Present Value of Annuity

How much is your annuity worth today? Present Value of Annuities?

You just bought an annuity or you’ve had one for a while that either has yet to start providing income or is in the middle of its income stream. If somebody, say, an attorney or financial advisor, asked you what your annuity is worth, how would you respond?

The answer is otherwise known as an annuity’s present value.

When you buy an annuity, you are giving an insurance company money to hold for a set period in exchange for periodic payments. The present value of the annuity is more than the amount of money — or premium — you pay. Its present value is the current value of a set of cash flows in the future, given a specified rate of return or discount rate.

One of the main reasons to calculate an annuity’s present value is to help determine your overall net worth. Annuity present value is also used to determine the tax treatment of a charitable gift annuity. And it’s used when you sell your future annuity payments on the secondary market to determine the current value of those payments.

An annuity’s present value is based on the concept of “time value of money.” That’s the idea that the longer you hold onto money, the more value it provides. In other words, it’s better to have $5,000 now — provided you save or invest it — than it is to have the same amount five years from now, because it can theoretically grow the longer you have it. Measuring the current value of a stream of future payments is also called discounting.

One of the first things is to know the difference between an ordinary annuity and an annuity due. The difference is subtle. An ordinary annuity makes payments at the end of a payment period, while an annuity due requires payment at the beginning of a payment period. Why is this distinction important? If your payment comes on the last day of the month instead of the first day, you will receive your first payment a month sooner with an annuity due. On the other hand, interest accrues for an extra month with an ordinary annuity.

To calculate the present value of an ordinary annuity, you will need to know:

  • The amount of each periodic payment (P)
  • The number of periods over which payments will be made (N)
  • An interest rate estimate or the actual annuity interest rate per period (R)

Then plug those numbers into the following formula:

Annuity Present Value = P x [(1 – (1 + R)N) /  R]

Instead of doing the math yourself, there are calculators online you can use.

So let’s say you have an annuity that will pay you $1,000 a year for 5 years at an annual interest rate of 6 percent. Your annuity’s present value is:

Annuity Present Value = 1,000 x [(1 – (1 + .06)-5 ) / .06]

A few things to note in case that looks confusing. First, percentages (such as interest rates) are expressed as decimals. So 6 percent becomes .06 (10 percent is .10; 100 percent is expressed as 1.00).

Second, algebraic equations dictate that totals inside parentheses are calculated together. So, the first step is to add 1 + .06, which equals 1.06

APV = 1,000 x [(1 – (1.06)-5 ) / .06]

Next, the 10 is an exponent, which means you multiply 1.06 by itself 5 times. Because it’s a negative exponent, you then take 1 and divide it by 1.065.

The final result is $4,212. This means that if you could get a return on your invested funds of 6 percent per year, receiving $4,212 today would have the same value to you as receiving $1,000 per year for five years.

If you want to determine the present value of an annuity due, just take the present value of the ordinary annuity and discount the formula one period forward. So it would look like this:

Annuity Present Value = P x [(1 – (1+R)N) /  R] x (1 + R)

Since the difference between the two is only one period of time, there won’t be much difference in the present values unless you’re using very large numbers. Therefore, unless you know for certain your payments will come at the beginning or end of the period, you can use either formula to obtain an accurate present annuity value.

To ensure accuracy, the formula’s variables should be consistent. That means if you’re using annual payment amounts, you should use annual interest rates. If you use monthly payment amounts and annual interest, you won’t obtain an accurate value. The easiest way to rectify a mismatch is to multiply your monthly payment by 12, your biennial payment by two or your quarterly payment by four, since most interest rates are expressed in annual terms. Otherwise, you can divide your annual rate by 12 to coincide with a monthly payment.

What if your annuity will pay out lifetime income? How do you put a present value when you don’t know how long it will pay out? There’s a formula call a Perpetuity Formula used to determine the present value of an income stream that doesn’t have a defined end. The simple formula is:

Present Value = Payment amount / Annual interest rate

So the present value of a lifetime of $5,000 annual payments assuming it would earn 5 percent a year would be:

$5,000 / .05 = $100,000