## Sunday, March 26, 2006

### What is Your Pension or Annuity Worth?

Many of you may want to either “juice-up” your net worth statements, or simply know what your pension is worth today, assuming your company remains solvent. Others may want to know what a fixed benefit annuity is worth.

John at ourmoneymatters blog posed the question: How do I determine the present value of my pension, if I retired today? He stated that he would collect \$525/month starting today and be able to collect this amount for life. I posted an initial solution on his site that was wrong (ran numbers around 1am PST, bit tired I guess). Here’s how to figure out the value of a pension (Method #1 using simple calculator, Method #2 using a finance calculator).

I assumed a personal discount rate (rate of expected return) of 0.5% per month and a life expectancy of 30 years (360 months) past-retirement date.

1. Using a simple calculator with an exponential “^” function (minimum requirement)

(a) Determine present value of an annuity. Using the formula

PV annuity = [ 1 – (1 + R)^-n] (P/R)

R = interest rate in decimal form
P= payment
N= number of periods

Filling in numbers you get:

PV annuity = [ 1 – (1 + 0.005)^-360] (525/0.005)
PV annuity = [ 1 – 0.166] (105,000)
PV annuity = \$87,570

Slight round of error, exact answer would be \$87,565.60

2. Using a financial calculator like TI BAII

This is a two step five value problem.

Step 1:
a) Assuming a 6% discount rate (6%/12 months = 0.5%/month)
b) Assuming 30yr life expectancy

N= 360 months
I/Y= 0.5%/month
PV= \$0
PMT= \$525/month
FV= ?

Plugging into financial calculator, you get a future value of \$527,370.40. Now working backwards in step 2:

N= 360 months
I/Y = 0.5%/month
PV= ?
PMT= \$0/month
FV= \$527,370.40

Solving for PV you get \$87,565.60.

Your present value (PV) will be smaller if you expect a rate of return higher than 6% on investments. These calculations are exactly the same for annuities too.

John OMM said...

Thank you for the help you've proved to date on figuring the value of my pension, but actually, as noted in my post, if I were to quit today I wouldn't be able to collect a pension until 2032. In 2032 my pension would be \$525 a month (in 2032 dollars, meaning not very much at all), and that from that point forward the amount received would begin to adjust for inflation.

So I'm trying to determine what would the FMV of such a pension be today.

John OMM said...

Thank you for the help you've proved to date on figuring the value of my pension, but actually, as noted in my post, if I were to quit today I wouldn't be able to collect a pension until 2032. In 2032 my pension would be \$525 a month (in 2032 dollars, meaning not very much at all), and that from that point forward the amount received would begin to adjust for inflation.

So I'm trying to determine what would the FMV of such a pension be today.

Finance Junkie said...

Ok, if your benefits are deferred for 16 years, then the Net Present Value is:

(1) Using last value of \$87,565.60
(2) Plug into equation:
NPV=FV(1+R)^-N
(3) FV (in 26yrs)=\$87,565.60
R=6%
N=26yrs

NPV=87,565.60(1.06)^-26
NPV=\$19,247.80