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

A product requires an initial reserving strain at time 0, followed by positive profits in later years. The insurer increases the risk discount rate used in profit testing, and all other assumptions stay unchanged. Which statement is correct?

The NPV falls. The initial strain occurs at time 0 and is not discounted, while the later positive profits are worth less at a higher risk discount rate. The profit signature itself is unchanged, and the discounted payback period gets longer.

  1. AThe NPV rises, because the initial strain is weighted more heavily at higher rates
  2. BThe NPV is unchanged, because the profit signature does not depend on the discount rate
  3. CThe NPV falls, because the later positive profits are discounted more heavily while the time 0 strain is not discountedCorrect
  4. DThe NPV falls, because the profit vector at time 0 becomes more negative
  5. The discounted payback period becomes shorter

Explanation

The time 0 strain is not discounted, so it is unaffected by the rate. The later positive profits have smaller present values at a higher rate, so the NPV falls. The payback period is lengthened, not shortened. The profit vector itself does not depend on the discount rate.

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