Payback period

The payback period answers a simple question: how many years until I get back the money I put in? It is used when deciding on solar panels, insulating a house, a machine for a business or a flat to let. It is the most intuitive measure of an investment's return, but far from the most complete.

Simple payback period

You add up the cash flows year by year until they equal the initial outlay. When the yearly flows are equal, a single division does it:

$$T = \frac{I_0}{CF}$$

• $T$: the payback period in years
• $I_0$: the initial investment in euros
• $CF$: the cash flow for one year in euros, such as a saving or a profit

With unequal flows you look for the year in which the running total turns from negative to positive, and the fraction of that year comes from how much was still missing.

Discounted payback period

The simple version assumes a euro in ten years is worth the same as a euro today. It is not: money tied up in the investment could be earning elsewhere. The discounted payback period therefore first converts each flow to today's value (discounts it) and only then adds them up:

$$\sum_{t=1}^{T_{disk}} \frac{CF_t}{(1 + r)^t} = I_0$$

• $CF_t$: the cash flow in year $t$
• $r$: the discount rate, i.e. the return you could get elsewhere, as a decimal
• $T_{disk}$: the discounted payback period in years

The discounted period is always longer than the simple one, because later flows have a smaller present value.

A worked example: solar panels on a family house

The installation costs €8,000 and saves €900 a year on electricity for 15 years. The alternative return is 4% a year.

Simple payback: after 8 years €800 is still missing, and year nine brings €900. Payback is therefore 8 + 800 / 900 = 8.89 years.

Discounted payback: in today's money €115.57 is still missing after 11 years, and year twelve brings 900 / 1.04¹² = €562.14. Payback is 11 + 115.57 / 562.14 = 11.21 years.

Over the full 15 years the panels save €13,500, i.e. €5,500 more than they cost. Converted to today's value, the net present value is €2,006.55.

You can check every figure in the investment appraisal calculator: enter an investment of €8,000, 15 years of €900 and a 4% discount rate.

What the payback period does not tell you

It ignores everything after payback. Two investments with the same five-year payback can differ in that one keeps paying for another 20 years and the other stops. The payback period rates them the same.

It says nothing about return. A shorter payback does not mean a higher return. To compare returns, use the net present value (NPV) and the internal rate of return (IRR), which the same calculator works out.

It depends on estimates. A saving of €900 a year assumes a stable electricity price and panel output. If the saving is 20% lower, €720 a year, the simple payback period lengthens by a quarter, to 11.11 years.

Where you will use it

The payback period is a good first filter: it shows quickly whether an investment pays back before the end of its useful life. For bigger decisions, add NPV and IRR in the investment appraisal calculator. The principle of converting future money to today's you can try in the discounting calculator.