How long until an investment pays for itself
The payback period is the time it takes for the money an investment brings in, or saves, to cover its initial cost. It is the most intuitive way to compare projects such as new equipment, solar panels or a more efficient furnace. The calculator gives the simple payback, the discounted payback, which accounts for the time value of money, and the net present value over the asset’s useful life.
The formulas
With I the investment, C the cash flow in year 1, g its yearly growth and d the discount rate:
- Simple payback with constant cash flows = I ÷ C
- With growing cash flows, the cumulative total after t years is C × ((1 + g)^t − 1) ÷ g, and the payback is the t that makes it equal to I
- Discounted payback: the same, with each year’s cash flow divided by (1 + d)^year
- Net present value = sum of discounted cash flows over the useful life − I
The calculator treats cash flows as spread evenly through each year, so it gives fractional years.
Worked example
A company spends $20,000 on a machine that saves $5,000 a year for 10 years. Its cost of capital is 6%.
- Simple payback = 20,000 ÷ 5,000 = 4.0 years.
- Discounted at 6%, the savings are worth less each year, and the investment is recovered after about 4.7 years.
- Over 10 years the machine saves $50,000, a simple return of 150%.
- Net present value: 5,000 × 7.360 − 20,000 = $16,800. A positive NPV means the project earns more than 6%.
Payback by first-year cash flow
| Yearly cash flow | Simple payback | Discounted payback | NPV |
|---|---|---|---|
| $2,000 | 10.0 years | 15.7 years | −$5,280 |
| $3,000 | 6.7 years | 8.8 years | $2,080 |
| $4,000 | 5.0 years | 6.1 years | $9,440 |
| $5,000 | 4.0 years | 4.7 years | $16,800 |
| $7,500 | 2.7 years | 3.0 years | $35,201 |
The first row shows the trap: a 10-year simple payback looks fine for a 10-year asset, but in present value the investment is never recovered.
Using growth for energy projects
Savings from insulation, a heat pump or solar panels usually rise with energy prices. Enter a yearly growth rate of 2 to 3% to reflect that; it shortens the payback noticeably on long-lived projects.
Strengths and limits
Payback is simple and highlights liquidity risk: the shorter it is, the sooner your money is free again. But it ignores everything that happens after the break-even point, so two projects with the same payback can have very different total value. Always check the NPV, or compare projects with the net present value calculator and the ROI calculator.