If I had written, "a photovoltaic system pays off in 8-18 years," would that have been better? ;-)
So: of course, as with all purchases, you need to do a bit of research beforehand to avoid the usual pitfalls. I’ll address your terms directly:
Turnkey: That’s what I meant. If you build it yourself, the system pays off in 2/3 of the time.
Normally sized: Normally sized is a system when all roof surfaces (house, garage, carport) are fully utilized, unless it faces FULL north AND is steeper than 25°. Normally sized is not what the solar installer recommends. He’s lazy and prefers to spend less time on the roof, so he can serve more customers with storage batteries... And yes – if you can only fit 5 kWp on a mid-terrace house, then the payback shifts backward, up to "unprofitability." These roofs will just have to wait until the next roof renovation...
Feed-in tariff: Once you have received your offer, you can calculate whether it is good. Determine the yield (yourself), multiply it by the feed-in tariff, times 20. If the offer is below that, good. If not, bad. The rest depends on self-consumption.
If you do it this way, 11-12 years is a good average. After that, you make money for 8 years and then have 18 years of cheap self-generated electricity.
You can optimize further by removing solar thermal systems and chimneys. Heat pumps will have to be installed in a few years anyway; currently, they are heavily subsidized. Moreover, heat pumps increase self-consumption and push the payback period further forward.
Two more notes:
- A storage battery does not pay off. Therefore, exclude it from calculations (and preferably also from the order).
- "No roof" is an excuse, "no money" is not. The KFW offers loans at 1%. Most banks are even cheaper since the installments are legally guaranteed to be paid by the energy supplier. So it is a very low-risk loan that everyone should get after talking to their banker.