In the third example of misuses (erroneously using a "best guess") verify that the expected value of

introducing the new product is $38,750.

Misuse 3: Erroneously using a "Best Guess": Let's consider the following problem. You are

considering introducing a new product that will sell for $10 per unit. Fixed costs per year are

$150,000. In volumes up to 75,000 units per year, the variable cost per unit is $8 but, because of

scale economies, each unit above 75,000 will cost only $5. It is easy to see that breakeven demand

is 75,000 units per year.

Demand is uncertain. You are sure it won't be less than 25,000 per year, or more than 150,000. This

range of demand overlaps the breakeven, and therefore we cannot decide without further analysis

whether to introduce the product or not. Suppose we assess the following probability distribution

for demand shown in Table:

Demand/Probability

25,000 .30

50,000 .25

80,000 .25

150,000 .20

Total 1.00

The most likely demand is 25,000, way below the breakeven,suggesting we should not introduce the

product. The probability that demand is less than the breakeven is 0.55, again suggesting that we

should not introduce the product. It is easy to see that the expected value of demand is 70,000,

which is below the breakeven; once again this suggests that the product should not be introduced.

If you draw the decision tree and compute the expected contributions of the two alternatives,

however, you will discover that the expected value of introducing the new product is $38,750, which

is greater than the $0 value of not introducing it.

The moral is that when your uncertainty overlaps the breakeven value, and there is no way to reduce

the uncertainty before a decision has to be made, there is in general no way to shortcut a fullblown

decision analysis.

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