What it means
The defining feature of an annuity certain is the word "certain": the number of payments is locked in at the start. This makes it different from a life annuity, where payments continue only for as long as the recipient lives and then stop, however early or late that happens.
Because the payment count is fixed, an annuity certain behaves much more like a bond or a loan repayment schedule than like an insurance product. There is no mortality risk for the provider to price in, so the terms are usually easier to compare across providers and easier to value with ordinary discounting maths.
In business, annuities certain turn up constantly even when nobody uses the phrase. A five-year equipment lease with level monthly payments, a structured settlement paying $4,000 a month for exactly 15 years, and a fixed-term instalment sale are all annuities certain in substance.
Valuing one is a matter of discounting: you work out what a fixed run of future payments is worth today at a chosen interest rate. Finance teams use this to decide whether to accept a lump sum instead of a payment stream, or to record the present value of a lease liability on the balance sheet.
The main nuance is timing. An ordinary annuity certain pays at the end of each period, while an annuity due pays at the beginning, which makes the annuity due worth slightly more because every payment arrives one period sooner.
In practice
Real-world examples.
Example
A regional haulage firm sells a depot and agrees to receive $25,000 a quarter for eight years instead of a lump sum. The finance director values the arrangement as an annuity certain to check the deal is worth more than the $600,000 cash offer on the table.
Example
A software company signs a four-year office lease with level monthly payments of $18,000. Under lease accounting rules the company must discount that annuity certain to a present value and put the resulting liability on its balance sheet.
Example
A court approves a structured settlement paying an injured claimant $3,500 a month for exactly 20 years. Because it is an annuity certain rather than a life annuity, the remaining payments pass to the claimant's family if they die in year 12.
Formula
Calculation
Present value of an ordinary annuity certain:
PV = PMT x [1 - (1 + r)^-n] / r
where PMT is the payment per period, r is the discount rate per period and n is the number of periods.
Suppose a supplier offers to settle a contract by paying you $10,000 at the end of each year for 10 years, and your discount rate is 5% a year.
Step 1: compute the annuity factor. (1 + 0.05)^-10 = 0.613913. So 1 - 0.613913 = 0.386087, and 0.386087 / 0.05 = 7.721735.
Step 2: multiply by the payment. $10,000 x 7.721735 = $77,217.35.
So the 10-year stream is worth $77,217.35 today. If the supplier instead offered a single cheque of $70,000 now, you would be better off taking the payments, because the payment stream is worth $7,217.35 more in present value terms.Case study
Seen in the real world.
In this illustrative example, Harbourline Ceramics, a fictional mid-sized manufacturer, sold a redundant kiln line to a competitor. The buyer offered either $340,000 in cash immediately or $50,000 a year at each year end for nine years, a total of $450,000 on paper.
Harbourline's controller resisted the temptation to compare the headline totals. She treated the offer as an annuity certain, applied the company's 7% cost of capital and found the payment stream was worth roughly $325,700 today, slightly less than the cash on offer. The larger nominal figure was doing the persuading, not the economics.
The board took the cash. The exercise became a standing rule at the fictional company: any offer involving a fixed run of future payments gets discounted before it gets discussed.
Watch out
Common mistakes.
- Confusing an annuity certain with a life annuity, and assuming payments stop on death when in fact they continue to the estate.
- Comparing the total nominal payments against a lump sum without discounting, which almost always makes the payment stream look better than it is.
- Using an annual discount rate with monthly payments. If payments are monthly, the rate must be a monthly rate and n must be the number of months.
Questions
People also ask.
Is an annuity certain a type of insurance product?
Not necessarily. Insurers sell them, but the structure carries no mortality risk, so it is closer to a fixed-income instrument than to insurance.
What is the difference between an annuity certain and an annuity due?
An annuity due pays at the start of each period rather than the end, which makes it worth one extra period of interest and therefore slightly more.
Can the payments in an annuity certain change over time?
In the strict definition they are level, but growing or indexed variants exist and need a modified formula that allows for the growth rate.
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