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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Projecting expected future cashflows and profit testing

A 3-year policy has profit vector (-80, 50, 60) for policy years 1 to 3, with cashflows at the end of each year. The probabilities that the policy is in force at the start of years 1, 2 and 3 are 1, 0.98 and 0.95 respectively. Using a risk discount rate of 10% per annum effective, what is the expected net present value of profit per policy issued?

The NPV is 10.59. Multiply each profit vector element by the probability the policy is in force at the start of that year to get the signature (-80, 49, 57), then discount at 10%. Using the raw vector instead gives 13.67, which is wrong.

  1. A13.67
  2. B10.59Correct
  3. C26.00
  4. D8.35
  5. 12.80

Explanation

Profit signature = vector × in-force probability: -80, 49, 57. NPV = -80/1.1 + 49/1.21 + 57/1.331 = -72.73 + 40.50 + 42.83 = 10.59. Discounting the profit vector without the in-force probabilities gives 13.67, which ignores withdrawal and death before each year starts.

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