =
$700
NPV0 (if failure): this issue must be further addressed
in detail. Either the project can be continued at t=1 or
it can be abandoned and the assets sold for $500
salvage value.
First, calculate the NPV0 if as though the project is
continued in operation as a failure with the $30 annual
cash flows:
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Failure NPV0 = -1100 + 30/0.1 = -1100 + 300 = -$800
8-15
Second example
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Now investigate abandoning the project at t=1
if we realize it is a failure. At t=1 one cash flow
(the only project cash flow since the project is
then cancelled) of $30 is received and then the
assets are sold for $500. This abandon upon
failure NPV0 is thus:
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NPV0 = -1100 + 30/(1+0.1) + 500/(1+0.1) = -1100 +
481.18 = -$618.18 if abandoned at t=1.
If a failure at t=1, the abandonment NPV is
higher than the NPV if allowed to continue.
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Second example
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If accepted today, at t=0, there is a 50% chance that the
project will be allowed to operate forever, and a 50%
chance that it will be abandoned for a $500 salvage
value.
Dynamic NPV0 = (0.5)[success NPV0] + (0.5)[failure
NPV0]
Dynamic NPV0 = (0.5)[700] + (0.5)[-618.18] = $40.91.
The project should now be accepted since the NPV
becomes positive when we allow for project
abandonment.
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Second example
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The NPV0 = –$50 if the project is treated as
continuing forever after acceptance.
The NPV0 = $40.91 when we include the
decision to abandon at t=1 when the project
becomes a failure.
The difference between these two NPVs is
called the value of the option to abandon.
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Value of option = 40.91 – (–50) = $90.91
8-18
Types of Real Options
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Investment timing options
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Abandonment/shutdown options
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Two example were previously shown
Growth/expansion options
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Often, the option to delay investment is valuable if market or
technology conditions are expected to improve.
May be valuable if the demand turns out to be greater than
expected
Flexibility options
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Projects may be more valuable if an allowance is made for
greater future modifications.
8-19