IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Project appraisal
A project requires outlays of ₹10,000 at time 0 and ₹10,000 at time 1, and returns ₹23,100 at time 2. What is the IRR (effective annual)?
The IRR is 10.00% effective per annum. At 10% the present value of the two outlays is 10,000 + 9,090.91 = 19,090.91, which equals the present value of 23,100 received at time 2 (23,100/1.21). The net present value is therefore zero.
- A7.47%
- B8.50%
- C11.50%
- D10.00%Correct
- 15.50%
Explanation
At i = 10%: PV of outlays = 10,000 + 10,000/1.1 = 19,090.91. PV of receipt = 23,100/1.21 = 19,090.91, so NPV = 0. Treating both outlays as occurring at time 0 gives (23,100/20,000)^(1/2) − 1 = 7.47%, which is wrong because the second outlay is a year later. 15.5% is the total return over the whole period, not annual.
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