How to use the equivalent annual cost calculator
- Enter the discount rate, the yearly return you could earn elsewhere or the cost of borrowing. The 8% shown is an example to replace.
- For option A enter the price, the life in years, the running cost per year and the resale value at the end of the life.
- To compare, fill in option B the same way. Leave the price of B empty to see option A alone.
- Read the equivalent annual cost of each option and which one is cheaper per year. Use Copy, Print or CSV to keep it.
Formula
Cost in today's money = price + running cost x annuity factor - resale value x (1 + r)^-n
Annuity factor = (1 - (1 + r)^-n) / r
Equivalent annual cost = cost in today's money / annuity factor
r is the discount rate as a decimal and n is the life in years. Running costs are assumed to be paid at the end of each year. With a rate of 0 the cost is simply the total cost divided by the years.
Ten thousand dollars over five years
An asset costs $10,000 and lasts 5 years, with no running cost or resale value. At 8% the annuity factor is (1 - 1.08^-5) / 0.08 = 3.99271, so the equivalent annual cost is 10,000 / 3.99271 = $2,504.56 a year.
Compare it with a cheaper asset at $6,500 that lasts 3 years, costs $400 a year to run and resells for $500. Its cost in today's money is $7,133.92 and its equivalent annual cost is $2,768.20. Even though it costs less to buy, option A is cheaper by $263.64 each year because it lasts longer.
Why comparing lifespans needs this
Two purchases with different lives cannot be compared by total cost. A $6,500 machine that lasts 3 years is not twice as good as a $10,000 machine that lasts 5. The equivalent annual cost spreads each cost over the years the asset lasts, with the time value of money built in, so the figures are comparable per year of use.
The method assumes you would replace each asset with the same one when it wears out. That is a fair comparison when the need is long lasting, such as a vehicle, an appliance or a piece of equipment.
Choosing a discount rate
The discount rate stands for what money costs you. If you would otherwise earn a return, or if you borrow, use that rate. A higher rate makes a large upfront price weigh more than later running costs. Trying two or three rates shows how sensitive the choice is.
For the pieces behind this tool, see the present value calculator and the annuity calculator. To spread an asset's cost over its life with depreciation, use the depreciation calculator, and to compare leasing and buying, the lease vs buy equipment calculator.
Assumptions and limits
- Running costs are paid at the end of each year and stay the same every year.
- Resale value is received at the end of the life. Taxes, inflation and financing fees are not modeled.
- Each option can be replaced by an identical one when it wears out.
- The comparison is of cost only. It does not value quality, reliability or the benefits of each option.
Frequently asked questions
What is equivalent annual cost?
It is the equal yearly amount that has the same value, in today's money, as all the costs of owning an asset for its whole life. It lets you compare assets with different lifespans.
Does a lower equivalent annual cost always mean the better choice?
It means cheaper per year of use. If an option gives you less, such as lower quality or fewer features, a slightly higher cost may still be the better choice.
What discount rate should I use?
Use the return you could earn on the money elsewhere, or the interest you would pay to borrow it. Try a range to see whether the answer changes.
Can I include resale value?
Yes. Enter the amount you expect to get at the end of the life. It cannot exceed the price, and it reduces the cost after being discounted back to today.