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In filling out a financial statement recently, I had to calculate the current value of a company paid annuity that pays me monthly for as long as I live. Is there a formula for doing so, or does one just take life expectancy less current age and multiply by the monthly annuity payment.?
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Greetings, Bestdayever, and welcome. You asked:

<<In filling out a financial statement recently, I had to calculate the current value of a company paid annuity that pays me monthly for as long as I live. Is there a formula for doing so, or does one just take life expectancy less current age and multiply by the monthly annuity payment.?>>

The normal way of doing so is to use a financial calculator, an assumed interest interest rate and life expectancy, and solve for the present value of an annuity due. If I understand the way you made the computation, then you ignored the time value of money and artificially inflated the present value of the lump sum that must be invested to produce the annuity income stream over your life.

As an example, say your annuity pays \$10K per year over your life expectancy of 20 years. Just multiplying those two values gives you \$200K, but that is not today's present value. Given any positive rate of return, it would take far less than \$200K invested to pay you that \$10K for each of 20 years. Even if your investment earned just 5%, it would only take \$130.9K invested at that 5% to give you the same \$200K in payments over the years.

Regards..Pixy
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Thanks Pixy...the problem here is the annuity was paid for many years ago when a pension plan was cashed in, and replaced with individual annuities for the participants. I have no way of knowing what kind of return the money earned or is earning over the years. I only know what it pays me per year, and what my life expectancy is (or is supposed to be anyway.)
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Subject: Current value of an annuity
Author: bestdayever Date: 9/26/00 2:48 PM Number: 5153
In filling out a financial statement recently, I had to calculate the current value of a company paid
annuity that pays me monthly for as long as I live. Is there a formula for doing so, or does one just
take life expectancy less current age and multiply by the monthly annuity payment.?

Hi Best,

Well, there are a few ways to do this and the one you suggest is dead wrong. \$10,000 a year for 20 years is simply not worth (10000 X 20 =) \$200,000. It is worth much less because the \$200,000 'up front' could have been earning a lot of interest even in a very 'safe' investment.

You could just set up a spreadsheet and plug in the numbers for a given interest rate and principal amount and then 'hunt' for a present worth that comes out the same on an alternate investment; or, go to a college-type web page that will be full of bugs but calculate it for you such as

http://www.eng.buffalo.edu/~paolo/factor.html

; or, buy a nice financial calculator and spend a bit of time (quite a bit of time, really) reading through the manual that comes with it;

Or, just use the 'real' formula with any calculator that can figure exponents (that's the little 'power' thingy on the keypad).

I do the last one pretty regularly when working with my annuity (pension) payout. Here is the formula:

P = A(((1+i)^n-1)/(i(1+i)^n))

where

P the present worth at the beginning of the period,

i is the interest rate expressed as a decimal (e.g .07, not 7.00%). Use the annual rate divided by 12 if you are doing on a monthly basis,

n is the number of periods (either number of months or years of your payout),

(1+i)^n just means raise 1+i to the power of n,

A is the amount of the equal payments at the end of the month or year--always figure your payments as coming in at the end of the period.

Hint: Try doing the calculation first for something you can almost figure in your head such as a 2-year payout of \$1000 a year at 10% interest (= \$1736), to see if you are doing it right. Then figure it for the real annual payout and then go back and refine it for a monthly calculation. The results are almost the same for the last two and will act as a check on the last.

You can sometimes 'cheat' by going to a book of financial tables which will give you something called the Present Worth Factor for a Uniform Series Payment which is simply the number in the ( ) part above. Just multiply it by your annual (or monthly) payment.

How long will you live? The IRS has this pinned down exactly in its publications for IRA payouts and they also have it for joint payouts (e.g. for the life of both you and your spouse). If you get it wrong by a few months or even years, it does not change the answer that much on long payouts.

What interest rate to use? A justifable number is the current federal interest rates on bonds or notes for your remaining life expectancy. The Present Worth is highly sensitive to the nuber you pick. The lower the rate you use, the higher the present worth, so use a higher rate, such as the average long-term corporate bond rate if you want a lower value. If you are making out a financial-eligibility statement for your kid's college assistance grant, go for 11%--the average stock market return over time and tell 'em the viability of you annuity payouts are just about as uncertain.

What if the annual payouts are not uniform? Some pensions and Social Security fall into this category. If so, you are in trouble. The formula is much more complex. An approximation, I am told, is to add the annual percentage growth to your present worth value. For example, if the Present Worth of an constant annuity or a pension is \$300,000 but the annuity increases by 3.5% each year for inflation, multiply 300,000 by 1.035 to get an adjusted Present Worth of \$310,500. I really don't know how accurate this approximation is.

Hope this helps,

-- John (who suffered through this present worth stuff for hours in his engineering economy classes)
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jpkilgan wrote,

What if the annual payouts are not uniform? Some pensions and Social Security fall into this category. If so, you are in trouble. The formula is much more complex. An approximation, I am told, is to add the annual percentage growth to your present worth value. For example, if the Present Worth of an constant annuity or a pension is \$300,000 but the annuity increases by 3.5% each year for inflation, multiply 300,000 by 1.035 to get an adjusted Present Worth of \$310,500. I really don't know how accurate this approximation is.

The link below from Nobel Laureate William F. Sharpe's web site has an annuity calculator that handles inflation-adjusted pay outs.

http://www.stanford.edu/~wfsharpe/ws/ws_ann.htm

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