ITPEC FE Morning April 2022 Question 77

Topic: Corporate Activities

Products A, B, C, and D are to be introduced to the market. The table below shows the expected profit for each product with three (3) sales forecasts (High, Medium, and Low) that are estimated to occur in accordance with the probability in the table. Which of the following is the product that is expected to make the highest profit according to the expected value principle?

ProductHighMediumLow
Profit ($)Probability (%)Profit ($)Probability (%)Profit ($)Probability (%)
A100,0007520,00020-40,0005
B130,0006030,00030-20,00010
C150,0005040,00030-20,00020
D100,0007010,00020-50,00010

Explanation

B, with an expected profit of 85,000 dollars — weight each forecast's profit by its probability, add, and pick the largest sum.

ProductHighMediumLowExpected profit
A75,0004,000−2,00077,000
B78,0009,000−2,00085,000
C75,00012,000−4,00083,000
D70,0002,000−5,00067,000

For example, B: 130,000 × 0.6 + 30,000 × 0.3 + (−20,000) × 0.1 = 78,000 + 9,000 − 2,000 = 85,000.

Answer (b)

Why not others:

  • •(a) A — 77,000; it has the most likely High outcome (75%), but a high chance of one outcome is not the expectation
  • •(c) C — 83,000; it has the largest possible profit (150,000), which is what a maximax choice would pick, but its 20% chance of a loss pulls the expectation below B
  • •(d) D — 67,000, the lowest, dragged down by the largest loss

Key rule: Expected value = Σ(probability × outcome) over all scenarios, with losses entered as negatives; the best single outcome or the most probable scenario answers a different question.

Corporate Activities · AI-written, may contain errors

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