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ENGM 661

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ENGM 661. Risk Analysis with @ Risk. A 1 A 2 A 3. 3. ,. 000. p. . 1. /. 4. . . A i. . 4. ,. 000. p. . 1. /. 2. . 1 2 3. . 5. ,. 000. p. . 1. /. 4. . 10,000. Class Problem.

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ENGM 661

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  1. ENGM 661 Risk Analysis with @ Risk

  2. A1 A2 A3 3 , 000 p  1 / 4   Ai  4 , 000 p  1 / 2  1 2 3  5 , 000 p  1 / 4  10,000 Class Problem Suppose we have the following cash flow diagram (MARR = 15%). Determine if the project is worthwhile.

  3. A1 A2 A3 3 , 000 p  1 / 4   Ai  4 , 000 p  1 / 2  1 2 3  5 , 000 p  1 / 4  10,000 Central Limit Theorem Preliminary

  4. A1 A2 A3 3 , 000 p  1 / 4   Ai  4 , 000 p  1 / 2  1 2 3  5 , 000 p  1 / 4  10,000 Central Limit Theorem Distribution of NPW

  5. A1 A2 A3 3 , 000 p  1 / 4   - = 867 E [ NPW ] Ai  4 , 000 p  1 / 2  1 2 3  5 , 000 p  1 / 4  10,000 Central Limit Theorem Distribution of NPW

  6. A1 A2 A3 3 , 000 p  1 / 4  N(-867, 938)  - = 867 E [ NPW ] Ai  4 , 000 p  1 / 2  1 2 3  5 , 000 p  1 / 4  10,000 -3,681 -867 1,947 Central Limit Theorem Distribution of NPW σ = 938

  7. A1 A2 A3 N(-867, 938) 1 2 3 10,000 -3,681 -867 1,947 Central Limit Theorem Distribution of NPW P {NPW>0 = P {(NPW-u)/σ > (0- (-867))/938 = P{Z>.92} = 1- P{Z<.92} = .178

  8. P{NPW >0} = .031 .063 .031 .016 .031 .016 .188

  9. Analytic P{NPW > 0} = 0.188 C.L.T. P{NPW > 0} = 0.178

  10. A1 A2 A3 3 , 000 p  1 / 4   Ai  4 , 000 p  1 / 2  1 2 3  5 , 000 p  1 / 4  10,000 Simulation

  11. A1 A2 A3 3 , 000 p  1 / 4   Ai  4 , 000 p  1 / 2  1 2 3  5 , 000 p  1 / 4  10,000 Simulation

  12. Simulation

  13. Simulation

  14. Simulation P{NPW > 0} = 5/20 = 0.25

  15. Simulation Analytic P{NPW > 0} = 0.188 C.L.T. P{NPW > 0} = 0.178 Simulation P{NPW > 0} = 0.25

  16. @Risk

  17. @Risk Analytic P{NPW > 0} = 0.188 C.L.T. P{NPW > 0} = 0.178 Simulation P{NPW > 0} = 0.25 @Risk P{NPW > 0} = 0.20 Next WEEK

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