lecture 03.0 project analysis copyright © 2006 by the mcgraw-hill companies, inc. all rights...

Lecture 03.0

Project analysis

Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved

McGraw-Hill/Irwin


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McGraw-Hill/Irwin

Topics Covered

Sensitivity Analysis– Break Even Analysis

Monte Carlo SimulationReal 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 + $6QRevenues = $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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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 = $79,774.33


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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 120See 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

Step 1: Modeling the ProjectStep 2: Specifying ProbabilitiesStep 3: Simulate the Cash Flows

Modeling Process


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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. Option to expand

2. Option to abandon

3. Timing option

4. 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 settingFirm is searching for and capitalizing on its

comparative advantageEmphasis on the ability of the firm to react

to complex situationsEmphasis 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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-200,000

80,000

-3,000,000

5,000,000

500,000

30,000

-3,000,000

5,000,000

500,000

NPV = 0

NPV = 0

50%

50%

90%

10%

25%

75%


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-200,000

80,000

-3,000,000

5,000,000

500,000

30,000

-3,000,000

5,000,000

500,000

NPV = 0

NPV = 0

50%

50%

90%

10%

25%

75%

Continue

STOP

Continue

STOP


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McGraw-Hill/Irwin

-200,000

80,000

-3,000,000

5,000,000

500,000

30,000

-3,000,000

5,000,000

500,000

NPV = 0

NPV = 0

50%

50%

90%

10%

25%

75%

Continue

STOP

Continue

STOP


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-200,000

80,000

30,000NPV = 0

50%

50%

Continue

STOP

NPV(1) = $1,550,000


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-200,000

30,000

50%

50%

80,000 + 1,550,000 = $1,630,000

NPV OF Total is: $1,481,818 + 27,273 -200,000 = 1,309,091

lecture 03.0 project analysis copyright © 2006 by the mcgraw-hill companies, inc. all rights...

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