Question

The ABC Co. is considering a new consumer product. They believe that the XYZ Co. may come out with a competing product. If ABC adds an assembly line for the product and XYZ does not follow with a competitive product, their expected profit is $40,000; if they add an assembly line and XYZ does follow, they still expect a $10,000 profit. If ABC adds a new plant addition and XYZ does not produce a competitive product, they expect a profit of $600,000; if XYZ does compete for this market, ABC expects a loss of $100,000. For what value of probability that XYZ will offer a competing product will ABC be indifferent between the alternatives

Answer 1

Answer:

Let X be probability XYZ offers a competing product

EMV (assembly line) = $10,000∗X+$40,000∗(1-X)

EMV (addition) = -$100,000∗X+$600,000∗(1-X)

$10,000∗X+$40,000∗(1-X) = -$100,000*X+$600,000∗(1-X)

$10,000∗X-$40,000∗X+$40,000 = -$100,000∗X-$600,000∗X$600,000

-$30,000∗X+$700,000∗X = $600,000-$40,000

$670,000∗X = $560,000

X = $560,000/$670,000

X = 0.836

ABC will be indifferent between the two alternatives if the probability that XYZ will offer a competing product is estimated to be 0.836.

ABC should invest in the addition if the probability that XYZ will offer a competing product is estimated to be less than 0.836.