1. Lecture 03.0 Project analysis Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin

2. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 2 McGraw-Hill/Irwin Topics Covered  Sensitivity Analysis –Break Even Analysis  Monte Carlo Simulation  Real Options and Decision Trees

3. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 3 McGraw-Hill/Irwin 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.

4. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 4 McGraw-Hill/Irwin 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

5. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 5 McGraw-Hill/Irwin 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: ???

6. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 6 McGraw-Hill/Irwin 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 =

7. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 7 McGraw-Hill/Irwin 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 = $79,774.33

8. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 8 McGraw-Hill/Irwin 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

9. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 9 McGraw-Hill/Irwin  What does Sensitivity analysis Tell You?

10. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 10 McGraw-Hill/Irwin 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?

11. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 11 McGraw-Hill/Irwin 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?

12. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 12 McGraw-Hill/Irwin 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

13. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 13 McGraw-Hill/Irwin Monte Carlo Simulation  Step 1: Modeling the Project  Step 2: Specifying Probabilities  Step 3: Simulate the Cash Flows Modeling Process

14. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 14 McGraw-Hill/Irwin Monte Carlo Simulation

15. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 15 McGraw-Hill/Irwin 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

16. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 16 McGraw-Hill/Irwin 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

17. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 17 McGraw-Hill/Irwin Real Options 1.Option to expand 2.Option to abandon 3.Timing option 4.Flexible production facilities

18. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 18 McGraw-Hill/Irwin 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.

19. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 19 McGraw-Hill/Irwin 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

20. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 20 McGraw-Hill/Irwin  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.

21. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 21 McGraw-Hill/Irwin 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?

22. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 22 McGraw-Hill/Irwin 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

23. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 23 McGraw-Hill/Irwin 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?

24. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 24 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 50% 90% 10% 25% 75%

25. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 25 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 50% 90% 10% 25% 75% Continue STOP Continue STOP

26. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 26 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 50% 90% 10% 25% 75% Continue STOP Continue STOP

27. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 27 McGraw-Hill/Irwin -200,000 80,000 30,000 NPV = 0 50% Continue STOP NPV(1) = $1,550,000

28. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved 10- 28 McGraw-Hill/Irwin -200,000 30,000 50% 80,000 + 1,550,000 = $1,630,000 NPV OF Total is: $1,481,818 + 27,273 -200,000 = 1,309,091