Re: how much reduction is typical for early retireees pension?
- From: "Tim" <me@xxxxxxx>
- Date: Wed, 27 Jun 2007 13:16:19 +0100
"Ronald Raygun" wrote"Ronald Raygun" wrote"Tim" 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. ...
Yep.
"Ronald Raygun" wrote
... But ..."Ronald Raygun" wrote
"Tim" wrote:
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.
For an active member, I mean current accrued
pension (the amount payable from future
normal retirement date just from past service,
and ignoring any future salary increases).
For a deferred member, I mean their
deferred pension revalued to date.
"Tim" wrote:"Ronald Raygun" wrote
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.
No, not all "years of service" are a red herring,
but only the *future* years service.
"Ronald Raygun" wrote
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".
I haven't checked all your formulae/working/figures,
but I can see your reasoning.
The problem is that the benefits for members of final
salary schemes are not related to any kind of
individual "pot" (or fund) of money for that member.
The benefits are defined first, and the employer(s)
just need(s) to pay whatever contributions are
required to pay for them, overall ("balance of cost").
So, you cannot say that "the employer has paid in 0.12155 of
salary for this member, so (s)he should get benefits to that value".
The benefits are what they are, and the
employer just pays the total amount necessary.
"Ronald Raygun" wrote
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?
Yes, it is! When the member becomes deferred, their entitlement is
suddenly reduced, from (accrued pension + future salary increases)
to (accrued pension + future RPI inflation).
The entitlement then *is* a "deferred pension payable from age 65".
If they want to take that pension early, then the
early pension is calculated to be equal in value
to the alternative entitlement payable from age 65.
If the early retirement pension was not calculated to
be equal in value to the one given up from age 65, then
every deferred member could easily increase the value
of their benefits just by taking their pension early!
"Ronald Raygun" wrote
As you can see, the "required p" values are much lower
for deferred members than for active members. ...
Yep, because of the design of the benefits.
You see, one of the reasons for a pension scheme is to retain
staff, and employers don't need to encourage deferred members
to stay employed with them -- because they've already left!
"Ronald Raygun" wrote
... 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, ...
Yes, that's the type of employee that the employer is trying to
retain. They have all the experience, and don't need training as much!
"Ronald Raygun" wrote
... to the detriment of the scheme) ...
Eh? How does it hurt the scheme?
"Ronald Raygun" wrote
If reduction is to be based on affordability, ...
No, reduction is based on "equivalence of value".
"Ronald Raygun" wrote
... 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)).
No, that much would only have been paid into the scheme fund if the
actuary had assumed that *everyone* would "continue to the bitter end"
when he recommended the contribution rate at each scheme valuation.
Actually, s/he's got a set of "withdrawal" rates for
the scheme, and can model 'so many' staying to
the end, 'so many' leaving 5 years early, etc etc.
"Ronald Raygun" wrote
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, ...
Eh? For someone who has left service,
deferment is the *default*, not a "choice"!
"Ronald Raygun" wrote
... an actuarial *increase* of 29% (that's 1-0.8615/0.12155).
You are suggesting that the deferred pension granted, on first
becoming deferred, should be equal in value to the "active
member" benefit from past service - rather than being calculated
on the usual "scale formula" (eg 'salary x years / 80').
But why would the employer (who is paying for the pension
scheme) want to be generous to someone who is *leaving* early?
"Ronald Raygun" wrote
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%).
As I suggested above, it would only be able to "afford"
that, if the contributions had totalled 0.12155 for
each & every member. In effect, that much is not paid
in because the recommended total contribution rate
is an "average" of the 0.12155, 0.08615 etc rates.
.
- References:
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