Sensitivity and Scenario Analysis

1. Sensitivity and Scenario Analysis

2. Financial Modeling • Any model we use has the potential to have error • How do we account for the uncertainty associated with our inputs into the model?

3. Three Types of Risk • Stand Alone Risk Views project in isolation • With-in firm (Corporate Risk) Looks at the firms portfolio of projects and how they interact • Market Risk Risk from the view of a well diversified investor.

4. Definitions • Risk Exposure to a chance of injury or loss • Probability The likelihood an event occurs • Risk vs. Uncertainty Risk – the probability of the outcome is known Uncertainty – includes judgment concerning the probability

5. Definitions and Terms Continued • Objective Prob –can measure prob. precisely • Subjective Prob. – Includes judgment or opinion • Variation Risk – We want to look at a range of possible outcomes

6. Issues in Risk Measurement • Stand Alone Risk is the easiest to measure • Market Risk is the most important to the shareholder • To evaluate risk you need three things • Standard deviation of the projects forecasted returns • Correlation of the projects forecasted returns with the firms other assets • Correlation of the projects forecasted returns with the market

7. Issues in Risk Management con’t • Using the numbers in 3) you can find the corporate beta and market beta coefficient (equal to ((s/s)r) • Most projects have a + correlation with other projects and a coefficient < 1 • Most projects are positively correlated with the market with coefficient < 1 • Corporate risk should also be examined • More important to small business • Investors may look at things other than market risk • Firm Stability is important to creditors, suppliers etc

8. Stand Alone Risk (Review) • The easiest approach to measuring stand alone risk is to use the standard deviation of the projects returns. • Just like security analysis you need to be careful looking at only standard deviation – don’t forget coefficient of variation

9. Measuring Stand Alone Risk • Sensitivity Analysis • Scenario Analysis • Monte Carlo Simulation

10. Sensitivity Analysis • Looks at the change in your decision variable when one input changes. • Examples: • what happens to the value of a project if sales are 10% higher than expected. • What happens to the cost of capital if the risk free rate increases.

11. Example 1 • Basic time value of money problem. • Assume you believe you need 2,000,000 when you retire and you are now 25 years old. • How much will you need to deposit each year at the end of the year if your account earns 8% each year? $27,357.56

12. Example 1 Change ONLY Expected return What if your estimated rate of return is of by 10% of the base (What if your account earns 8.8% each year? Or 7.2% each year)?

13. Example 2: change ONLYAmount Needed for Retirement Now assume that the amount you need for retiremetn may be off either way by 10%

14. Sensitivity Analysis • Usually the results are represented in a table where the response of the decision variable to changes in more than one individual variable are reported. • Then you can compare across variables to see which one has the largest impact on your decision

15. Example Results

16. Sensitivity Analysis • Benefits • Easy to Calculate and Understand • Measures risk associated with individual inputs • Weaknesses • Ignores probability of event • Ignores interaction among the variables • Ignores gains from diversification

17. Scenario Analysis • Differences from Sensitivity Analysis • Allows you to change more than one variable at a time • Look at a group of scenarios (best case, base case, and worst case) for example worst case – what if all variables change against us by 20%…. • Includes probability estimates of each scenario

18. Scenario Analysis • Now let both the future cash flows and the cost of capital change. Worst Case Scenario Best Case Scenario (SavingshReturni)(SavingsiReturnh) Need $2,200,000Need $1,800,000 Return = 7.2% Return = 8.8% PMT = 33,796.89PMT = $21,890.20

19. Scenario Analysis • Given the NPV and Probability you can find the expected NPV and standard deviation Scenario NPV Prob. NPV(Prob) Worst $33,796.89 .33 $11,265.63 Base $27357.56 .33 $ 9,119.17 Best $21,890.20 .33 $ 7,296.73 Expected NPV $27,681.55 Standard Deviation $ 5,959.95

20. Interpreting the Results • The project has an expected return on 4204.94 with standard deviation of 741.38 • This implies a 68 % confidence interval of (3463.56 to 4946.32) a large range of possible outcomes • The coefficient of variation would be .1763 (you are accepting .1763 units of risk for each unit of return)

21. Scenario Analysis • Benefits • More than one variable changes at a time • Accounts for probability • Easy to perform • Weaknesses • Small number of scenarios is unrealistic • Probability distributions difficult to estimate

22. Monte Carlo Simulation • A more advanced form of scenario analysis • Utilizes the computer to make random choices for each variable input then calculate the expected return and standard deviation

23. Mont Carlo Simulation • Construct a model of the firms cash flows and NPV’s • Specify a probability distribution for each uncertain variable (characterized by mean and standard dev) and correlation among variables. • Allow computer to select a random draw form the distribution for each variable • Calculate NPV (this is one scenario). • Repeat 3) an 4) (10,000 or 100,000 times) equal chance of each scenario –Calculate expected NPV and standard deviation.

24. Monte Carlo Simulation • Benefits • More realistic selection of variables • Easy to understand results • Weaknesses • Only as good as probability estimate and correlation of variables

25. Quick Review • Sensitivity Analysis Scenario Analysis and Monte Carlo Simulation were all used to measure stand alone risk • Each is designed to provide more information about the uncertainty associated with the project – they do not provide a clear cut decision rule.