5.+decision+treee+approach+in+capital+budgetingd

8/10/2019 5.+DECISION+TREEE+APPROACH+IN+CAPITAL+BUDGETINGD

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Chapter 8: Strategy and Analysis

Using NPV Where are the sources of positive NPV

Introduction to real options and decisions trees


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Introduction to Real Options Traditional NPV analysis (Chapters 4, 6, and 7)

usually does not address the decisions that managershave aftera project has been accepted. In reality, capital budgeting and project management is

typically dynamic, rather thanstaticin nature.

Real optionsexist when managers can influence thesize and riskiness of a projects cash flows by taking

different actions during the projects life. Real option analysis incorporates typical NPV

budgeting analysis and also incorporates opportunitiesresulting from managers decisions.


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Real options and decision trees,

an example A new proposed project would cost $500 now (t=0) in order to

explore the projects feasibility.

Next year, it will cost an additional $1500 at t=1 upon final

acceptance, and is expected to produce cash flows in years 2through 6 (from t=2 to t=6).

Our current (t=0) forecast for cash flows CF2through CF6is: 70% probability of $1000 per year

30% probability of $400 per year Next year (t=1), we will know cash flows CF2through CF6with

certainty; they will be either $1000 or $400 per year.


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Traditional orstaticNPV Calculate the expectedcash flows CF2through CF6

E(CF) = (0.70)(1000) + (0.30)(400) = $820 per year

A time line of expectedcash flows is shown below.

t=0 t=1 t=2 t=3 t=4

CF1= -1500 CF2= 820 CF3= 820 CF4= 820

t=5

CF5= 820CF0= -500

t=6

CF5= 820


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Traditional orstaticNPV Now calculate the NPV of the projects timeline.

This projects NPV consists of the following items: $500 spent today

$1500 spent at t=1

Five expected cash flows of $820 each from t=2 to t=6 (an=5 year annuity). The PV annuity formula produces a valuefor t=1, which must be discounted by n=1 years from t=1 tot=0.

585.884NPV

0.151

0.1510.15

1

0.15

1820

0.151

1500-500-NPV

0

5

0


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Traditional orstaticNPV This estimated NPV of $585.884 is incomplete. It

assumes the continuation of the project from t=0 totermination at t=6 if the project is accepted today.

All we have is the NPV of expected future cash flows,ignoring the option to abandonthe 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. The decision at t=1 to continue or abandon depends on

whether CF2to CF6are then known to be $1000 or $400 peryear. If the project is believed to be negative NPV at t=1,then it will be cancelled at that time.


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NPV including the option to

abandon When the $1500 expenditure is made at t=1, we know

if CF2through CF6is either $1000 or $400 per year.

We first calculate the projects NPV1

, for CF1

throughCF6being $1000 per year. We deem this as the

successNPV. From todays (t=1) perspective, thissuccessNPV has a

p=70% chance of occurring.

$1852.15552155)(1000)(3.31500-NPV

15.0115.0

1

15.0

110001500-NPV

1

51


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abandon Next we calculate the projects NPV1, for CF1

through CF6being $400 per year. We deem this

as thefailureNPV. From todays (t=1) perspective, thisfailureNPV

has a p=30% chance of occurring.

$159.138-2155)(400)(3.351500-NPV

15.0115.0

1

15.0

14001500-NPV

1

51


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abandon What is todays (t=0) decision, based on this new

scenario analysis of next years likelihood of p=70%success and p=30% failure? 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 NPV

1

is ZERO, as the project willjust be cancelled at t=1 if CF2through CF6are thenknown to be $400 per year. PV0= -500 + (0.7)[1852/(1+0.15)] + (0.3)[0] = $627.399


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abandon

Note that this dynamicNPV=$627.399 is greater thanthe earlierstaticNPV=$585.884. The $41.52difference is the value of the option to abandon.

A decision tree of the project is shown below.ACCEPT,NPV1=$1852

do nothing

conduct$500 study

failure,p=30%

success,p=70%

REJECT,NPV1=$0


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Second example of incorporating

the option to abandon

A project has a k=10% cost of capital. If accepted, the projectcosts $1100 today at t=0.

Next year, at t=1, we will know whether or not the project is

actually a successor failure. Today at t=0, all we know are theprobabilitiesof future success or failure. Success: probability=50%, and the project will generate cash flows of

$180 per year forever (perpetuity) if asuccess.

Failure: probability=50%, and the project will generate cash flows of

$30 per year forever (perpetuity) if afailure. Project X can be abandoned at t=1 for $500 salvage value.

CFs here are perpetuities. The PV of a perpetuity is alwaysPV=CF/r


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Second example, NPV while

ignoring the option to abandon

Expectedannual CF = (psuccess)(180) + (pfailure)(30) = (0.5)(180) + (0.5)(30) = $105

The expectedcash flow is $105 per year forever. NPV0= -1100 + 105/0.1 = -1100 + 1050 = -$50

If treated as a project that is allowed to continueforever after t=0 acceptance, the expected NPV isnegative.

Under this type of analysis (ignoring theabandonment option), the project should be rejected.


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Second example

A tree diagram of the project is shown below. Thereare really two NPVs for this project; one for successand one for failure, each with a probability of 50%.

Success,

p=50%

Failure,

p=50%

CF = $180/year, forever,

PV0 = 180/0.1 = $1800

CF = $30/year, forever,

PV0= 30/0.1 = $300

Or abandon at t=1 for $500

Investment costs$1100 today


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Second example

The first timeline shows the project, if successful and, of course, neverabandoned.

The second timeline shows the project, if an eventual failure and notabandoned.

The third timeline shows the project, if known to be a failure at t=1 andabandoned at t=1 for $500 (the projects t=1 cash flow will be earned).

t=0 t=1 t=2

CF1= 180 CF2= 180CF0= -1100

t=0 t=1 t=2

CF1= 30 CF2= 30CF0= -1100

t=0 t=1

CF1= 30

+ 500 salvage

CF0= -1100


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Second example

NPV0(if success)= -1100 + 180/0.1 = -1100 + 1800 =$700

NPV0(if failure): this issue must be further addressedin detail. Either the project can be continued at t=1 orit can be abandoned and the assets sold for $500salvage value.

First, calculate the NPV0if as though the project iscontinuedin operation as a failure with the $30 annualcash flows: Failure NPV0= -1100 + 30/0.1 = -1100 + 300 = -$800


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Second example

Now investigate abandoningthe project at t=1if we realize it is a failure. At t=1 one cash flow(the only project cash flow since the project isthen cancelled) of $30 is received and then theassets are sold for $500. This abandon uponfailure NPV0is thus: NPV

0= -1100 + 30/(1+0.1) + 500/(1+0.1) = -1100

+ 481.18 = -$618.18if abandoned at t=1.

If a failure at t=1, the abandonment NPV ishigher than the NPV if allowed to continue.


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Second example

If accepted today, at t=0, there is a 50% chance that theproject will be allowed to operate forever, and a 50%chance that it will be abandoned for a $500 salvage

value. DynamicNPV0= (0.5)[success NPV0] + (0.5)[failure

NPV0]

DynamicNPV0= (0.5)[700] + (0.5)[-618.18] = $40.91.

The project should now be accepted since the NPVbecomes positive when we allow for projectabandonment.


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Second example

The NPV0 =$50 if the project is treated ascontinuing forever after acceptance.

The NPV0 = $40.91 when we include thedecision to abandon at t=1 when the projectbecomes a failure.

The difference between these two NPVs iscalled the value of the option to abandon.

Value of option = 40.91(50) = $90.91


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Types of Real Options

Investment timing options Often, the option to delay investment is valuable if market or

technology conditions are expected to improve.

Abandonment/shutdown options Two example were previously shown

Growth/expansion options May be valuable if the demand turns out to be greater than

expected Flexibility options

Projects may be more valuable if an allowance is made forgreater future modifications.

5.+decision+treee+approach+in+capital+budgetingd

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