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# Module17 - Making the Decision for a Single Project...

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Making the Decision for a Single Project Considering Risk II Part I

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Key Concepts Last Module: Evaluation of a Single Project under Risk This Module: Continue Evaluation of a Single Project under Risk Introduce simulation as an evaluation tool.
Risk Analysis Risk and Uncertainty are mathematically different. Risk assumes one has probabilistic information about future outcomes. Uncertainty assumes there is no probabilistic information, just which outcomes are possible. Many forms of risk (probable data). Actual cash flow magnitudes. Length of horizon. Timing of cash flows. Interest rate (although fairly fixed as we set it). We will assume we can estimate the probability distribution of our required parameters for analysis.

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Probability Review Discrete Case PDF (probability of a certain value): CDF (probability of a range of values): Expectation (expected value): f ( x ) = Pr( D = x ) = F ( x ) - F ( x - 1) F ( x ) = Pr( D x ) = f ( x i ) x i x E ( D ) = x i f ( x i ) x i
Common Distributions BERNOULLI BINOMIAL GEOMETRIC POISSON

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Probability Review Continuous Case PDF: CDF: Expectation: f ( x ) = F ( x ) x F ( x ) = Pr( a D b ) = f ( x ) dx a b E ( D ) = xf ( x ) dx -∞
Common Distributions UNIFORM EXPONENTIAL GAMMA NORMAL

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Measures of Risk Variance in return The larger an investment’s return varies, the greater the risk σ 2 = ( x - μ ) 2 -∞ f ( x ) dx Expected Value Variance measures deviation in either direction from the mean.
Measures of Risk Semi-variance in return Only examines variability in the negative return (as positive variance is good) S b = ( b - μ ) 2 -∞ b f ( x ) dx Expected Value Measures deviation in negative direction direction

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Measures of Risk Probability of loss Also known as the “safety first” rule L = f ( x ) dx -∞ b b Measures area under curve up to critical value (zero )
Making the Decision for a Single Project Considering Risk II End Part I

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Making the Decision for a Single Project Considering Risk II Part II
Probabilistic Scenario Analysis Define optimistic, pessimistic, and average scenarios in scenario analysis.

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