IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Projecting expected future cashflows and profit testing
A insurer's profit vector for a policy gives expected profits (per policy issued) of -100 at time 0, 30 at time 1, 50 at time 2 and 60 at time 3 (years). Using a risk discount rate of 10% per year effective, what is the net present value of the profit?
The NPV is 13.67. Discount each profit at 10% (27.27, 41.32 and 45.08 for years 1 to 3) and add the time-0 amount of -100. Simply summing the undiscounted profits gives 40, which ignores the time value of money.
- A40.00
- B13.67Correct
- C12.43
- D113.67
- 15.00
Explanation
NPV = -100 + 30/1.1 + 50/1.1^2 + 60/1.1^3 = -100 + 27.27 + 41.32 + 45.08 = 13.67. Adding the profits without discounting gives 40, and omitting the time-0 outgo gives 113.67; discounting the whole result by an extra year gives 12.43.
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