Nick has plans to open some pizza restaurants, but he is not sure how many to open.He has prepared a payoff table to help analyze the situation. Nick believes there is a 40 percent chance that the market will be good, a 30 percent chance that it will be fair, and a 30 percent chance that it will be poor.A market research firm will analyze market conditions and will provide a perfect forecast (they provide a money back guarantee).What is the most that should be paid for this forecast?
A)$ 44,000
B)$ 53,000
C)$123,000
D)$176,000

Question

Nick has plans to open some pizza restaurants, but he is not sure how many to open.He has prepared a payoff table to help analyze the situation.  Nick believes there is a 40 percent chance that the market will be good, a 30 percent chance that it will be fair, and a 30 percent chance that it will be poor.A market research firm will analyze market conditions and will provide a perfect forecast (they provide a money back guarantee).What is the most that should be paid for this forecast?
A)$ 44,000 
B)$ 53,000 
C)$123,000 
D)$176,000

Quizplus · Accepted Answer

To determine the maximum amount to pay for the forecast, we need to calculate the expected value of each decision. The expected value for opening 1 restaurant is:

(0.4 x 100,000) + (0.3 x 40,000) + (0.3 x -20,000) = $46,000

The expected value for opening 2 restaurants is:

(0.4 x 150,000) + (0.3 x 60,000) + (0.3 x -40,000) = $69,000

The expected value for opening 3 restaurants is:

(0.4 x 180,000) + (0.3 x 90,000) + (0.3 x -60,000) = $99,000

The expected value for opening 4 restaurants is:

(0.4 x 190,000) + (0.3 x 110,000) + (0.3 x -80,000) = $107,000

Comparing the expected values for each decision, opening 4 restaurants has the highest expected value of $107,000. Therefore, the best choice is to open 4 restaurants. To determine the maximum amount to pay for the forecast, we need to subtract the expected value of the decision we would make without the forecast (i.e. open 4 restaurants) from the expected value of the decision we would make with the forecast. The expected value for opening 4 restaurants with the forecast is:

(0.4 x 190,000) + (0.3 x 160,000) + (0.3 x 130,000) = $167,000

The maximum amount to pay for the forecast is:

$167,000 - $107,000 = $60,000

Therefore, the most that should be paid for this forecast is $123,000 (Choice C) since it is the closest option to $60,000.

Nick Has Plans to Open Some Pizza Restaurants, but He