Calculating present value of a COLA'd pension

[David1961]

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?

 

[MasterBlaster]

Here's everything you ever want to know about present value calculations in one convienient location

Present value - Wikipedia, the free encyclopedia

 

[Independent]

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+i-cola)
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.)

 

[scrinch]

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 10-12%. The time value of money is different for different people, I guess.

 

[clifp]

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.

 

[utrecht]

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.

 

[braumeister]

When I recently looked at a SPIA with a COLA tied to the CPI, the cost was about 175% of the cost of a non-COLA 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.

 

[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.

 

[RockyMtn]

Here's an interesting article on including NPV of SS as a portion of your asset allocation.

Social Security as part of your portfolio - Andrea Coombes' Ways and Means - MarketWatch

 

[Mulligan]

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!

 

[jclarksnakes]

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

Don't worry, I have been collecting mine for over 20 years and am still here.

 

[Big_Hitter]

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