ACCA Applied Skills · Financial Management · Adjusting for risk and uncertainty in investment appraisal
A project has an NPV of $80,000 with probability 0.5 and an NPV of $20,000 with probability 0.5. What is the standard deviation of the NPV?
The standard deviation is $30,000. The expected NPV is $50,000, and both outcomes lie $30,000 from it. The variance is the probability-weighted sum of squared deviations, 900,000,000, and its square root is $30,000.
- A$30,000Correct
- B$900,000,000
- C$50,000
- D$15,000
Explanation
EV = $50,000. Each outcome deviates from the EV by $30,000, so the variance = 0.5 × 30,000² + 0.5 × 30,000² = 900,000,000. The standard deviation is the square root, $30,000. $900,000,000 is the variance, not the standard deviation. $50,000 is the EV. $15,000 is half the deviation, from weighting the deviations by probability without squaring.
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