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Session 1339

Economic Simulations for Risk Analysis John H. Ristroph University of Louisiana at Lafayette

Introduction and Overview Errors in estimates of cash flows are the rule rather than the exception, so inclusion of risk analy- sis in an engineering economics course is essential to a student's becoming a practicing engineer. Teaching this topic, however, can be difficult due to the lack of readily available tools. This pa- per presents a student-friendly software system named Econsim that performs economic simula- tions. It is a Microsoft Excel 2000™ workbook containing easy-to-use macros and functions that perform simulations and provide reports. Ready-to-run copies of workbooks with examples are freely available from the author at ristroph@louisiana.edu. Provided below is a concise explanation of simulation concepts and their implementation in Econsim. Specific topics include a general treatment of risk analysis, basic simulation con- cepts, random numbers and generators, and then Econsim's simulation logic. This is followed by observations regarding the system's use in the classroom. The presentation is suitable for use as student handouts. Risk Analysis and Simulation A primary question involving most cash flows in not whether they will be incorrect, but rather by how much will they be incorrect. In routine analyses involving relatively small cash flows, po- tential errors frequently are ignored, and each cash flow is estimated using an average value known as an expected value. The expected value of a randomly varying cash flow C is the sum of each of its possible values cj multiplied by its probability of occurrence pj , E(C ) = c1 p1+ c2 p2+ ⋅⋅⋅ + cn pn , (1) where the probabilities sum to 1.0. For example, if a cash flow is estimated to be $30,000 with probability 20% and $40,000 with probability 80%, then its expected value is: $38,000 = 30,000(0.2) + 40,000(0.8) (2) Using expected values for routine decisions works because errors tend to average out. For example, suppose that a company has about 100 small projects of roughly the same size. If each project's actual present worth independently varies by 20% about its estimated value, statistical theory indicates that the actual value of the total present worth of all projects varies by only 2% about the estimated total present worth. In general, if there are N projects each having a percent- age variation of PV, then the total percentage variation TPV is: TPV = PV / N 1/2 (3) Companies also have a few large projects where there is little opportunity for errors to average out, and the effects of the errors can be damaging. Sensitivity analyses can help deter- mine breakeven points or limits beyond which a project is no longer desirable. Simulation is an- other helpful tool that can be performed using Excel, as described in the following sections.

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Ristroph, J. H. (2000, June), Economic Simulations For Risk Analysis Paper presented at 2000 Annual Conference, St. Louis, Missouri. 10.18260/1-2--8323