Re: how much reduction is typical for early retireees pension?
- From: Ronald Raygun <no.spam@xxxxxxxxxxxxxxxxxxxxx>
- Date: Mon, 25 Jun 2007 11:57:17 GMT
Tim wrote:
"Ronald Raygun" wrote
Could you run that by me again, slowly? ...
OK, let's try this - with some numbers(!) :-
To make things simple, let's use:
Inflation : 2%pa
Salary increases : 4.5%pa
Investment Return / discount rate : 7%pa
Value ("cost") of a pension payable immediately...
... to a 60-year-old : £1,800 per £100pa pension
... to a 55-year-old : £2,000 per £100pa pension
OK so far, and the last two lines are just saying that
the annuity factors which apply when a pension is brought
into payment at 60 and 55 are 18 and 20. But ...
Let's consider a member currently aged 55,
with a "current pension" of £1000pa.
... I can't quite relate to this as you haven't defined
what "current pension" means, as a result of which the
argument below doesn't make sense to me.
First look at an "active member" (still employed) ...
The pension is expected to rise at 4.5%pa to about:
(£1,000pa x 1.045^5) = £1,246pa in the next 5 years,
so its value then is:
(£1,246pa /£100pa x£1,800) = £22,431.
That value now is: (£22,431 / 1.07^5) = £15,993.
To give an equivalent value now, the reduced
early retirement pension would have to be:
(£15,993 /£2,000 x£100pa) = £800pa.
That's a reduction from the "current pension"
of £1000pa, of 20.0% (4.0% for each year early).
Now look at a "deferred member" (no longer employed)...
The pension is expected to rise at 2%pa to about:
(£1,000pa x 1.02^5) = £1,104pa in the next 5 years,
so its value then is:
(£1,104pa /£100pa x£1,800) = £19,873.
That value now is: (£19,873 / 1.07^5) = £14,169.
To give an equivalent value now, the reduced
early retirement pension would have to be:
(£14,169 /£2,000 x£100pa) = £708pa.
That's a reduction from the "current pension"
of £1000pa, of 29.2% (5.83% for each year early).
I am unconvinced by your assertion that the number of years
of service is a red herring, since it affects entitlement
and affordability differently.
Let's say:
s is the salary inflation factor, 1.045 from your figures above,
r is the RPI inflation factor, 1.02,
g is the investment growth factor, 1.07,
and let's suppose (however unrealistically) that they are
constant throughout a person's career, with s representing
salary increases for all reasons, i.e. not just ordinary
increments but promotions too. That being the case, a
person's salary in any year can be expressed in terms of his
starting salary k in year 1.
Then his salary in year n is ks^(n-1), and hence his pension
entitlement after y years' service and x years' deferment is
ky/80 s^(y-1) r^x
(if he retires directly from active status, just use x=0)
and the cost of providing it is equal to that amount multiplied
by the annuity factor appropriate to the age at which it is
brought into payment.
If throughout his career a fixed proportion p of his salary was
invested into the pension fund, the value of that fund will be:
after year 1: pk,
after year 2: pkg+pks,
after year 3: pk(g^2+gs+s^2), etc, and
after year n: pk Sum[i=0 to n-1](g^i s^(n-1-i)),
which is equal to pk s^(n-1) Sum((g/s)^i).
So x years after y years of service the fund will be worth
pk s^(y-1) (e^y-1)/(e-1) g^x, where e=g/s (the "excess" factor which
indicates by how much investment growth exceeds salary inflation).
For this amount to be able to fund the cost of the pension, we need
pk s^(y-1) (e^y-1)/(e-1) g^x >= A(a) ky/80 s^(y-1) r^x
where A(a) is the annuity factor appropriate to age a.
[You've suggested A(55)=20 and A(60)=18 and, though it's probably
not particularly linear in real life, I'll use A(65)=16 below]
Noting that ks^(y-1) appears both on the value and cost sides, and
rearranging to see what the contribution rate p ought to have been
for all these years to make the cost affordable, we get:
p >= A(a) y/80 (r/g)^x (e-1)/(e^y-1)
For the "normal" scenario (x=0, y=40, a=65, A=16), p must be at least
0.12155. With a 5-year early retirement (x=0, y=35, a=60, A=18) we get
0.14633, and for 10 years early (x=0, y=30, A=20) it's 0.17378.
These figures show that if a reduction is to be justified on the basis
of what the fund can afford (since p cannot actually be changed in
retrospect), then a reduction of 17% or 30% for retiring 5 or 10 years
early would be "fair".
Looking now at someone who defers at 55 for 10 years, to draw at 65,
we get (x=10, y=30, a=65, A=16) 0.08615 for p, and if this deferred
pension is to be brought into payment 5 years early, i.e. for the case
(x=5, y=30, a=60, A=18) we get 0.12312.
This does indeed rather suggest that a 30% reduction would be appropriate
for going 5 years early, *provided* you look at it only relative to the
"deferred until 65" position. But is it appropriate to look only there?
As you can see, the "required p" values are much lower for deferred
members than for active members. Indeed deferred members represent
superb value to the pension scheme, and this is in part because, so
long as e>1 (i.e. investment growth exceeds salary inflation), the
early career years make a greater contribution to the retirement fund
than the later years, and in part because the entitlement formula is
inherently unfair (in favour of the member who stays on until the bitter
end, to the detriment of the scheme) and makes the entitlement grow
rather faster than the fund towards the end.
If reduction is to be based on affordability, and if the affordability
benchmark is to be determined by the "normal" scenario, then p=0.12155
should be the benchmark (for our given g/s/r triple and A(65)).
It would then be fair for a 10-year deferred member (x=10, y=30, a=65,
A=16, p=0.08615) to get, as a kind of reward for choosing to defer,
an actuarial *increase* of 29% (that's 1-0.8615/0.12155). This would
subsequently be followed by a reduction by 30% if deferment to 65 is
shortened to deferment to 60.
What it boils down to is that a fund which can afford to pay someone
a 40/80 salary if he retires at 65, then it can afford to pay a 30/80
salary at 60 to a member who left at 55, and without reduction (or
with a tiny one -- 1.3%).
.
- Follow-Ups:
- References:
- how much reduction is typical for early retireees pension?
- From: Johndigits
- Re: how much reduction is typical for early retireees pension?
- From: Norman Wells
- Re: how much reduction is typical for early retireees pension?
- From: RobertL
- Re: how much reduction is typical for early retireees pension?
- From: Tim
- Re: how much reduction is typical for early retireees pension?
- From: Ronald Raygun
- Re: how much reduction is typical for early retireees pension?
- From: Tim
- how much reduction is typical for early retireees pension?
- Prev by Date: Re: C&P card 'nuked' in Greece
- Next by Date: Re: mysterious credit card transaction
- Previous by thread: Re: how much reduction is typical for early retireees pension?
- Next by thread: Re: how much reduction is typical for early retireees pension?
- Index(es):
Relevant Pages
|
