Following is the payoff table for the Pittsburgh Development Corporation (PDC) C
ID: 3244406 • 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 (S_1) and a corresponding probability of 0.2 that demand will be weak (S_2). 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 exist17.5 million and as long as the payoff for the weak demand was greater than or equal to -exist19 million. (a) Consider the medium complex decision. How much could the payoff under strong demand increase and still keep decision alternative d_3 the optimal solution? If required, round your answer to one decimal place. The payoff for the medium complex under strong demand remains less than or equal to exist 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 d_3 the optimal solution? If required, round your answer to one decimal place. The payoff for the small complex under strong demand remains less than or equal to exist million, the large complex remains the best decision.Explanation / Answer
Solution:
(a) Since the expected value of d3 with 0.8 probability for a strong demand and 0.2 for a weak demand is$14.2 million, then d3 will remain the optimal solution as long as the expected values for d2 and d1 areless than or equal to $17.5 million.
To calculate the maximum payoff under strong demand for d2 that will keep decision alternative d3 theoptimal solution:EV(d2) 17.5
Say:
S = the payoff of decision alternative d2 when demand is strong
EV(d2) = 0.8S + 0.2 * 5 17.5
0.8S + 1 17.5
S 20.6
The payoff for the medium complex under strong demand remains less then or equal to $20.6 million, the large complex remains the best decision.
(b) Since the expected value of d3 with 0.8 probability for a strong demand and 0.2 for a weak demand is$17.5 million, then d3 will remain the optimal solution as long as the expected values for d1 and d2 areless than or equal to $17.5 million.
To calculate the maximum payoff under strong demand for d1 that will keep decision alternative d3 theoptimal solution:EV(d1) 17.5
Say:
S = the payoff of decision alternative d1 when demand is strong
EV(d1) = 0.8S + 0.2 * 7 17.5
0.8S + 1.4 17.5
S 20.13
The payoff for the small complex under strong demand remains less then or equal to $20.13 million, the large complex remains the best decision.