IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Project appraisal
For a project the net present value is +₹4,000 at 10% per annum and -₹1,000 at 15% per annum. Using linear interpolation between these two rates, what is the estimated IRR?
The interpolated IRR is 14.00%. NPV falls from +4,000 to -1,000 across 5 percentage points, so it hits zero 4/5 of the way along: 10% + 5% × 4,000/5,000 = 14%. Using the midpoint or reversing the weights gives wrong values.
- A12.50%
- B11.00%
- C13.00%
- D14.00%Correct
- 16.00%
Explanation
Interpolating: IRR = 10 + 5 × 4,000/(4,000 + 1,000) = 10 + 4 = 14.00%. The 12.50% option takes the midpoint, ignoring that NPV is much closer to zero at 15%. The 11.00% option reverses the weights (10 + 5 × 1/5).
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