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. As Nick does not know how his product will be received, he assumes that all three states of nature are equally likely to occur. If he uses the equally likely criterion, what decision would he make?a. Open 1b. Open 2c. Good marketd. Fair market

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.

             States of Nature      Good             Fair                      Poor

Alternatives

 Open 1                            380,000        70,000              -400,000

 Open 2                           200,000        80,000              -200,000

Do nothing                           0                    0                          0

Nick believes there is a 40% chance that the market will be good, a 30% chance that it will be fair, and a 30% chance that it will be poor.

a. What is Nick's expected monetary value?

b. 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) Nick's expected monetary value

For Alternative A (Open 1) = 0.4(380,000) + 0.3(70,000) + 0.3(-400,000)

                                           = 152,000 + 21,000 - 120,000

                                           = $53,000

For Alternative B (Open 2) = 0.4(200,000) + 0.3(80,000) + 0.3(-200,000)

                                           = 80,000 + 24,000 - 60,000

                                           = $44,000

For Alternative C (Do Nothing) = 0.4(0) + 0.3(0) + 0.3(0)

                                                   = 0

From the 3 scenarios, Nick would opt for the highest possible value which would be Alternative A to Open 1 outlet as that would yield an expected value of $53,000 in all states of nature

B) A perfect forecast would be yield perfect information, so we calculate Expected Profit with perfect information (EPPI)

= 0.4(380,000) + 0.3(80,000) + 0.3(0)

= 152,000 + 24,000 + 0

= $176,000

This is the amount(profit) that would be gotten if the investor (Nick) had perfect knowledge of each state of nature.

The amount that should therefore be paid for this, also known as Expected Value of Perfect Information (EVPI) =   EPPI - EMV

                                                          = 176,000 - 53,000

                                                          = $123,000                            

Explanation:

A) Expected monetary value = probability * outcome

B) The expected profit with perfect information formula assumes that the investor knows what the outcome would be in each state of nature and is then in a position to decide what alternative to pursue. For example in a Good market, the highest outcome is $380,000. Therefore he opens 1 restaurant while in a fair market, the highest outcome is $80,000. So, he opens 2 restaurants and $0 is the highest outcome in a poor market, so he does nothing.

This together gives the investor the opportunity to earn a maximum in all state of nature.

The expected value of perfect information on the other hand is how much the investor would be willing to pay to get the information that would yield maximum profit. Without perfect information, he can make $53,000 based on the probability while $176,000 would be made with perfect information. So the maximum that should be paid for this perfect information is the difference between the profit with perfect information and the profit without perfect information.

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