IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Project appraisal
An investment of ₹1,000 at time 0 produces cashflows of ₹600 at the end of year 1 and ₹600 at the end of year 2. What is the IRR, to two decimal places?
The IRR is 13.07% per annum. Setting 1,000 = 600v + 600v² gives the quadratic 3v² + 3v − 5 = 0, so v = 0.88444 and i = 1/v − 1 = 13.07%. Discounting both receipts at that rate returns exactly 1,000.
- A10.00%
- B11.50%
- C13.07%Correct
- D14.50%
- 20.00%
Explanation
Solve 1,000 = 600v + 600v², i.e. 3v² + 3v − 5 = 0. v = (−3 + √69)/6 = 0.88444, so i = 1/0.88444 − 1 = 13.07%. Check: 600/1.1307 + 600/1.2784 = 530.66 + 469.34 = 1,000. The 10% option comes from averaging total profit (200) over two years on 1,000 and ignoring timing.
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