Photovoltaic system - rough cost estimate

With a non-financed investment, however, you still have to offset the interest you would otherwise receive on the invested money.
And with a financed investment, you have to add the interest for the financing.

Yep. That's why it's also 10 years. With financing, it usually takes longer because loan costs generally exceed the costs of an investment (excluding stock speculations, etc.).

I wouldn’t get my hopes up too high for a heat pump + electric car with 4 kWp.

Here’s an example. We have 12 kWp without storage, the system is new and I have been tracking the performance since February 8th.

For February, there is 400 kWh production, of which 170 kWh was self-consumed, 230 kWh fed in. Of the 400 kWh, 150 were produced on three sunny days. February was extremely gloomy here with very little sun, but even so, that is only a drop in the bucket for the heat pump (electricity consumption in the same period 600 kWh). Overall, we currently have 28% self-consumption. Since March, there has been significantly more sun here, which pushes self-consumption down; on good days we have 70 kWh production and 6 kWh total consumption.

From an economic perspective, the motto must be: €/kWp down (usually achieved by fully occupying the roof) and then calculate with the feed-in tariff.

Our system cost us 1350€/kWp.

We did a rough calculation and found that with realistic self-consumption rates (achievable without absurd effort to increase the SCR, i.e., 20-30%) at current electricity prices, full feed-in is generally more advantageous (for 10 kWp, 8.11 vs 12.87 cents / kWp). This changes if one assumes a moderate increase in electricity prices (e.g., like the last 20 years, about 4% per year) or manages to raise the self-consumption rate somehow. However, there is also an argument against increasing electricity prices: the energy transition. If it succeeds, electricity will potentially not get more expensive. Because generation would become cheaper, only grid fees would rise. CO2 as well, but the CO2 costs cannot be passed on to renewable energies. So wait until 2025. If CDU wins next year and it looks like a grand coalition, better to rely on self-consumption. If the Greens somehow manage again, then rather full feed-in – provided it is absolutely necessary to make a business case out of it. If you have many differently oriented roof surfaces, you could also register multiple systems. For example, an east-west system as a self-consumption system and the rest (especially south) as full feed-in.