What is present value of annuity?

Most retirees rely on their savings and social security payments to meet their expenses in retirement, but the income is hardly enough for their needs. An annuity can provide an extra income stream that can last over your lifetime or a specified period. You can calculate the present value of annuity to know how it will impact your retirement.

The present value of annuity is the current value of all future payments, given a specified rate of return or discount rate. It allows individuals to compare the value of receiving a lump sum payment today to the value of receiving a series of payments in the future. By calculating the value of the annuity, individuals can decide which is more beneficial of the two options. The present value of annuity relies on the concept of the time value of money, where a sum of money today is more valuable than the same amount in the future.

How the present value of annuity works

An annuity provides a stream of income payments to individuals over a specified period or lifetime. The annuities can be immediate or deferred; an immediate annuity is paid immediately after you purchase the annuity, while a deferred annuity has a delay before it starts making payments. Usually, when you purchase an annuity, you will be required to pay a lump sum in the form of a premium in exchange for a series of payments.

Present value of annuity helps individuals decide between receiving a lump sum payment today and a stream of future payments. When you calculate the present value of an annuity, you can determine which option is better: to take a lump sum payment today or a series of payments over a specified future period.

The present value concept is based on the time value of money, where a dollar today is more valuable in terms of purchasing power than a dollar in the future. For example, $4,000 today has more purchasing power than $4,000 payable in four installments of $1,000 in the next four years.

How to calculate the present value of an annuity

The formula for calculating the present value of an annuity is as follows:

P = PMT x ((1 – (1 / (1 + r) ^ -n)) / r)

Where:

P is the present value of the annuity

PMT is the dollar amount of each annuity payment

R is the interest rate/discount rate

N is the number of periods in which you will receive payments

You can use this formula to calculate the present value of an annuity and determine whether it is better to take a lump sum today or a series of future payment.

Present value of annuity example

Assume that John has been contributing to his retirement plan each year for 30 years and wants to withdraw his retirement funds. The retirement plan is offering to pay John a one-time lump sum payment of $400,000, or $25,000 at the start of each year for the next 25 years. Assuming an average discount rate of 6%, you can calculate the present value of annuity as follows:

P = 25,000 x ((1 – (1 / (1 + 0.06) ^ -25)) / 0.06)

The present value of the annuity equals $338,758, which is less than the lump sum payment. Therefore, it would be better to take the lump sum payment today instead of waiting to receive the annuity payments in the future, which are worth, $61, 242 less than the lump sum payment.

How discount rate affects the present value of an annuity

The discount rate, sometimes known as the interest rate, is the assumed rate of return that is used to calculate the present value of future payments. If the discount rate is zero, it means that the future value and the present value of the annuity are the same, and the annuity owner is indifferent to the passage of time. However, there is always a discount rate since it is more valuable to have the cash immediately instead of on a delayed basis.

Generally, the discount rate used to determine the present value of money should reflect the return that an individual expects to earn by investing the funds in other investment products. For example, if you could earn a 6% return by investing in corporate bonds, you might use the same rate of return to calculate the present value of an annuity. The lowest discount rate you can use is the rate of return of US Treasury bills, which are considered to have the lowest risk.

If the projected cash flows from the annuity are unusually risky, you might apply a high discount rate in the calculation. The high discount rate will lower the present value of the annuity, which will make future annuity payments heavily discounted. In contrast, a lower discount rate will result in a higher present value of the annuity, and future annuity payments will be less discounted.

Ordinary annuity vs. annuity due

Annuity due refers to annuity payments that are paid at the beginning of each period. For example, rent is an annuity due since it is paid at the beginning of the month. On the other hand, an ordinary annuity is an annuity payment that is paid at the end of the month, quarter, or year. Examples of ordinary annuities may include retirement accounts and mortgage payments.