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?

Let X = probability XYZ offers a competing product. Then:

EMV(assembly line) = $10,000X + $40,000(1 - X)
EMV(addition) = -$100,000X + $600,000(1 - X) or:

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

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

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

$670,000X = $560,000

X = $560,000/$670,000 = 0.836

If the probability that XYZ will offer a competing product is estimated to be 0.836, then ABC will be indifferent between the two alternatives. If the probability that XYZ will offer a competing product is estimated to be less than 0.836, then ABC should invest in the addition.