
Calculating present value of a COLA'd pension
08182013, 05:16 PM

#1

Thinks s/he gets paid by the post
Join Date: Jul 2007
Posts: 1,081

Calculating present value of a COLA'd pension
I know I had a class in college where I studied present value, future value, interest rate, etc for various scenarios. But my memory is fuzzy. I'm interested in computing the present value of a COLA'd pension. Here's the terminology and what I am looking for a formula for.
PV = present value of the pension
n = number of years of collecting pension (I know is not known because this is the number of years you have left to live)
i = inflation rate, also the rate that the pension goes up each year.
A = the pension amount paid during the first year.
I know that the inflation rate would not be constant. And it seems like I may also need another rate (maybe for the return of the portfolio). Not sure.
Am I missing any other variables?
Basically, I'm looking for PV given an assumed n, i, and A. Can anyone point me in the right direction?
__________________




Join the #1 Early Retirement and Financial Independence Forum Today  It's Totally Free!
Are you planning to be financially independent as early as possible so you can live life on your own terms? Discuss successful investing strategies, asset allocation models, tax strategies and other related topics in our online forum community. Our members range from young folks just starting their journey to financial independence, military retirees and even multimillionaires. No matter where you fit in you'll find that EarlyRetirement.org is a great community to join. Best of all it's totally FREE!
You are currently viewing our boards as a guest so you have limited access to our community. Please take the time to register and you will gain a lot of great new features including; the ability to participate in discussions, network with our members, see fewer ads, upload photographs, create a retirement blog, send private messages and so much, much more!

08182013, 08:30 PM

#2

Thinks s/he gets paid by the post
Join Date: Jun 2005
Posts: 4,359

Here's everything you ever want to know about present value calculations in one convienient location
Present value  Wikipedia, the free encyclopedia
__________________



08182013, 08:56 PM

#3

Thinks s/he gets paid by the post
Join Date: Oct 2006
Posts: 4,297

Yes, you need another rate. Any PV calculation requires a discount rate.
The formula for a life annuity with an annual payment of A, with the first payment made today, is:
A +
A x p1 x (1+cola)/(1+i) +
A x p2 x ((1+cola)^2)/((1+i)^2) +
A x p3 x ((1+cola)^3)/((1+i)^3) +
...
where
px = probability of being alive i years after the start date
cola = annual growth rate of the payment, e.g. assumed inflation rate
i = interest discount rate.
Given the crude nature of the assumptions, lots of people assume px = 1.00 for x<life expectancy, and px = 0 for x>life expectancy.
The calculation is simpler if you replace the term (1+cola)/(1+i) with 1/(1+icola)
for example, if you assume cola is 3% and the discount rate is 5%, just use a discount rate of 2%. It's not exact, but, again, the assumptions are crude anyway.
(In your college class, you learned a neat closed form solution for this geometric series. But it's obsolete in the days of free spreadsheet software.)



08182013, 11:15 PM

#4

Thinks s/he gets paid by the post
Join Date: Apr 2006
Location: North Bay
Posts: 1,049

So this is looking at the PV relative to an inflation discount rate...really a summation of the real value of each payment (times the likelihood of collecting it).
It's subtly different than looking at the NPV of an investment. In both cases the discount rate is defined as the annual cost of delaying payment. In the case of the pension the cost of a year's delay in each subsequent payment is its lost purchasing power, or inflation. In the case of an investment valuation the discount rate is the opportunity cost of making the investment, or the expected rate of return in another investment of similar type and risk profile. So for the pension the discount rate might be 3%, for a regulated utility company it is more like 7%, for an oil company it is more like 1012%. The time value of money is different for different people, I guess.



08192013, 07:55 AM

#5

Give me a museum and I'll fill it. (Picasso) Give me a forum ...
Join Date: Oct 2006
Posts: 7,539

I think it is also worth going to a couple of the annuity quote places on the web and getting finding how much you would need to invest to get $X/month at 65 or whatever.
Now it is more difficult to find COLA annuities (the TSP annuity calculator was taken off line .) and most insurance companies have a cap on the COLA adjustment. However, for ballpark figures I think it is reasonably accurate.



08192013, 08:27 AM

#6

Thinks s/he gets paid by the post
Join Date: Nov 2006
Posts: 2,286

I looked around for a quote and couldn't find what I was looking for which is a annuity with a 50% survivor benefit. The ones I found had a survivor benefit of X amount of years instead of X% for life.



08192013, 08:30 AM

#7

Moderator
Join Date: Feb 2010
Location: Northern Kentucky
Posts: 12,158

When I recently looked at a SPIA with a COLA tied to the CPI, the cost was about 175% of the cost of a nonCOLA SPIA for the same monthly payment, for my age and state (I was looking at 100% survivor benefit, and DW is two years younger).
My situation is only one data point, and most people will have a somewhat different outcome, but it may provide a reference.



08192013, 08:38 AM

#8

Thinks s/he gets paid by the post
Join Date: Mar 2005
Posts: 2,452

Once read John Bogle says use 15 times annual payout (simple enough).
Believe the theory is we'll collect  on average  for 15 years.
__________________
FIRE'd since 2005



08192013, 12:03 PM

#10

Give me a museum and I'll fill it. (Picasso) Give me a forum ...
Join Date: May 2009
Posts: 8,100

Quote:
Originally Posted by tryan
Once read John Bogle says use 15 times annual payout (simple enough).
Believe the theory is we'll collect  on average  for 15 years.

Well since I started collecting mine at 45, I sure hope John is wrong concerning me. I don't want to go at 60!



08192013, 12:09 PM

#11

Full time employment: Posting here.
Join Date: Jun 2006
Posts: 926

Don't worry, I have been collecting mine for over 20 years and am still here.
__________________
CW4, USA(ret)
RN, BSN(ret)



08192013, 02:48 PM

#12

Thinks s/he gets paid by the post
Join Date: May 2013
Location: In the fairway
Posts: 4,681

for the 50% J&S factor you need to add in 50% of the probability your spouse is alive minus 50% of the probability you are both alive to the formula in post 3 and you also need to adjust that formula for the frequency of payment
__________________
__________________
Swing hard, look up




Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)


Thread Tools 
Search this Thread 


Display Modes 
Linear Mode

Posting Rules

You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts
HTML code is Off




» Recent Threads













» Quick Links


