Comparing things that last different lengths of time
Should a contractor buy a cheaper excavator that lasts 8 years or a better one that lasts 12? Should a homeowner pick a furnace with a lower price or one with lower running costs and a longer life? Comparing total costs is misleading, because the longer-lived option will always look more expensive. Comparing purchase prices ignores running costs. The equivalent annual cost (EAC) solves both problems by turning every option into a constant cost per year.
The method
- Compute the present value of all costs: the purchase price, plus each year’s running cost discounted to today, minus the resale value discounted from the end of the asset’s life.
- Divide by the annuity factor for the asset’s lifespan: (1 − (1 + r)⁻ⁿ) ÷ r.
The result is the yearly payment that would cost you exactly the same, in today’s money, as owning the asset. Because it is a yearly figure, it can be compared directly between options with different lifespans, assuming each one would be replaced by a similar asset at the end of its life.
Worked example
Two machines, with a 6% discount rate:
| Option A | Option B | |
|---|---|---|
| Purchase price | $30,000 | $45,000 |
| Running cost per year | $2,000 | $1,200 |
| Lifespan | 8 years | 12 years |
| Resale value | $3,000 | $5,000 |
| Present value of all costs | $40,537 | $52,576 |
| Equivalent annual cost | $6,528 | $6,271 |
Option B costs $12,000 more in present value but serves 4 years longer, and it comes out $257 a year cheaper.
Choosing the discount rate
The discount rate is your cost of money. A household might use the interest rate on a loan or the return it gives up on savings. A business usually uses its weighted average cost of capital. Higher rates penalize options that cost more up front, so it is worth testing a few rates to see whether the conclusion changes.
What the method leaves out
- Inflation in running costs. Use a real discount rate, net of inflation, with today’s prices, or a nominal rate with inflated costs, but do not mix them.
- Taxes: depreciation deductions and investment credits can change the answer for businesses.
- Risk and flexibility: a shorter-lived asset lets you switch to newer technology sooner.
- Rising maintenance as equipment ages. If running costs increase over time, the true optimum may be to replace earlier.
This calculator gives estimates for education and planning. It is not investment, tax or legal advice; for decisions about your own situation, talk to a qualified financial professional.