The formula
saving for the year = used × price of electricity + exported × export rate
Where it comes from
The quick sum — cost divided by annual saving — is both too long and too short, because it ignores three things pulling in different directions. Panels lose around 0.5 % of their output every year, which stretches the payback. Electricity gets more expensive, which shortens it. And what you export is paid a good deal less than what it costs to buy, so two installations generating the same amount pay back over very different periods depending on how much is used as it is generated.
How to work it out by hand
- Split the output between what you use as it is generated and what you export
- Multiply each part by its own price: they are not the same
- Subtract maintenance and you have the saving for the year
- Repeat with output down 0.5 % and the price of electricity up
- The year the cumulative saving reaches the cost is the payback
What is worth knowing
The field that moves the answer most is not the cost or the sunshine: it is the share you use as it is generated. Taking that from 30 to 60 % is worth more than adding half the panels again, and you get there by moving loads into the middle of the day — washing machine, dishwasher, hot water cylinder, electric car — or with a battery, although a battery has to pay for itself separately. It is also worth looking at the twenty-five-year balance and not only at the payback period: two installations that pay back at the same time can leave very different money behind them.