Many of you may want to know what your civil service or military pension is worth today. Some may even want to try and monetize other passive income streams. Determining the value of a pension or other income stream is either a two step or one step process. It's one step if you're in (or near) day one of retirement or just established a passive income stream. It's a two step problem if you still have a number of years to work.
Well, I want to know what my military pension would be worth today if I enjoyed a successful career and retired as a Captain / Colonel after 30 yrs of military service. This situation would give me $7763 / month which would be 75% of my base pay (ref: 2012 pay table, O-6 over 26yrs).
Here’s two methods to determine the value of my pension (Method #1 using a basic calculator, Method #2 using a finance calculator).
Assuming a personal discount rate / IRR of 0.3% per month (equal to 3.66% APY) and a life expectancy of 30 years (360 months) past my retirement date.
1. Using a simple calculator with an exponential “^” function (minimum requirement)
(a) First find the present value of an "immediate annuity." Using the formula
PV immediate 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 immediate annuity = [ 1 – (1 + 0.003)^-360] (7763/0.003)
PV immediate annuity = [ 1 – 0.3401] (2,587,667)
PV immediate annuity = $1,707,601
This is the present value of the stream of pension payments the day I retire. This equation alone may suffice if you're at retirement or very close to retirement age.
However, I have 14 more years to work till retirement. To get the Present Value today, you have to discount the value determined above ($1,707,601) over the time I have left till retirement (14 yrs or N = 168 periods).
Present Value With Zero Payments Formula:
PV = FV (1+R)^-N
PV = $1,707,601 * (1+.003)^-168
PV = $1,707,601 * 0.6046
PV = $1,032,356
$1,032,356 is what my retirement is worth to me today assuming a discount rate of 0.3% per month or 3.66% APY.
2. Using a financial calculator like a Texas Instruments BAII, you get a two step problem.
a) Assuming a 3.66% discount rate (~ 0.3%/month)
b) Assuming 30yr life expectancy once I hit retirement
N = 360 months
I/Y = 0.3%/month
PV = $0
PMT = $7763/month
FV = ?
Plugging into a financial calculator, you get a future value of $5,019,873. Now working backwards in step 2:
N= 528 (360 months for length of retirement + 168 months left till I retire)
I/Y = 0.3%/month
PV = ?
PMT = $0/month
FV = $5,019,873
Solving for PV you get $1,032,286
The difference between the financial calculator method and the basic calculator method is simply due to round-off error. The biggest determinant in figuring the present value of any stream of income is what interest rate you use for your "discount rate." Your present value (PV) will be smaller if you use a discount rate higher than 3.66% APY or 0.3% per month. I figured that 0.3% per month is reasonable and close to what one can get on medium to long term bonds.
Keywords / phrases: how much is an annuity worth