A U.S.-based manufacturer of personal computers is planning to build a new manuf
ID: 2756638 • Letter: A
Question
A U.S.-based manufacturer of personal computers is planning to build a new manufacturing and distribution facility in one of the countries: China, the Philippines, or Mexico. The eventual benefit of the facility will differ between countries and will even vary within countries depending on the economic and political climate. The company has estimated the expected total profit (in millions of dollars) for the facility in each country under three different future economic/political climates, as follows:
Country Improvement Same Decline
China 21.4 17.5 16.2
Philippines 23.8 16.5 17.8
Mexico 24.2 21.0 14.0
assume that the probability of improvement in economic/political climate is 0.4, the probability of same economic/political climate is 0.2, and the probability of decline in economic/political climate is 0.4.
(a) Calculate the expected value of each decision alternative. What is your recommendation using the expected value criterion?
(b) Calculate the expected opportunity loss value of each decision alternative. What is your recommendation using the expected opportunity loss criterion?
(c) Calculate and interpret the value of perfect information.
Explanation / Answer
a)China: expected value = Total profit if Improvement*probability of improvement in economic/political climate+Total profit if Same*probability of Same economic/political climate+Total profit if Decline*probability of Decline in economic/political climate=21.4*.4+17.5*.2+16.2*.4=18.54 millions of dollars
Philippines : expected value = 23.8*.4+16.5*.2+17.8*.4=19.94 millions of dollars
Mexico: expected value = 24.2*.4+21.0*.2+14.0*.4=19.48 millions of dollars
recommendation using the expected value criterion would be to choose to invest in Philippines with the highest expected value of 19.94 millions of dollars.
b)opportunity loss value if invested in China=-Sum of expected values of profits in Philippines and Mexico
=-(19.94 +19.48 )=-39.42
opportunity loss value if invested in Philippines =-Sum of expected values of profits in China and Mexico
=-(18.54 +19.48 )=-38.02
opportunity loss value if invested in Mexico=-Sum of expected values of profits in Philippines and China
=-(19.94 +18.54 )=-38.48
recommendation using the expected opportunity loss criterion would be to choose to invest in Philippines with the lowest opportunity loss value of 38.02 millions of dollars.
c)The value of perfect information
If we know where the market would move then expected value =.4*24.2+.2*21.0+.4*17.8=21 millions of dollars.
we invest in the country with max profit for each climate that is if we are ascertain that there should be improvement we invest in Mexico with max profit of 24.2, if we are ascertain that there should be same we invest in Mexico with max profit of 21, if we are ascertain that there should be decline we invest in Philippines with max profit of 17.8.
Thus value of perfect information=expected value when we are certain(perfect information)-max expected value when we are uncertain= 21 -19.94 =1.06 millions of dollars.
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