Lecture
03.0
Project analysis
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Topics Covered
Sensitivity Analysis
– Break Even Analysis
Monte Carlo Simulation
Real Options and Decision Trees
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How To Handle Uncertainty
Sensitivity Analysis - Analysis of the effects
of changes in sales, costs, etc. on a project.
Scenario Analysis - Project analysis given a
particular combination of assumptions.
Simulation Analysis - Estimation of the
probabilities of different possible outcomes.
Break Even Analysis - Analysis of the level of
sales (or other variable) at which the
company breaks even.
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Steps in Sensitivity Analysis
 Define Costs as a function of output
 Define Revenue as a function of output
– Usually Price X Quantity
 Define expected (initial) variables
 Estimate worse and best case variables
 Get NPV’s for expected and also for worst case
and best case situations
 Determines where you might want to concentrate
your efforts to assure correct forecasts
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International Widget Company
 The Company is thinking of introducing a new
version of widgets designed for the under 30
crowd. To do this requires an initial investment of
$150,000 and it is expected to payoff $20,000 per
year for 4 years. At the end of the four years IWC
will be able to sell the fixed assets and equipment
for $100,000. If the real Cost of Capital is 4%, is
this a good investment? All numbers are in real
terms
 The NPV is: ???
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Sensitivity Analysis
Cost = $10,000 + $6Q
Revenues = $9Q
Initial Variables
–
–
–
–
–
Initial Investment = $150,000
Output (Q)
= 10,000
Life
=
4 years
Discount Rate
=
4%
Scrap Value
= $100,000
NPV
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=
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Sensitivity Analysis
 Assume these are in real terms
 Cost = $10,000 + $6 X Q
 Revenues = $9 X Q
 Initial Variables
–
–
–
–
–
Initial Investment = $150,000
Output
= 10,000
Life
=
10 years
Discount Rate =
4%
Scrap Value
= $100,000
 NPV
McGraw-Hill/Irwin
= $79,774.33
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Sensitivity Analysis

Pessimistic Optimistic
– Initial Investment 155
140
– Sales price
8
10
– Fixed cost
12
8
– Unit Variable Cost
7
5
– Output
9
13
– Life
3
7
– Discount Rate
5%
3%
– Scrap Value
95
120
See excel file: International Widget Company
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What does Sensitivity analysis Tell You?
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Scenario Analysis
We have assumed that inflation, over the
period will be zero. What if we assume that
the inflation rate is 1% per year
Assume this will have the following impact
on the cash flow:
– Real CF will increase to $21,
– The real amount that you can sell the assets for
declines to $90,000 at the end of ten years.
What is the new NPV?
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Breakeven Analysis
Breakeven is that level of output for which
the investment “breaks even”
What is meant by “breaks even”
– Where NPV = 0
What is that in terms of output?
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Break Even Analysis
 Now suppose that you have a “real margin” of $2 per unit,
and CF is simply the margin times the units sold, so that to
generate $20 you must sell 10 units. What is the minimum
units you have to sell to “break even” in PV terms? That
is: what is the sales level which will give you a zero NPV.
Note, this is not the zero profit level.
 The Cash Flows PV must equal $150,000
 How do you do this? Find the Payments that have a PV
of $150,000
 So Breakeven is: $10,164.54
– So quantity must be 5,082.27
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Monte Carlo Simulation
Modeling Process
Step 1: Modeling the Project
Step 2: Specifying Probabilities
Step 3: Simulate the Cash Flows
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Monte Carlo Simulation
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Flexibility & Real Options
Decision Trees - Diagram of sequential decisions
and possible outcomes.
Embedded in a typical project are options
which are not adequately dealt with by the
standard DCF Analysis.
These Options are typically contingent on
observing new information
Options: To Expand, or Contract
To Cease Operations
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Flexibility & Real Options
 Decision trees help companies determine their
Options by showing the various choices and
outcomes.
 The ability to create an Option thus has value that
should be included in the PV of a project
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Real Options
1.
2.
3.
4.
Option to expand
Option to abandon
Timing option
Flexible production facilities
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Classic Analysis
Search for projects with a positive NPV.
Typically this entails generating a stream of
Expected Cash Flows and appropriately
discounting.
However, this could miss some of the
strategic value associated with an
investment opportunity.
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The Strategic Approach
Views the Firm in a dynamic setting
Firm is searching for and capitalizing on its
comparative advantage
Emphasis on the ability of the firm to react
to complex situations
Emphasis on the firm’s reaction to change
and capitalizing on changing environment
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Typically the cash flow from an investment
is determined initially with no concept of
dynamic reactions.
The use of Real Options allows us to
integrate the two concepts into project
analysis.
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International Widget Company
Thinking of expanding into China. the plant will
cost $3 million to build and the marketing
department tells you that the market will generate
the equivalent of about $500,000 per year forever
if successful, but may produce as little as $50,000
per year if unsuccessful. the probability of
success is 50%. At a 10% discount rate, what is
the NPV of the project.
Accept or Reject this project?
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Widget’s China Experiment
However, if you develop a pilot project it
will only cost $200,000 and if successful,
then the pilot project will generate $80,000
if unsuccessful it will only generate
$30,000, each outcome equally likely . In
either case, the pilot project will not be able
to be continued thereafter.
Note that this is also a losing project by
itself, but it does allow you to get valuable
information about the full scale production
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Widget’s China Experiment
Marketing people again tell you that if the
pilot project is successful, then there is a
90% chance of the full scale project being
successful and generating $500,000 and
year, but if the pilot project is unsuccessful
then the full scale project will only generate
the $500,000 with a probability of 25%.
Should we undertake the Pilot Project, or
should we go immediately into production
full scale, or should we do neither?
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5,000,000
-3,000,000
80,000
500,000
NPV = 0
5,000,000
-200,000
-3,000,000
500,000
30,000
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NPV = 0
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5,000,000
-3,000,000
80,000
500,000
NPV = 0
5,000,000
-200,000
-3,000,000
500,000
30,000
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NPV = 0
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5,000,000
-3,000,000
80,000
500,000
NPV = 0
5,000,000
-200,000
-3,000,000
500,000
30,000
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NPV = 0
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NPV(1) = $1,550,000
80,000
-200,000
30,000
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NPV = 0
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80,000 + 1,550,000 = $1,630,000
-200,000
NPV OF Total is: $1,481,818 + 27,273 -200,000 = 1,309,091
30,000
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