Following is the payoff table for the Pittsburgh Development Corporation (PDC) C
ID: 2748009 • Letter: F
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 $16 million and as long as the payoff for the weak demand was greater than or equal to -$21 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.
Explanation / Answer
Considering the medium complex decision, payoff under strong demand has to be less than or equal to 16 million , so that the large complex remains the best decision. The current payoff for medium complex strong demand is 13 million, so it can increase by another 3 million to become 16 milion.
calculation is given hereunder :
Payoff for large complex strong demand = 13.4 million
Payoff for medium complex should be less than or equal to 13.4 million, so that decision of large complex still remains optimal solution. So required payoff for medium complex under strong demand = (13.4 - 0.2*3 ) / 0.8 = 16 million. Incremental payoff = 16 - 13 = 3 million.
So Payoff for medium complex under strong demand should remain less than or equal to 16 million , so that large complex remains the best decision.
Similarly for small complex decision, required payoff under strong demand = (13.4 - 0.2*8 ) /0.8 = 14.75 million , so payoff under strong demand could increase by 5.75 million and still keep d3 the best decision.
Payoff for small complex under strong demand remains less than or equal to 14.75 milion, so that large complex remains the best decision
Payoff Table uncertainties Strong Demand S1 Weak Demand S2 EMV Decision 0.8 0.2 Small Complex d1 9 8 8.8 Medium Complex d2 13 3 11 Large Complex d3 19 -9 13.4