# How much is my annuity worth? Calculating present (commuted) value of an annuity or pension?

I have a lifetime annuity which adjusts with cost of living increases in my state. Is it possible to compute the present value of this annuity? If so, how might I go about that?

Perhaps I am referring to this incorrectly. This may more accurately be termed a "defined benefit pension plan"

Actuary tables estimate that I will live 44 more years.

• You will need to have not just a calculator or formula, but also the index that it is based on. – mhoran_psprep Feb 23 '12 at 11:10
• It is a state retirement plan and the only number I have is the monthly payout, which adjusts annually. The links I googled were only helpful if I know the amount invested, and since it is a group retirement plan, I'm not sure how to find the inputs I need. – Chris Ballance Feb 23 '12 at 14:50
• @ChrisBallance - please update the question with the details so it becomes more answerable? I would not actually call this an annuity; in Canada at least it would be called a "defined benefit pension plan" – sdg Feb 23 '12 at 15:36

To add to what sdg said, there are many variables that affect the present value of your lifetime annuity. That said, the best way to start to understand the calculation is to begin with the actuarial definition of a "Contingent Annuity", that is the annuity payment is contingent on you still being alive.

From Models for Quantifying Risk Second Edition, by Cunningham, Herzog, and London, the base definition of a contingent annuity is given as the following in Section 6.1.1:

Annuity Present Value = [Payment Amount] * {Infinite Sum(t=1 to Infinity) [v^t * tPx]

Where : v = 1/(1+[interest rate]) And : tPx = the probability of survival t more years, given the current age x

Later in the chapter the modification for an increasing annuity is described and shown using an additional function of t in the infinite sum that represents the growth function of the annuity payout.

The probability of survival from age x to x+t is usually derived from experience and shown in a life table, which are usually published publicly if I remember correctly. This will be based on many factors as was mentioned earlier such as smoker/non-smoker, gender, and any other practical, predictive factor allowed by law and the Actuarial Standards of Practice.

It would be good to do some further reading into actuarial calculations regarding lifetimes if you are interested to learn more. The book I mention earlier was my textbook in school, there are also many study manuals available for SOA exam MLC that might be useful. Good Luck!

The PV, or Present Value, of a defined benefit pension plan (or lifetime annuity) is impossible to accurately calculate.

As outlined from The Canadian Institute of Actuaries there are many far too many assumptions to be made to make an accurate calculation.

The core formula looks enticingly simple:

``````Lump sum present value of pension = [pension amount] x [present value (PV) factor]
``````

However the PV-factor is basically one big fudge. It is calculated statistically from your age, expected lifespan, and many other factors outlined on their web site.

Large companies that have these plans will do the calculation on your behalf, particularly if you are let go, or quit before you start to draw a pension (but have worked there long enough to be vested.) They tend to have whole pension departments whose job it is to work with those fudge factors, and the calculations are indeed somewhat opaque without obtaining actuarial support of your own.