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# 38 mul ple dms contd director a is highly risk averse

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Unformatted text preview: worth to Liedtke? 41 Taking u-li-es into account Original Decision Tree EU Analysis •  U(x) = 1- exp(- x/R), R=1 •  U(0) = 0 •  U(2) = 0.865 •  U(3) = 0.950 •  U(5) = 0.993 •  U(10.3) = 1 EU(counteroﬀer) = (.17)(0.993) + (0.5)(0.697) + (0.33)(0.950) = 0.8308 CE(counteroﬀer) = - ln(1- 0.8308) = \$1.777 Bn => Leidtke should accept \$2 Bn oﬀer 42 With Informa-on •  Take 5 Bn if Texaco accepts •  Take 2 Bn if Texaco refuses •  Take 3 Bn if Texaco counteroﬀers •  EU(Info) = (0.17) (0.993)+ (0.5) (0.865) + (0.33) (0.950) = 0.9148 •  => CE(Info) = \$2.463 Bn 43 T- P One More Time - Cont’d. •  Assuming that C = 0, the certainty equivalent for the informa-on branch is about \$2.463 Bn. •  EVPI thus would be \$2.463 Bn - \$2.00 Bn = \$463 million •  Liedtke should spend no more than \$0.46 billion on informa-on about Texaco’s response. If the informa-on were to cost more, Liedtke would be beeer oﬀ simply accep-ng the \$2 billion counteroﬀer. 44 Value of Informa-on •  Problems involving value of informa-on calcula-ons can quickly become complicated •  Example – Problem 12.14, p. 557 45 Problem 12.14 - a EVPI of weather informa-on = 13.75 – 11.25 = 2.5K = \$2,500 Clearly, the farmer beneﬁts from knowing the weather 46 Problem 12.14 - b •  Let X = loss if burners are used and freeze occurs and Y= loss if sprinklers are used and freeze occurs •  Expected loss with informa-on = E[min(5 + ½ X, 2 + ½ Y)] •  This is diﬃcult to calculate •  Use Extended Pearson- Tukey 3- point approxima-on •  Procedure: calculate x.05, x.5, x.95, y.05, y.5, y.95. Assign probabili-es 0.185 to the 5th and 95th percen-les and probability 0.63 to the median •  Calculate expected loss with informa-on •  Calculate EVPI = 13.5K – 13.741K = \$9 •  The farmer b...
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