## EXPERT ANSWER

a)

Expected value of each case is given by:

EVsmall = Probability of worst case*CF of worst case + Probability of basecase*CF of base case + Probability of best case*CF of best case

EVsmall = 0.1*400 + 0.6*500+0.3*660= 40+300+198 =538

Similarly

EVmedium = 0.1*(-250) + 0.6*650 + 0.3*800 = 605

EV large = 0.1*(-400)+0.6*580+990*0.3 = 605

Thus based on Expected value we would go for Medium or Large size as both are having EV=605

Demand Scenario | A*D | ||||

Center Size | Worst-Case | Base-Case | Best-Case | Expected Value | |

A | Small | 400 | 500 | 660 | 538 |

B | Medium | -250 | 650 | 800 | 605 |

C | Large | -400 | 580 | 990 | 605 |

D | Probability | 10% | 60% | 30% |

b)

Risk Profile calculations | |||||||||||||

1 | 2 | 3 | (1+2+3)/3 | Avg-x | (Avg-x)^2 | sum of (Avg-x)^2*prob | Squareroot (Variance) | ||||||

Center Size | Worst-Case | Base-Case | Best-Case | Average | Worst-Case | Base-Case | Best-Case | Worst-Case | Base-Case | Best-Case | Variances | SD | |

A | Small | 400 | 500 | 660 | 520 | 120 | 20 | -140 | 14400 | 400 | 19600 | 7560 | 86.94826048 |

B | Medium | -250 | 650 | 800 | 400 | 650 | -250 | -400 | 422500 | 62500 | 160000 | 127750 | 357.42132 |

C | Large | -400 | 580 | 990 | 390 | 790 | -190 | -600 | 624100 | 36100 | 360000 | 192070 | 438.2579149 |

D | Probability | 10% | 60% | 30% |

Sample calculation for medium size

Average = (-250+650+800)/3 = 400

Avg-x = 400 – (-250) = 650 (worst)

= 400 – 650 = -250 (base)

= 400- 800 = -400 (best)

(Avg- x)^2 = 650^{2} = 422500 , (-250)^2 = 62500 , (-400)^2 = 160000

Variance = Prob * (Avg- x)^2

= 422500*0.1 + 0.6 * 62500 + 0.3*160000 = 122750

SD = Sqrt(Var) = 122750^0.5 = 357.42

Caclulation above shows that Standard deviation ie risk for medium size is 357.42 while that for LArge is 438.26. Thus Large size has more risk for same EV. Hence Medium size should be prefered

C)

EV without perfect information = 605,000

Center Size | Worst-Case | Base-Case | Best-Case | |

Small | 400 | 500 | 660 | |

Medium | -250 | 650 | 800 | |

Large | -400 | 580 | 990 | |

Probability | 10% | 60% | 30% | |

Payoff using perfect prediction | 400 | 650 | 990 | Max of above values |

EVwPI | 727 | 400*0.1+650*0.6+990*0.3 |

Expected value with perfect information = 727

Value of perfect Information = Expected value with perfect information – Expected value withou perfect information

Value of perfect Information = 727-605 = 122 ie $122,000

To pursue additional information would benefit the city since it would possibly increase its net cash flow up $122,000

d)

Demand Scenario | sum of A*D | ||||

Center Size | Worst-Case | Base-Case | Best-Case | Expected Value | |

A | Small | 400 | 500 | 660 | 528 |

B | Medium | -250 | 650 | 800 | 515 |

C | Large | -400 | 580 | 990 | 507 |

D | Probability | 20% | 50% | 30% |

This would change the recommendation to small size with EV 528,000

e)

Demand Scenario | sum of A*D | ||||

Center Size | Worst-Case | Base-Case | Best-Case | Expected Value | |

A | Small | 400 | 500 | 660 | 564 |

B | Medium | -250 | 650 | 800 | 710 |

C | Large | -400 | 580 | 990 | 744 |

D | Probability | 0% | 60% | 40% |

This would change recommendation to Large size with EV 744,000

Base case EV= 605,000

Difference = 744,000-605,000 = 139,000 which is less than expenditure

of $150,000 on promotional campaign. Thus i would not recommend promotional campaign based on expected value only

Using the campaign would reduce the net cash flow of all of these centers

but since the mayor is concerned about the risk of losing money, possibly

affecting their re-election, this route would be more favorable to them to eliminate risks.