What it means
Net present value tells you how much value a project adds in today's money, and normally the highest figure wins. The comparison breaks down when the projects last different lengths of time, because a longer project has more years in which to accumulate value.
The equivalent annual annuity fixes this by asking a different question: if this project's total value were spread evenly across each year of its life, how much would each year be worth? Converting both projects into an annual figure puts them on the same footing regardless of duration.
The arithmetic uses an annuity factor, which is the present value of receiving $1 each year for a given number of years at a given discount rate. Dividing the net present value by that factor gives the level annual amount that has the same present value as the project itself.
The approach assumes the projects can be repeated indefinitely on the same terms, which is its main weakness. If a piece of machinery will not be available again, or if the market for the product will have moved on, the assumption of endless replacement does not hold and plain net present value may be the better guide.
It is most useful in operational decisions where replacement really does recur, such as fleet vehicles, production equipment, leases and IT infrastructure. It is less useful for one-off strategic bets like entering a new country or acquiring a competitor.
In practice
Real-world examples.
Example
A haulage firm compares a truck that lasts six years with a cheaper model that lasts four, and uses equivalent annual annuities to see which delivers more value per year of service rather than per purchase.
Example
A hotel group weighs a three-year refurbishment cycle for guest rooms against a seven-year cycle, converting both into annual figures before presenting the choice to the board.
Example
A software company evaluates a two-year licence against a five-year platform build, and finds that the shorter option wins on an annual basis even though the longer one has a much bigger total net present value.
Formula
Calculation
Equivalent annual annuity = Net present value / Annuity factor
Annuity factor = (1 - (1 + r) to the power of -n) / r, where r is the discount rate and n is the number of years.
A company must choose between two mutually exclusive projects, both discounted at 10%.
Project A: net present value of $150,000 over three years.
Annuity factor for 3 years at 10% = 2.4869.
Equivalent annual annuity = $150,000 / 2.4869 = $60,317.
Project B: net present value of $200,000 over five years.
Annuity factor for 5 years at 10% = 3.7908.
Equivalent annual annuity = $200,000 / 3.7908 = $52,759.
Project B has the larger headline net present value, but Project A creates $60,317 of value for every year it runs against Project B's $52,759, so Project A is the better choice if it can be repeated once it ends.Case study
Seen in the real world.
The following is an illustrative and fictional case. Larkfield Coffee Roasters, an invented specialty roasting business, had to choose between two ways of expanding capacity, using a 9% discount rate for both.
Option one, a four-year equipment lease, produced a net present value of $120,000, giving an equivalent annual annuity of $120,000 / 3.2397, which is $37,040. Option two, an eight-year outright purchase, produced a net present value of $200,000, giving $200,000 / 5.5348, which is $36,135 per year.
On raw net present value the purchase looked far better, and the operations director had assumed it would win comfortably. On an annual basis the lease was slightly ahead, and the board chose it partly for that reason and partly because it kept the company free to change technology after four years.
Watch out
Common mistakes.
- Applying the method to projects of equal length, where it adds nothing because plain net present value already gives the right ranking.
- Assuming a project can be repeated forever when the underlying opportunity is genuinely one-off.
- Using a different discount rate for each project without a real difference in risk, which distorts the comparison.
Questions
People also ask.
Is this the same as equivalent annual cost?
They use identical arithmetic, but equivalent annual annuity is applied to net value created while equivalent annual cost is applied to total costs when the benefits are the same.
What discount rate should be used?
Normally the company's weighted average cost of capital, adjusted upwards if the specific project carries more risk than the business as a whole.
Does a higher equivalent annual annuity always mean the better project?
It means better value per year under the repeatability assumption, so it should be weighed alongside strategic fit, flexibility and the capital available.
From the founder's library
Take it further with the book.
Build your financial confidence beyond this definition. Shihan's full-length guide, Accounting Fundamentals, takes the same plain-English approach and turns it into a complete, practical playbook for non-finance managers, business owners and students - with chapter-end quiz answers and presentation slides included.
25% off with code MMHQ25, applied at checkout. Priced in USD - checkout may show the equivalent in your local currency.
View the book and save 25%