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

A profit signature is -100 at time 0, 55 at time 1 and 60.5 at time 2 (rupees), so its internal rate of return is exactly 10% per annum. A sensitivity test raises the initial expense by Rs 10 so that the time 0 profit becomes -110, with no other change to the signature. What is the new internal rate of return, to two decimal places?

The new IRR is 3.26%. Setting 110 = 55v + 60.5v^2 gives 11v^2 + 10v - 20 = 0, so v = 0.96841 and i = 1/v - 1 = 3.26%. Scaling the old IRR by 100/110 to get 9.09% ignores the timing of the later cashflows.

  1. A3.26%Correct
  2. B4.55%
  3. C6.00%
  4. D9.09%
  5. 0.00%

Explanation

Solve 110 = 55v + 60.5v^2, i.e. 11v^2 + 10v - 20 = 0. Then v = (-10 + sqrt(980))/22 = 0.96841, so i = 1/v - 1 = 3.26%. The 9.09% figure comes from scaling 10% by 100/110, which is not valid for a multi-period cashflow.

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