Question

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Following is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars. State of Nature Strong Demand Si Weak Demand S2 Decision Alternative Small complex, di 7 6 Medium complex, d2 15 3 Large complex, dz 23 -7 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 0.78 that demand will be strong (S1) and a corresponding probability of 0.22 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 $17.82 million and as long as the payoff for the weak demand was greater than or equal to - $25.36 million. a. Consider the medium complex decision. How much could the payoff under strong demand increase and still keep decision alternative dz 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 $ 20.18 million, the large complex remains the best decision. b. Consider the small complex decision. How much could the payoff under strong demand increase and still keep decision alternative dg 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 $ 19.33 million, the large complex remains the best decision.

Answer 1

ExpectedValue = (ProbabilityX Payoff)

Expected value for large complex = (0.78 × 23) + (0.22 × -7)

Expected value for large complex = 16.40

(A)

Let payoff of medium complex under strong demand = P

Expected value for medium complex = (P × 0.78) + (3 × 0.22)

Now, for large complex to remain the best decision:

Expected value for medium complex ≤ Expected value for large complex

(P × 0.78) + (3 × 0.22) ≤ 16.40

P × 0.78 ≤ 15.74

P ≤ 20.18

Therefore, expected value for medium complex should be equal to or less than $ 20.18 million for the large complex to be the best decision.

(B)

Let payoff of small complex under strong demand = P

Expected value for small complex = (P × 0.78) + (6 × 0.22)

Now, for large complex to remain the best decision:

Expected value for small complex ≤ Expected value for large complex

(P × 0.78) + (6 × 0.22) ≤ 16.40

P × 0.78 ≤ 15.08

P ≤ 19.33

Therefore, expected value for small complex should be equal to or less than $ 19.33 million for the large complex to be the best decision.