Question

1. The CEO must determine whether to build a small plant or a large plant for the company. The CEO believes that the profit made will depend in the level of future demand. The payoff table (in $) is as follows: Event High Demand Low Demand Probability 0.65 0.35 Action Small Plant 270 195 Action Large Plant 480 100 a. Compute the EMV for each action b. Compute the expected value of perfect information (EVPI) C. Provide the interpretation of the EVPI

Answer 1

a)

The EMV for small plant = 0.65 x 270 + 0.35 x 195

EMV for small plant = 243.75

EMV for large plant = 0.65 x 480 + 0.35 x 100

EMV for large plant = 347

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b)

Expected value of perfect information (EVPI) = Expected value with perfect information - Maximum EMV

Expected value with perfect information = Best outcome for 1st state of nature * probability of 1st state of nature + Best outcome for 2nd state of nature * probability of 2nd state of nature

Best outcome for high demand is to build a large plant with a payoff of 480. The best outcome for low demand is to build a small plant with a payoff of 195

Expected value with perfect information = 480 x 0.65 + 195 x 0.35

Expected value with perfect information = 380.25

The maximum EMV is 347 for large plant

Expected value of perfect information (EVPI) =  380.25 - 347

Expected value of perfect information (EVPI) = 33.25

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c)

Expected value of perfect information is the difference between the payoff that results under perfect information and the payoff resulting under risk.