IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Projecting expected future cashflows and profit testing
A product has an expected profit signature of -200 at time 0, 110 at time 1 and 121 at time 2. What is the internal rate of return of this profit signature?
The internal rate of return is 10.00%. At 10% the discounted inflows are 110/1.1 = 100 and 121/1.21 = 100, totalling 200, which equals the initial strain of 200, so the NPV is zero at that rate.
- A15.50%
- B7.75%
- C12.50%
- D21.00%
- 10.00%Correct
Explanation
The IRR is the rate i at which the NPV is zero. At i = 10%, 110/1.1 + 121/1.21 = 100 + 100 = 200, which exactly offsets the initial outlay. Dividing the undiscounted profit of 31 by 200 gives 15.50%, but this ignores the time value of money.
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