April 2019 Qu 3i)

[Ben Hughes]

Hi all,

When going through past papers, specifically qu 3 i) of the April 2019 paper, I am unsure of why they have used the formula given in the mark scheme. The question is to recalculate commutation factors due to a change in the net discount rate, wherein the mark scheme they have given the answer (for the age 60 member) below. My question is on where the ratio part of the answer comes from i.e. 1.021/1.023. In my attempt I used the standard formula for an annuity to calculate the ratio but this obviously slightly different, is the one used in the question just a simplification of this formula? Any help would be much appreciated!

16.45 * (1.021/1.023) ^ 18 = 15.88

 

[Gresham Arnold]

Hi Ben

I agree that a commutation factor is essentially the present value of £1 pa of pension given up, ie an annuity. The annuity is going to be based on a particular mortality table and net interest rate.

As we don't know anything about the mortality table used, we can't really calculate the annuity / commutation factor from scratch. Instead, we need to use the existing commutation factor and adjust for the change in net rate, which we are told is changing from 2.1% to 2.3%.

In order to do an approximate adjustment we need to estimate the duration of the payments under the annuity (broadly speaking, the average time to payment). The examiners have assumed this was 18 years from age 60, but would have accepted any reasonable figure.

As the net rate is increasing, we would expect the value of the annuity to decrease, so we multiply the annuity by (1.021 / 1.023). As the average time to payment is 18 years, the formula is (1.021/1.023)^18

I hope that helps
Gresham

 

[Ben Hughes]

Hi Gresham,

Thanks for your quick reply! That makes a lot of sense, much appreciated.

Thanks,
Ben