Converting Pension to a Lump Sum

Non-investing personal finance issues including insurance, credit, real estate, taxes, employment and legal issues such as trusts and wills.
Post Reply
Topic Author
Scorpion
Posts: 388
Joined: Mon Sep 14, 2009 6:56 am

Converting Pension to a Lump Sum

Post by Scorpion »

The following is a purely theoretical question to, in a sense, value someone's net worth. No actually conversion will be done.

If a ~60 year old has a pension that pays $3,500 a month, what is that worth in lump sum terms? Would you just divide by 4% or 3% as a SWR and that's the answer? For example, at 4% it would be worth $1,050,000. It's a teacher pension and I believe gets a COLA each year, maybe more than COLA. Thoughts?
Harold
Posts: 3154
Joined: Sat Mar 03, 2007 6:50 pm
Location: San Francisco

Post by Harold »

The actuarial way is to add up the present values of all the payments.

If you think about it, this makes sense. Your theoretical "lump sum" is like the price of a bond with coupon payments payable as long as you are alive. The price of a bond is the sum of the present value of the coupon payments (along with the present value of return of principal, which in your case is zero).

In your case, that requires several assumptions:
- a discount rate (which would probably be current bond rates)
- a COLA assumption (which you'd use to increase the $3,500 prior to discounting)
- a mortality assumption (that is, a probability of survival for each payment)

I'm sure you'll get lots of short cut answers, in part because the math of the correct way seems too hard, but you could easily set it up in a spreadsheet.
Stonebr
Posts: 1472
Joined: Wed Jan 21, 2009 10:19 am
Location: Maine

Post by Stonebr »

You can get a rough idea of the amount by inputting your $3,500 on immediateannuities.com. This will tell you how much you need to pony up to buy such a benefit on the open market. For a male age 60 with no dependents the purchase cost for a life annuity would be about $616,000. This would be roughly equal to the lump sum that a pension plan might offer, but plans sometimes use different mortality tables and a fixed interest assumption that might not be tied to current market conditions. The purchase cost of an annuity also includes expense charges and possible state premium taxes.
Topic Author
Scorpion
Posts: 388
Joined: Mon Sep 14, 2009 6:56 am

Post by Scorpion »

Wow - good thoughts. So what would current bond rates be for the discount rate? If I assume a 3% COLA, a 3% discount rate and living to 95 without discounting for mortality, that yields $1.427M in NPV. Obviously it would be less if I discount for mortality.
Topic Author
Scorpion
Posts: 388
Joined: Mon Sep 14, 2009 6:56 am

Post by Scorpion »

Stonebr wrote:You can get a rough idea of the amount by inputting your $3,500 on immediateannuities.com. This will tell you how much you need to pony up to buy such a benefit on the open market. For a male age 60 with no dependents the purchase cost for a life annuity would be about $616,000. This would be roughly equal to the lump sum that a pension plan might offer, but plans sometimes use different mortality tables and a fixed interest assumption that might not be tied to current market conditions. The purchase cost of an annuity also includes expense charges and possible state premium taxes.
Thanks - the only problem with that website is that it doesn't include a COLA. Over 30-some years, that would make a huge difference. Enough of a difference to explain the difference between $1.4M and $646K? I wouldn't think so, but I welcome your thoughts.
Harold
Posts: 3154
Joined: Sat Mar 03, 2007 6:50 pm
Location: San Francisco

Post by Harold »

Scorpion wrote:So what would current bond rates be for the discount rate?
Here's one place:
http://www.soa.org/files/xls/pen-discount-curve.xls
Topic Author
Scorpion
Posts: 388
Joined: Mon Sep 14, 2009 6:56 am

Post by Scorpion »

Thanks - I guess i would use the 30 year spot rate at 5.9%. That reduces the lump sum to about $900,000.
Penguin
Posts: 696
Joined: Sat Mar 03, 2007 12:52 pm

Post by Penguin »

Scorpion wrote:
Thanks - the only problem with that website is that it doesn't include a COLA. Over 30-some years, that would make a huge difference. Enough of a difference to explain the difference between $1.4M and $646K? I wouldn't think so, but I welcome your thoughts.
From Vanguard:




Primary Annuitant -- Birth date: 08/18/1950 Sex: M
Quote Expiration Date: 08/25/2010
Benefit Commencement Date: 09/24/2010
State of Residence: NY
Payments per Year: 12
Initial Payment Amount: $3,500.00
Total Premium Amount for Fixed Single Life Annuity with inflation adjustments: $955,809.12

Qualified Assets: No
Exclusion Amount: $3,290.00

You can get a quote at this site:
http://www.aigretirementgold.com/vlip/V ... uestaQuote
Jon
Harold
Posts: 3154
Joined: Sat Mar 03, 2007 6:50 pm
Location: San Francisco

Post by Harold »

Scorpion wrote:Thanks - I guess i would use the 30 year spot rate at 5.9%. That reduces the lump sum to about $900,000.
Strictly speaking, you'd want to use the rates corresponding with the timing of each payment (so pretty much all the spot rates). As you can see though, the rates move around a lot, so it's all an approximation (just like a bond price!).
User avatar
BruceM
Posts: 1851
Joined: Fri Aug 08, 2008 1:09 pm
Location: Manzanita, Oregon

Re: Converting Pension to a Lump Sum

Post by BruceM »

Scorpion wrote:The following is a purely theoretical question to, in a sense, value someone's net worth. No actually conversion will be done.

If a ~60 year old has a pension that pays $3,500 a month, what is that worth in lump sum terms? Would you just divide by 4% or 3% as a SWR and that's the answer? For example, at 4% it would be worth $1,050,000. It's a teacher pension and I believe gets a COLA each year, maybe more than COLA. Thoughts?
I think what you are asking is how to calculate the present value of a stream of payments, both fixed and inflation indexed, over one's life expectancy. Assuming there are no other provisions to the life annuity, such as a joint-survivor benefit, guaranteed period certain, death benefit or the like, and it is a single person, life annuity, then the present value would be determined, using a straight time-value-of-money (TVM) calculation, where:

PV = the dollar value today of the amount that would pay out the life annuity, at a given average annual rate of investment return (the discount rate)

I = discount rate = the average annual expected rate of invetment return over ones lifetime

FV = any residual value of the life payments. For most, this is usually 0

N = life expectancy in years

PMT = Monthly annuity payment that will continue over one's life expectancy

For the fixed life annuity assuming it were to begin today, the PV would be calculated as follows:

PMT = 3500
N = 20.7 (from IRS life expectancy table for a 60 year old male)
I = 6.28% (the composite average corporate bond rate published by the IRS)
FV = 0

PV = 509,327

If the annuity payments are indexed for inflation each year at, say, 3%, then the I above would be inflation adjusted as follows:

adj I = (1.0628/1.03) - 1 = 3.1845%

So the new PV for the annually inflation adjusted payment would = $649,672

As you can see, inflation adjusting a pension/annuity benefit is expensive.

Of course, the PV above will change if your assumptions change, particularly the discount rate and life expectancy.

BruceM
Topic Author
Scorpion
Posts: 388
Joined: Mon Sep 14, 2009 6:56 am

Post by Scorpion »

Thanks everyone. this was very helpful.
Harold
Posts: 3154
Joined: Sat Mar 03, 2007 6:50 pm
Location: San Francisco

Post by Harold »

Not that it matters much for this exercise, but using life expectancy as Bruce did above will overstate the value.

This is an illustration of Jensen's inequality. (The expected value of a function is less or equal to the function of an expected value.)
Post Reply