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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.
A. For the third outlet opening C, the expected value to be opted for Nick has been the high yield similar to outlet A, i.e. $ 53,000 in all states of nature.
B. The Expected Value of Perfect Information has been $123, 000. Thus, option E is correct.
A. The expected monetary value, has been the statistical analysis that has been helpful in assessing the future for the business and the market.
The expected monetary value, EMV can be expressed as:
[tex]\rm Expected\; monetary\; value=\sum\;\%\; chance \;\times\;payoff[/tex]
The expected monetary value for outlet A, [tex]E_A[/tex] has been:
[tex]E_B= (0.4\;\times\;200,000)\; +\; (0.3\;\times\;80,000) \;+ \; (0.3\;\times\;-200,000)\\E_B= 152,000 \;+ \;21,000\; -\; 120,000\\E_B= \$44,000[/tex]
The expected monetary value for outlet A has been $ 53, 000.
The expected monetary value for outlet B, [tex]E_B[/tex] has been:
[tex]E_B= (0.4\;\times\;200,000)\; +\; (0.3\;\times\;80,000) \;+ \; (0.3\;\times\;-200,000)\\E_B= 152,000 \;+ \;21,000\; -\; 120,000\\E_B= \$44,000[/tex]
The expected monetary value for outlet B has been $ 44, 000.
The expected monetary value for outlet C, [tex]E_C[/tex] has been:
[tex]E_C= (0.4\;\times\;0)\; +\; (0.3\;\times\;0) \;+ \; (0.3\;\times\;0)\\E_C= 0 \;+ \;0\; -\; 0\\E_C= \$0[/tex]
The expected monetary value for outlet C has been $ 0.
For the third outlet opening C, the expected value to be opted for Nick has been the high yield similar to outlet A, i.e. $ 53,000 in all states of nature.
B. The expected value for perfect information has been the amount that has been paid to yield the information helpful in making the decision based on the market analysis.
The expected perfect information, EPI has been given by:
[tex]EPI=Good\;\;market\;\times\;value\;+\;Fair\;market\;\times\;value\;+\;Poor\;market\;\times\;value[/tex]
Substituting the values for outlet A, B and C:
[tex]EPI=(0.4\;\times\;380,000)\; +\; (0.3\;\times\;80,000) \;+ \; (0.3\;\times\;0)\\EPI=152,000 \;+ \;24,000\; +\; 0\\EPI=\$\;176,000[/tex]
The expected perfect information cost has been $ 176,000.
The amount paid for the as Expected Value of Perfect Information (EVPI) has been given by subtracting the expected information from the expected monetary value.
The EVPI has been given as:
[tex]EVPI=EPPI\;-\;EMV\\EVPI= 176,000 \;- \;53,000\\EVPI=\$\;123, 000[/tex]
The Expected Value of Perfect Information has been $123, 000. Thus, option E is correct.
For more information about expected value of perfect information, refer to the link:
https://brainly.com/question/11964455
