The operations manager for a well-drilling company must recommend whether to build a new facility, expand his existing one, or do nothing. He estimates that long-run profits (in $000) will vary with the amount of precipitation (rainfall) as follows: If he feels the chances of low, normal, and high precipitation are 30 percent, 20 percent, and 50 percent respectively, what is his expected value of perfect information?
A) $140,000
B) $170,000
C) $285,000
D) $305,000
E) $475,000

Question

The operations manager for a well-drilling company must recommend whether to build a new facility, expand his existing one, or do nothing. He estimates that long-run profits (in $000) will vary with the amount of precipitation (rainfall) as follows:  If he feels the chances of low, normal, and high precipitation are 30 percent, 20 percent, and 50 percent respectively, what is his expected value of perfect information?
A) $140,000 
B) $170,000 
C) $285,000 
D) $305,000 
E) $475,000

Quizplus · Accepted Answer

To determine the best choice, we need to calculate the expected value of each option:

- Build a new facility: 
    - Expected profit = (0.3 x 400) + (0.2 x 200) + (0.5 x 100) = $190,000

- Expand existing facility:
    - Expected profit = (0.3 x 300) + (0.2 x 150) + (0.5 x 75) = $127,500

- Do nothing:
    - Expected profit = (0.3 x 0) + (0.2 x 0) + (0.5 x 250) = $125,000

Therefore, the best choice is to build a new facility.

To calculate the expected value of perfect information, we need to find the difference between the expected value with perfect information and the expected value without perfect information.

If the manager had perfect information on the amount of precipitation, he would always choose the option that yields the highest profit. Therefore, the expected value with perfect information would be:

- Expected profit with perfect information: 
    - Build a new facility if precipitation is high (Expected profit = $400,000)
    - Expand existing facility if precipitation is normal (Expected profit = $150,000)
    - Do nothing if precipitation is low (Expected profit = $0)
    - Expected profit with perfect information = (0.3 x 400) + (0.2 x 150) + (0.5 x 0) = $135,000

The expected value without perfect information has already been calculated as $190,000. Therefore, the expected value of perfect information is:

- Expected value of perfect information = Expected profit with perfect information - Expected profit without perfect information
- Expected value of perfect information = $135,000 - $190,000
- Expected value of perfect information = -$55,000

Since the expected value of perfect information is negative, it does not provide any additional benefit to the manager's decision-making process. Therefore, the manager should make the decision based on the expected values calculated without perfect information.

The Operations Manager for a Well-Drilling Company Must Recommend Whether