PV Gap

Willie Said:

What is the payback time when (Physics question here)?

We Answered:

Contrary to your added remark, there is no single exactly correct answer, because the annual energy you get from a solar panel is subject to random variations in weather, panel aging, maintenance, etc. So one must start with assumptions and end up with estimates.
Suppose a 1-kw solar panel costing £6400 generates 1/3*24*365 = 2920 kwh/yr (1/3 is optimistic; it's the average fraction of each day that rated power is generated.) This corresponds to a payback rate of 0.08*2920 = £233.6/yr.
Payback time = 6400/233.6 = 27.4 yr (ignoring the lost interest from the capital expenditure).
If you try a slightly less optimistic day fraction, say 1/4, you can bring the payback period to 36.5 yr. Etc.
Note that payback times are independent of the household's actual energy consumption, assuming that the power company pays the same rate for excess energy returned to the grid that it charges for consumed energy.
Ultimately the homeowner's decision is a process of weighing these costs against his/her own feelings of societal benefit from power generated in a non-fossil, non-nuclear mode. The possibility of future changes (e.g., lower solar panel cost, higher energy prices) can also influence the decision.