IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Project appraisal
A project costs ₹10,00,000 now and returns ₹6,00,000 at the end of year 1 and ₹5,50,000 at the end of year 2. What is its internal rate of return, effective annual?
The IRR is 10.00%. Setting 1,000,000 = 600,000v + 550,000v^2 gives v = 1/1.1, so i = 10%. Checking, the present values are 545,455 and 454,545, which sum to 10,00,000. Ignoring the timing of receipts yields misleading figures such as 15%.
- A15.00%
- B7.50%
- C10.00%Correct
- D11.50%
- 5.00%
Explanation
Solve 550v^2 + 600v - 1000 = 0 (in thousands): v = (-600 + sqrt(2,560,000))/1100 = 1000/1100 = 0.90909, so i = 10%. Check: 600/1.1 + 550/1.21 = 545.45 + 454.55 = 1000. The 15% option divides the total profit of 1,50,000 by cost without allowing for timing; 7.50% averages that profit over two years.
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