Question

Your company has a customer who is shutting down a production line, and it is your responsibility to dispose of the extrusion machine. The company could keep it in inventory for a possible future product and estimates that the reservation value is $250,000. Your dealings on the secondhand market lead you to believe that if you commit to a price of $300,000, there is a 0.4 chance you will be able to sell the machine. If you commit to a price of $350,000, there is a 0.2 chance you will be able to sell the machine. If you commit to a price of $400,000, there is a 0.1 chance you will be able to sell the machine. Finally, there is a 0.3 chance the machine will not sell at all. These probabilities are summarized in the following table.

4. Individual Problems 17-4 Your company has a customer who is shutting down a production line, and it is your responsibility to dispose of the extrusion machine. The company could keep it in inventory for a possible future product and estimates that the reservation value is $250,000. Your dealings on the secondhand market lead you to believe that if you commit to a price of $300,000, there is a 0.4 chance you will be able to sell the machine. If you commit to a price of $350,000, there is a 0.2 chance you will be able to sell the machine. If you commit to a price of $400,000, there is a 0.1 chance you will be able to sell the machine. Finally, there is a 0.3 chance the machine will not sell at all. These probabilities are summarized in the following table For each posted price, enter the expected value of attempting to sell the machine at that price. (Hint: Be sure to take into account the value of the machine to your company in the event that you are not be able to sell the machine.) Posted Price Expected Value $400,000 $350,000 $300,000 Probability of Sale 0.1 0.2 Assume you must commit to one posted price In order to maximize the expected profit of the potential sale, which posted price would you commit to in order to maximize the expected value of the potential sale of the machine? $300,000 $350,000 $400,000 Correct

Answer 1

Calculate the expected value when the posted price is $400,000 as follows: Expected value = (400,000x0.1)+(250,000x0.9) = 40,000 + 225,000 = $265,000 Thus, the expected value when the posted price is $400,000 is $265,000 Calculate the expected value when the posted price is $350,000 as follows: Expected value = (350,000x0.2)+(250,000x0.8) = 70,000+ 200,000 = $270,000 Thus, the expected value when the posted price is $350,000 is $270,000 Calculate the expected value when the posted price is $300,000 as follows: Expected value = (300,000x0.4)+(250,000x0.6) = 120,000 +150,000 = $270,000 Thus, the expected value when the posted price is $300,000 is $270,000 Though expected value of posted price $450,000 and $350,000 is equal i.e. $270,000 but $350,000 posted price is committed as the probability of scale is higher for it. Thus, in order to maximize the expected profit of the potential sale, posted price of $300,000 would be committed.

Thus, the correct answer is option A