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ACCA Applied Skills · Financial Management · Adjusting for risk and uncertainty in investment appraisal

A project's NPV depends on two independent variables. Sales volume is high (probability 0.6) or low (0.4). Selling price is high (probability 0.5) or low (0.5). The NPVs are: high volume/high price $100,000; high volume/low price $20,000; low volume/high price $10,000; low volume/low price -$60,000. What is the expected NPV?

The expected NPV is $26,000. Because volume and price are independent, the joint probabilities are 0.3, 0.3, 0.2 and 0.2. Multiplying each NPV by its joint probability gives 30,000, 6,000, 2,000 and -12,000, which total $26,000.

  1. A$26,000Correct
  2. B$17,500
  3. C$38,000
  4. D$36,000

Explanation

Joint probabilities are 0.30, 0.30, 0.20 and 0.20. EV = 30,000 + 6,000 + 2,000 - 12,000 = $26,000. $17,500 is the simple average of the four NPVs. $38,000 leaves out the loss-making outcome. $36,000 uses only the two extreme combinations with the volume probabilities (0.6 × 100,000 + 0.4 × -60,000).

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