September 2013 - Q1(iii)

[Páudi Hegarty]

Hi there,

This Q is also in the tutorial 2 slides and tutorial 2 Qs.

Mark scheme for roll forward:

Pensioners – £100m x 1.04 - (£5m x 1.04^0.5 x 1.029^0.5)= £98.8m

Why doesn't the £100m get pension increases, aka 100m x 1.029 x 1.04 - (£5m x 1.04^0.5 x 1.029^0.5)

Similarly, why does the roll forward for actives not apply one year of salary increases (£70m x 1.055 x 1.04) as opposed to just £70m x 1.055?

 

[Gresham Arnold]

Hi

In summary, when we roll forward accrued liabilities, the pension increases or salary increases are already in the liability figure, so we just need to multiply by (1+i). Consultancies that I worked for called this 'unwinding the discount rate'.

More formally, we can demonstrate this by valuing a deferred pension at the beginning of the year (BOY) and end of the year (EOY) and then comparing the values. Let:
- DP be the amount of the deferred pension (£ pa) at a particular point in time
- other nomenclature be as per the SP4 / SA4 courses

Value of DP@BOY = DP@BOY x [(1+r)/(1+i)]^(NRA-x) x annuity

Value of DP@EOY = DP@EOY x [(1+r)/(1+i)]^(NRA-(x+1)) x annuity
(since at the end of the year, the member will be a year older)

Assume that DP@EOY = DP@BOY x (1+r)
(in other words, actual DP revaluation that year was as assumed)

Therefore: Value of DP@EOY:
= DP@BOY x (1+r) x[(1+r)/(1+i)]^(NRA-x-1) x annuity
= DP@BOY x (1+r)^(NRA-x) / [(1+i)^(NRA-x-1)] x annuity

So, Value of DP@EOY / Value of DP@BOY = (1+i)

Therefore Value of DP@EOY = Value of DP@BOY x (1+i)

Hope that helps!
Gresham

 

[Páudi Hegarty]

Perfect, thanks Gresham!