1. Hosted by Decisioneering, Inc. May 31, 2006 How To Incorporate Crystal Ball Into Your Finance Course To listen to the session on your phone, follow the instructions in the “Join Teleconference” pop up dialog box which will appear in a few moments. To listen to the session on your computer speakers instead of your phone, follow the instructions in the “Join Internet Phone” pop up dialog box which will appear in a few moments. Please DO NOT join both, as this is redundant. Guest Speaker John Charnes Professor, Scupin Faculty Fellow

2. Crystal Ball 7 www.crystalball.com 2 Crystal Ball is an Excel® based, easy-to-use Monte Carlo simulation program that helps you understand and quantify the uncertainty (variation) inherent in a spreadsheet-based business decision. Crystal Ball Excel-based Monte Carlo simulation tool, includes plug-in tools for setup and analysis (CB Tools) OptQuest Global optimization for uncertain models CB Predictor Time-series forecasting and multiple linear regression Crystal Ball and CB Predictor Developer Kits VBA customization tools Professional Edition includes:

3. Crystal Ball 7 www.crystalball.com 3 What does CB look like in Excel? Crystal Ball Toolbar Define Menu Run Menu Analyze Menu

4. Crystal Ball 7 www.crystalball.com 4 How does Crystal Ball (CB) work? 1.Determine which model inputs are uncertain and define a probability distribution. 2.Identify which forecasts you want to analyze/measure (e.g., NPV, Sigma level, process efficiency) 3.Run Simulation 4.Analyze Results

5. Crystal Ball 7.0 1. Define your Distributions The first step to using Crystal Ball is to determine which model inputs are uncertain. Which values are estimates? Which are averages? Once you have identified these, you use your knowledge of the uncertainty around the input to create a probability distribution for that cell (what CB calls an assumption). Crystal Ball lets you define these distributions using the Distribution Gallery

6. Crystal Ball 7 www.crystalball.com 6 Assumption Dialog Enter variety of parameters to define distributions Can fit distributions to raw data Can cell reference all fields Can correlate pairs of assumptions Marker lines

7. Crystal Ball 7 www.crystalball.com 7 2. Identify Your Forecasts The next step is to identify a forecast. A forecast is a formula cell that you want to measure and analyze. In this model, you select the Net Profit (cell C23).

8. Crystal Ball 7 8 3. Run Simulation Number of simulation trials performed Display range Certainty (probability) that the forecast will reach $2,812,558 Parts within the spec limits are shown in blue, parts outside spec limits are shown red Number of data points displayed in the chart Crystal Ball uses Monte Carlo simulation to randomly generate thousands of what-if scenarios Each scenario is then captured and presented in a frequency chart – (Forecast Chart)

9. Crystal Ball 7 www.crystalball.com 9 4. Analyze Results What’s responsible for most of the variation in the forecast? The sensitivity chart shows the influence each assumption cell has on the forecast. Crystal Ball 7.0

10. Reports Select a pre-defined report or create your own custom report. Reports now include new statistics and more control over data and charts. Crystal Ball 7.0 Extract Data You can extract data from both forecasts and assumptions and extract multiple types of data.

11. Crystal Ball 7 www.crystalball.com 11 Stochastic Optimization OptQuest enhances simulation models by automatically searching for and finding optimal “Best” solutions. Applications Finding the most cost effective inventory policy. Determining the best investment portfolio. Choosing the ultimate product selection. Deciding which projects will maximize total profit.

12. Crystal Ball 7 www.crystalball.com 12 Applications: Financial Services, Banking, Insurance Maximize the expected NPV of the firm's credit policy while requiring a solution with a specified maximum standard deviation Bank capital adequacy simulation Determine an optimal investment strategy Maximizing client's portfolio returns Assessing retirement plan returns based on variable levels of risk tolerance Evaluating the current and future positions of employer granted options

13. Crystal Ball 7 www.crystalball.com 13 Other Applications: Pharmaceutical Determine a bottom-line negotiation price and the model variables that drive the variability in the NPV and IRR forecasts for potential drugs Decide whether to scrap a project or to proceed to develop and market a potentially profitable new drug Measure the NPV of the introduction of a new pharmaceutical product

14. Crystal Ball 7 www.crystalball.com 14 Other Applications Six Sigma, Manufacturing & Engineering Minimize total inventory costs while deciding the optimal order quantity and reorder point Determine the most cost-effective way in which to maintain the operation of machines Determine how much of each product to produce to maximize gross profit without running out of raw materials Optimize product design

15. Crystal Ball 7 www.crystalball.com 15 Other Applications: Oil, Gas, and Energy Calculate the cash flow of a well Determine the optimum drill bit replacement policy Roll up two objective zones in a single oil and gas prospect Estimate multi-zone reserves Quantify and optimize the Net Present Value (NPV) of an Oil Field

16. Crystal Ball 7 www.crystalball.com 16 …And More Cost Estimation Demand/Sales Forecasting Project Management Valuation Resource Allocation/Workforce Planning …To Name a Few

17. Crystal Ball 7 www.crystalball.com 17 Crystal Ball Academic Program Software used in over 650 schools, domestic and international Taught in Top MBA Programs In technical, business, graduate, and undergraduate classes Published in over 50 textbooks as a student version Academic licenses are available for individual students and professors as well as course, department and school wide licenses Decisioneering will assist you with course materials

18. Crystal Ball 7 Financial Modeling and Risk Analysis Professor John Charnes Finance, Economics, and Decision Sciences (FEDS) Area

19. Crystal Ball 7 www.crystalball.com 19 Pedagogical Themes of Financial Modeling and Risk Analysis Spreadsheet models are very useful for helping to make financial decisions Microsoft Excel is the lingua franca of the business world Risk analysis is the systematic investigation and forecasting of risks in business Financial Modeling and Risk Analysis course focuses on building models to support decision making in finance

20. Crystal Ball 7 Risk Analysis Most real-world business situations today are probabilistic, but the decision models used to deal with them are deterministic How to deal with randomness? –Ignore it –Simplify problem to make it analytically tractable, get solution, then ignore real-life complications –Find a way to obtain an approximate solution to real-world problems

21. Crystal Ball 7 www.crystalball.com 21 Monte Carlo Simulation Monte Carlo simulation is a method by which approximate solutions are obtained to realistic (and therefore complicated) problems This is in contrast to analytical methods, which obtain exact solutions to highly stylized problems Tradeoff between rigor and relevance Crystal Ball is an Excel add-in for Monte Carlo simulation

22. Crystal Ball 7 www.crystalball.com 22 Simulating European Options Purpose –Even though simulation is not necessary to determine fair price of European options, it is used with European options to test algorithms and variance reduction techniques

23. Crystal Ball 7 www.crystalball.com 23 How To Price European Options with Simulation Simulate future stock price using risk-free rate of growth and assumed level of volatility Evaluate discounted (at risk-free rate) cash flow for each simulated price Average discounted cash flows over iterations of simulation

24. Crystal Ball 7 www.crystalball.com 24 Geometric Brownian Motion (GBM) Model for Future Price

25. Crystal Ball 7 www.crystalball.com 25 Example EuroCall.xls How many iterations (n) must be run to achieve a specified precision? Precision is increased with larger n or smaller  2

26. Crystal Ball 7 www.crystalball.com 26 Example: Up-and-In Barrier Call Options The New York Times reported (28 September 1998, p. C4) that Sprint chairman William T. Esrey stands to earn call options having a strike price of $47.94 for one million shares of Sprint stock if the stock reaches a price of $95.875 Assume it is 1 October 1998 Estimate (1) value on 31 December 2000, and (2) market value on 1 October 1998

27. Crystal Ball 7 www.crystalball.com 27 Estimated Value at Century End Using monthly closing FON prices since January 1996, find historical growth and volatility rates Assuming historical rates continue, simulate 1,000 sample paths with geometric Brownian motion (GBM) For each path, determine value of options on 31 December 2000 See esreyopt.xls

28. Crystal Ball 7 www.crystalball.com 28 Using simulation to price options References : –McDonald, R. L. Derivatives Markets, Boston, MA: Addison-Wesley, 2003. –Hull, J. C. Fundamentals of futures and options markets, 4th ed. Upper Saddle River, NJ: Prentice-Hall, 2002.

29. Crystal Ball 7 www.crystalball.com 29 Simple Real Options Example Firm can invest in a project having a 3- year life and terminal value that depends on cash flow in final quarter of third year Two sources of uncertainty –Avg. quarterly revenue growth ~ N(5%, 5%) –Var. Cost as % of Revenue ~ N(50%, 5%) Discount rate is 12.5%

30. Crystal Ball 7 www.crystalball.com 30 No Flexibility Once project is begun, is run to end of 3 years with no expansion if successful, and no abandonment if unsuccessful E(NPV) = $18.19 Pr(NPV 40%

31. Crystal Ball 7 www.crystalball.com 31 Abandonment Option Same project with option to abandon when unfavorable circumstances obtain Decision Rule: –Begin checking in Q2 of Y2, abandon if three consecutive quarters of negative cash flow E(NPV) = $61.98 Value(Abandonment Option) = 61.98 – 18.19 = $43.79

32. Crystal Ball 7 www.crystalball.com 32 Abandonment and Expansion Options Add option to expand Decision Rule –Begin checking in Q2 of Y2, expand if three consecutive quarters of cash flow greater than $15.00 Investment = $200, expansion will double quarterly revenue E(NPV) = $301.12 Value(Expansion Option) = 301.12 – 61.98 = $339.14

33. Crystal Ball 7 Optimization Using OptQuest

34. Crystal Ball 7 www.crystalball.com 34 Real Options Valuation Example

35. Crystal Ball 7 www.crystalball.com 35 Optimal Solution

36. Crystal Ball 7 www.crystalball.com 36 Network Evolution Option Valuation Sprint or Nortel Networks Business Case NPV Calculations Decision Variables Stochastic Assumptions Random Outputs, e.g., NPV Option Valuation Tool

37. Crystal Ball 7 www.crystalball.com 37 Conclusion Project goals 1.Provide Sprint and Nortel Networks with a usable valuation model for making decisions affecting the evolution of the global telecommunication network, and 2.Expand the existing base of academic research into valuation of real options –Use of real data and opportunities to accomplish (1) helps determine general techniques to be published in academic literature to help accomplish (2)

38. Crystal Ball 7 www.crystalball.com 38 American Put Option Early exercise feature makes valuation difficult In practice, find value of Bermudan put option, which can be exercised only at a finite number of opportunities, k, before expiration

39. Crystal Ball 7 www.crystalball.com 39 Valuing Bermudan Put Options Analytical solution given by Geske and Johnson, JF 1984, for small k Simulation approach given by Broadie and Glasserman, JEDC 1997, for small k Forward Monte Carlo method (Charnes and Shenoy 2003) With OptQuest, package for stochastic optimization using tabu search

40. Crystal Ball 7 www.crystalball.com 40 Free-Boundary Problem For each exercise opportunity, must estimate optimal early-exercise boundary, the prices below which put option should be exercised and above which put option should be held See BermuPut.xls Uses Tabu search to select an optimal policy, then a final set of iterations to estimate value under optimal policy

41. Crystal Ball 7 www.crystalball.com 41 Example: Bermudan Put Option Current Stock Price = 80 Strike Price = 100 Volatility = 0.4 Risk-free rate = 0.06 Time until expiration, T = 0.5 May exercise at T/3, 2T/3, or T

42. Crystal Ball 7 www.crystalball.com 42 CB Model

43. Crystal Ball 7 www.crystalball.com 43

44. John Charnes Professor, Scupin Faculty Fellow E-mail: jcharnes@ku.edu Phone: 1-785-864-7591 Thank you for attending the Web Seminar How To Incorporate Crystal Ball Into Your Finance Course May 31, 2006 Decisioneering, Inc. 1515 Arapahoe St., Ste 1311 Denver, Colorado 80202 303-534-1515 www.crystalball.com