Following is the payoff table for the Pittsburgh Development Corporation (PDC) C

Question

Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars.

Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak (S2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $15.75 million and as long as the payoff for the weak demand was greater than or equal to -$22 million.

Consider the medium complex decision. How much could the payoff under strong demand increase and still keep decision alternative d3 the optimal solution? If required, round your answer to two decimal places.

The payoff for the medium complex under strong demand remains less than or equal to $____ million, the large complex remains the best decision.

Consider the small complex decision. How much could the payoff under strong demand increase and still keep decision alternative d3 the optimal solution? If required, round your answer to two decimal places.

The payoff for the small complex under strong demand remains less than or equal to $_____ million, the large complex remains the best decision.

State of Nature Decision Alternative Strong Demand S1 Weak Demand S2 Small complex, d1 7 6 Medium complex, d2 12 6 Large complex, d3 19 -9

Explanation / Answer

P(s1) = 0.8

P(s2) = 0.2

EV(d1) = 0.8(7) + 0.2(6) = 6.8

EV(d2) = 0.8(12) + 0.2(6) = 10.8

EV(d3) = 0.8(19) + 0.2(-9) = 13.4

With 0.8 probability for the state of nature s1 the resulting decision alternative d3 will receive a payoff of $15.75 million . Similarly, with state of nature s2 the best decision alternative would be d1 will receive a payoff of -$22 million.

So, if s1, select d3 and receive a payoff of $15.75 million

if s2, select d1 and receive a payoff of -$22 million

0.8(15.75) - 0.2(22) = 8.2

The expected value of $8.2 million is the expected value with perfect information (EVwPI)

The expected value of 13.4 million is the expected value without perfect information (EVwoPI)

So, expected value of the perfect information is

EVPI = EVwPI - EVwoPI

= $8.2 - $13.4

= -$5.2 million (Loss)

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