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.

1 comment:

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:
(3) FV (in 26yrs)=$87,565.60