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Mr. Annan is contemplating setting up a shopping mall in Accra or Sunyani but not both. Patronage could be high or low. He estimate there is a 50% chance patronage could be high in Accra with an associated profit of Ghc 140,000 per year, and 55% chance patronage could be high in Sunyani with a profit of 110,000 per year. If in Accra and patronage is low, he can either put in an aggressive advertisement at an estimated cost of Ghc 70,000 per year or close down the business at a loss of Ghc -150,000. Similarly, if in Sunyani and patronage is low, he can put in an aggressive advertisement at an estimated cost of 15,000 per year or close down at a cost of Ghc 50,000.Advertisement in Accra has a 55% chance of generating high patronage at a profit of Ghc 140,000 per year or medium patronage at a profit of Ghc 65,000 per year. Advertisement in Sunyani has a 65% chance of generating high patronage at a profit of Ghc 110,000 per year or medium patronage at a profit of Ghc 60,000 per year. What is the expected monetary value at for choosing Accra as the location for the mall ? Your answer must be in 2 decimal place  Ghc

Question

Mr. Annan is contemplating setting up a shopping mall in Accra or Sunyani but not both. Patronage could be high or low. He estimate there is a 50% chance patronage could be high in Accra with an associated profit of Ghc 140,000 per year, and 55% chance patronage could be high in Sunyani with a profit of 110,000 per year. If in Accra and patronage is low, he can either put in an aggressive advertisement at an estimated cost of Ghc 70,000 per year or close down the business at a loss of Ghc -150,000. Similarly, if in Sunyani and patronage is low, he can put in an aggressive advertisement at an estimated cost of 15,000 per year or close down at a cost of Ghc 50,000.Advertisement in Accra has a 55% chance of generating high patronage at a profit of Ghc 140,000 per year or medium patronage at a profit of Ghc 65,000 per year. Advertisement in Sunyani has a 65% chance of generating high patronage at a profit of Ghc 110,000 per year or medium patronage at a profit of Ghc 60,000 per year. What is the expected monetary value at for choosing Accra as the location for the mall ? Your answer must be in 2 decimal place  Ghc

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Solution

To calculate the expected monetary value (EMV) for choosing Accra as the location for the mall, we need to consider all possible outcomes and their probabilities.

  1. High Patronage without Advertisement: The profit is Ghc 140,000 and the probability is 50%. So, the expected value is 0.50 * 140,000 = Ghc 70,000.

  2. Low Patronage with Advertisement: There are two possible outcomes - high patronage and medium patronage. The expected value for high patronage is 0.55 * 140,000 = Ghc 77,000 and for medium patronage is 0.45 * 65,000 = Ghc 29,250. The total expected value for low patronage with advertisement is 77,000 + 29,250 - 70,000 (cost of advertisement) = Ghc 36,250. The probability of low patronage is 50%, so the expected value is 0.50 * 36,250 = Ghc 18,125.

  3. Low Patronage without Advertisement: The loss is Ghc -150,000 and the probability is 50%. So, the expected value is 0.50 * -150,000 = Ghc -75,000.

Adding all these expected values together, the EMV for choosing Accra as the location for the mall is 70,000 + 18,125 - 75,000 = Ghc 13,125.

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