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Unformatted text preview: Probabilistic Decision Making Business decisions are routinely made on incomplete and inaccurate information. The question is "how accurate does the information have to be to arrive at the "correct" decision?" In the last lesson, we reviewed methods that treat risk and uncertainty utilizing deterministic computations that bound the range of uncertainty (breakeven analysis) and prioritize the level of risk by input variable (sensitivity analysis). We also studied how concepts from probability theory can be applied to measure the uncertainty of results in project decision making by using the technique of expected worth. This lesson will extend the application of probability theory to two situations that confront decision makers. The first situation involves determining the total level of risk that a project will be deemed economically attractive when it is not. In this case we use the Monte Carlo simulation. The second situation involves the treatment of a decision set that can contain mutually exclusive and dependent alternatives. In this arena the process of forming and analyzing decision trees can help. Monte Carlo Sampling The use of expected worth in Lesson 7 gave us the tools to determine boundaries on the expected worth of a project given the probabilities of various input variables. This is an approximation of the entire worth distribution for the project. To calculate the worth distribution of a project in its entirety, we must use the Monte Carlo simulation technique. Consider the following sample project. Example: In the sample project, I is investment, A is the annual cashflow, D is the disposal cost, and n is the economic life. Each of these variables is assumed to be distributed according to a mutually independent distribution function. For example, I A D n (I) (A) (D) (n) 3000 0.20 1000 0.75 300 0.90 4 0.60 4000 0.80 2000 0.20 3000 0.10 5 0.30 1.00 3000 0.05 1.00 6 0.10 1.00 1.00 For one Monte Carlo experiment, we select at random a set of outcomes, establishing values for each input parameter, and compute the resulting present worth. Selecting a second set of values for each parameter, a second present worth is computed, and so on for a number of trials which then define a set of present worths equal to the number of trials. If the number of trials is sufficiently large, the set of present worths determined by this method computes the entire distribution of worth for the project. The accuracy of this method depends on the selection criteria for input parameter values. The selection method must be according to random generation. Random Generation The input variables to a project are assumed to range from a lower value to a higher value and the potential values that the variable may take on are assumed to be random between these limits. In this case, the selection of a value can be put in the context of selecting at random a value between 0 and 1, and then applying that value to select the variable value. Computers are quite capable of selecting a select the variable value....
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 Fall '09
 Johnson
 Economics, Decision Making

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