The Lake Placid Town Council decided to build a new community center to be: used for conventions, concerts, and oilier public events, but considerable controversy is appropriate size. Many influential citizens want a large center that would be a showcase for the area. But the mayor feels that if demand does not support such a center, the community will lose a large amount of money. To provide structure for the decision process, the council narrowed the building alternatives to three sizes: small, medium and large. Everybody agreed that the critical factor in choosing the best size is the number of people who will want to use the new facility. A regional planning consultant provided demand estimates under three responds to a situation in which tourism drops substantially, the base-case scenario coroner spends to a situation in which Lake Placid continues to attract visitors consultant has the best-case scenario corresponds to a substantial increase in tourism. The consultant has provided probability assessments of 0.10, 0.60, and 0.30 for the worst case, base-case, and best-case scenarios, respectively. The town council suggested using net cash flow over a 5-year planning horizontal as the criterion for deciding on the best size. The following projections of net cash flow (in thousands of dollars) for a 5-year planning horizon have been developed. All costs, in the consultant’s fee, have been included. What decision should Lake Placid make using the expected value approach? Construct risk profiles for the medium and large alternatives. Given the mayor s concern over the possibility of losing money and the result of part (a), which alternative would you recommend? Compute the expected value of perfect information. Do you think it would be worth trying to obtain additional information concerning which scenario is likely to occur? Suppose the probability of the worst-case scenario increases to 0.2, the probability of the base-case scenario decreases to 0.5, and the probability of the best-case scenario remains al 0.3. What effect, if any, would these changes have on the decision recommendation? The consultant has suggested that an expenditure of $150,000 on a promotional campaign over the planning horizon will effectively reduce the probability of the worst-case scenario to zero. If the campaign can be expected to also increase the probability of the best-case scenario to 0.4, is if a good investment?

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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 ScenarioA*D
Center SizeWorst-CaseBase-CaseBest-CaseExpected Value
ASmall400500660538
BMedium-250650800605
CLarge-400580990605
DProbability10%60%30%

b)

Risk Profile calculations
123(1+2+3)/3Avg-x(Avg-x)^2sum of (Avg-x)^2*probSquareroot (Variance)
Center SizeWorst-CaseBase-CaseBest-CaseAverageWorst-CaseBase-CaseBest-CaseWorst-CaseBase-CaseBest-CaseVariancesSD
ASmall40050066052012020-1401440040019600756086.94826048
BMedium-250650800400650-250-40042250062500160000127750357.42132
CLarge-400580990390790-190-60062410036100360000192070438.2579149
DProbability10%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 = 6502 = 422500 , (-250)^2 = 62500 , (-400)^2 = 160000

Variance = \sumProb * (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 SizeWorst-CaseBase-CaseBest-Case
Small400500660
Medium-250650800
Large-400580990
Probability10%60%30%
Payoff using perfect prediction400650990Max of above values
EVwPI727400*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 Scenariosum of A*D
Center SizeWorst-CaseBase-CaseBest-CaseExpected Value
ASmall400500660528
BMedium-250650800515
CLarge-400580990507
DProbability20%50%30%

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

e)

Demand Scenariosum of A*D
Center SizeWorst-CaseBase-CaseBest-CaseExpected Value
ASmall400500660564
BMedium-250650800710
CLarge-400580990744
DProbability0%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.