Question

7. The Miramar Company is going to introduce one of three new products: a widget, a hummer, or a nimnot. The market conditions (favorable, stable, or unfavorable) will determine the profit or loss the company realizes, as shown in the following payoff table: Product Widget Hummer Nimnot Favorable (P=0.2) Stable (P=0.5) Unfavorable (P=0.3) 100,000 60,000 -40,000 50,000 50,000 30,000 35,000 30,000 25,000 a) Compute the expected value for each decision, and select the best one. b) Develop the opportunity loss table, and compute the expected opportunity loss for each product. c) Determine the expected value of perfect information (EVPI).

Answer 1

a) Expected value =

Στ* p(x)

So Expected value for Widget, 100,000*0.2 + 60,000*0.5 - 40,000*0.3 = 38,000

Hummer= 50000*0.2 + 50000*0.5 + 30000*0.3 = 44,000

Nimnot= 35000*0.2 + 30000*0.5 + 25000*0.3= 29,500

So from above we can see that the maximum expected value is 44,000 under Hummer. Hence the best alternative is Hummer here.

b) Opportunity loss= Best payoff- Actual payoff

So for example, the state of nature is Favorable, then best payoff is 100,000

If we have selected Product Hummer, then Actual payoff is 50,000

So opportunity loss= 100,000- 50,000= 50,000

So the opportunity loss table is as follows:

Obbortunity less - Favorable (0.2 stable (0.5) Widget 0 o Hummer 50,000 10,000 Nimnot 65,000 30000 Unfavorable (0.3) 70,000 o 9000 Wid Expected opportunity logs: oxo. ato koost 70ooo *0.3=21000 Hummer: 50 000X 0.2 +10000X0.5 tox0.3 = 15,000 Alimnot: 65000x0.2 + 30000 хo st 5000x0.3=29,500 since least Expected opfatturity loss is Plenary ito the best option wde

c) EVPI = EVwithPI - EVwithoutPI

Now, EVwithoutPI = Max Expected value = 44,000

EVwithPI= Max value under each state of nature*Probability = 100,000*0.2 + 60,000*0.5 + 30,000*0.3= 59,000

So required EVPI = 59,000-44,000 = 15,000