What it means
What makes an annuity special is its predictability. The amount stays the same and the timing is regular, which allows its value to be calculated with a neat formula.
A business uses that formula to compare a stream of future payments with a single sum today. The reason it matters is the time value of money, the idea that a dollar received today is worth more than a dollar received later.
A promise of $10,000 a year for three years is worth less than $30,000 in cash now, because the later payments could not be invested in the meantime. Discounting each payment at a chosen interest rate converts them into today's value, called the present value.
There are two main types. An ordinary annuity pays at the end of each period, which is how most loans work, while an annuity due pays at the start of each period, as with rent.
The difference changes the value because the annuity due payments arrive one period sooner. Annuities also appear in the wider world of insurance, where the word often means a contract that pays a retiree a regular income in return for a lump sum.
In that setting the insurer calculates payments using life expectancy and interest rates. The underlying idea is the same, but the contract carries its own terms and fees.
Finance teams use annuity calculations to value leases, price loans, assess pension obligations and compare financing offers. The calculation assumes the rate stays fixed, so it is less reliable when rates are variable.
A useful rule of thumb is that the higher the discount rate, the lower the present value of an annuity, and the longer the payments run, the more sensitive the value is to the rate. A small change in the rate can therefore move the valuation of a long-dated stream of payments by a surprising amount.
Analysts often test several rates to see how much the answer depends on the assumption.
In practice
Real-world examples
Example 1
A landscaping company signs a four-year equipment lease with a payment of $2,000 at the end of each quarter. The finance team treats the 16 payments as an annuity and discounts them to work out the lease liability for the balance sheet.
Example 2
A retiring teacher uses part of her savings to buy an insurance annuity that pays $1,500 a month for life. She values the certainty of the income, although she gives up access to the lump sum.
Example 3
A property investor is offered $12,000 a year in rent for five years. She discounts the payments at 8% to see whether the purchase price is justified, rather than comparing the price with the simple total of $60,000. She also tests rates of 6% and 10% to see how sensitive the answer is.
Think of it
An annuity is a stream of equal payments over time-like monthly loan payments or pension checks.
Formula
Calculation
Present value of an ordinary annuity = Payment x (1 - (1 + r)^-n) / r
where r is the interest rate per period and n is the number of payments.
Suppose a company will receive $10,000 at the end of each of the next 3 years, and the discount rate is 10%. Year 1: 10,000 / 1.10 = $9,090.91. Year 2: 10,000 / 1.21 = $8,264.46. Year 3: 10,000 / 1.331 = $7,513.15. Present value = 9,090.91 + 8,264.46 + 7,513.15 = $24,868.52. Using the formula, (1 - 1/1.331) / 0.10 = 2.48685, and 10,000 x 2.48685 = $24,868.52, which matches.Case study
Seen in the real world
Redhill Packaging is an illustrative, fictional manufacturer that was offered two ways to pay for a $90,000 labelling machine. The supplier proposed either a lump sum today or payments of $20,000 at the end of each year for five years.
The finance manager treated the instalments as an ordinary annuity and discounted them at the company's borrowing rate of 8%. The present value came to roughly $79,900, which was lower than the $90,000 cash price.
Choosing the instalments therefore saved money in present-value terms and preserved cash for the busy season. This illustrative example shows why comparing the total of payments with a lump sum, without discounting, can lead to the wrong decision. She also tested a 10% rate, which gave a present value of about $75,800, and the instalments still came out cheaper than the cash price.
Watch out
Common mistakes
- Adding up the payments and calling that the value, when future payments must be discounted to reflect the time value of money.
- Mixing up an ordinary annuity with an annuity due, which changes the present value because payments arrive a period earlier.
- Using an annual rate with monthly payments without converting it to a monthly rate, which gives a materially wrong answer.
Questions
People also ask
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period, while an annuity due pays at the start, making it slightly more valuable.
Is an annuity the same as a perpetuity?
No, an annuity ends after a set number of payments, whereas a perpetuity is assumed to continue forever.
Can the payments in an annuity change?
In the strict sense they are equal, though real contracts may include increases, in which case a growing annuity formula is used.
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