April 2014 Q2(iii)

[lyndon46]

Hi quick question on the calculation for the commutation bit.
Current Assumption is 75% take 25% lump sum, with commutation factors equal half cost of pension.
I would value the liability as:
75% x (25% x 0.5 x post-ret value + 75% x post-ret value) + 25% x 100% x post-ret value
= 0.90625 x post-ret value

New Assumption is 100% take 25% lump sum, which I would value as:
100% x (25% x 0.5 x post-ret value + 75% x post-ret value
= 0.875 x post-ret value
ie a reduction of approx 3.45%, or 21m, vs 3.125% or 19m per ASET answer (examiner's report also has the 3.125%)

Can someone please guide me on what I am doing wrong?
Ultimately I don't think the difference is material but for mathematical curiosity, I wanted to know what is wrong with the above.

 

[Gresham Arnold]

Hi lyndon46

I don't think you've done anything wrong here, arguably you've taken a more accurate approach than ASET

I think you've essentially said the non-pensioner liability, allowing for 75% of 25% lump sum, is £600m

So, the liability allowing for no commutation would be 600/0.90625 = £662m

If we allow for 25% commutation, the liability would become 0.875 x 662m = £579m

So the saving from changing the commutation assumptions is 600 - 579 = £21m

An alternative way of calculating this would be 3.125% x 662m = £21m, where 3.125% comes from 0.90625-0.875

ASET takes a more approximate approach than you by applying the 3.125% saving to the £600m ie it doesn't attempt to back out the (£662m) liability allowing for no commutation to use in the calculation.

Hope that helps

Gresham