Question

Chris Suit is administrator for Lowell Hospital. She is trying to determine whether to build a large wing on the existing hospital, a small wing, or no wing at all. If the population of Lowell continues to grow, a large wing could return $150,000 to the hospital each year. If a small wing were built, it would return $100,000 to the hospital each year if the population continues to grow. If the population of Lowell remains the same, the hospital would encounter a loss of $85,000 with a large wing and a loss of $45,000 with a small wing. Unfortunately, Suit does not have any information about the future population of Lowell.

Answer 1

Answer:

A) Expected monetary value (EMV) is how much money you should expect to receive from different options. The EMV of both options are:

• EMV large wing = (50% x $150,000) - (50% x $85,000) = $75,000 - $42,500 = $32,500
• EMV small wing = (50% x $100,000) - (50% x $45,000) = $50,000 - $22,500 = $27,500

Since the EMV of the large wing is higher, then the large wing is the best alternative.

B) If the likelihood of the population growing reduces to 40% and the likelihood that it will remain unchanged increases to 60%, then the new EMVs for both options are:

• EMV large wing = (40% x $150,000) - (60% x $85,000) = $60,000 - $51,000 = $9,000
• EMV small wing = (40% x $100,000) - (60% x $45,000) = $40,000 - $27,000 = $13,000

Now the EMV of the small wing is higher, then the small wing is the best alternative.

C) EVPI is the expected value of perfect information, that means how much you are willing to pay to get the information you need to avoid any possible loss or increase your gains.

EVPI = EVwPi - highest EMV

EVwPi = (highest possible outcome of situation 1 x probability of situation 1) + (highest possible outcome of situation 2 x probability of situation 2)

• situation 1 is the wing being built, and the highest possible outcome is $150,000 when the population grows.
• situation 2 is not building anything at all, and the highest possible outcome is $0 when the population doesn't grow.

EVwPi = ($150,000 x 40%) + ($0 x 60%) = $60,000

EVPI = $60,000 - $13,000 = $47,000

This means that Chris would be willing to pay a maximum of $47,000 to know the perfect information about what investments should be carried out by the hospital.