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ACCA Strategic Professional · Strategic Business Leader · Financial analysis and decision-making techniques

Brandt Ltd is considering a project with two possible outcomes: a profit of $400,000 with probability 0.6, or a loss of $100,000 with probability 0.4. Brandt has a similar-sized project available with a certain profit of $180,000. A director argues that the project should be accepted because its expected value is higher. What is the most appropriate evaluation?

The expected value of the risky project is $200,000, which is 0.6 x 400,000 less 0.4 x 100,000. That beats the certain $180,000, but expected value is a long-run average. For a one-off decision, a risk-averse board may reasonably prefer the certain profit.

  1. AExpected value is $200,000, so the risky project is higher; but it is a long-run average that may not suit a one-off decision by a risk-averse boardCorrect
  2. BExpected value is $280,000, so the risky project is clearly better and risk preferences are irrelevant
  3. CExpected value is $200,000, so the certain project is better because it has a lower standard deviation, regardless of returns
  4. DExpected value is $240,000, so the risky project should be accepted as it is a repeated decision

Explanation

EV = 0.6 x 400,000 + 0.4 x (-100,000) = 240,000 - 40,000 = 200,000. This exceeds 180,000, but EV is a long-run average and ignores the dispersion of outcomes and the decision maker's attitude to risk, which matters for a one-off project. Option B miscalculates by ignoring the loss, and the other options misstate the calculation or the logic.

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