cost of monthly power bills (do people include that in their payback calculations?)
Absolutely.
There are a number of variables in play when doing the calculations but frankly it's no more complicated than doing a basic cash flow analysis between two scenarios - with and without solar PV.
There are some less tangible factors as well. For instance, along with solar PV for us came far better metering data. Armed with much better data on consumption I have been able to zero in on what other actions I can take which make financial and environmental sense.
This includes assessment of energy efficiency options, shifting of loads to different times of day, optimising our choice of retail electricity plan.
Payback period however can be a little misleading when assessing the value of a system. It's but one measure but it can also lead to perverse outcomes if that's your only measure of system value.
For example, sensible action which results in reducing energy consumption lengthens the payback of our solar PV. But such actions also result in reducing our bills further and the combined effect is far more worthwhile than concern for pushing out solar PV payback.
Conversely I can artificially reduce my solar PV payback period - all I have to do is consume more energy, e.g. I could put the aircon system on when it is not needed. But that's not a rational (nor environmentally sensible) choice. Or I could choose a more expensive retail plan. My payback period on solar PV would reduce but my bills would be higher, again hardly a rational choice.
Based on our consumption and retail plan when we started with solar PV, payback period would be 4 years. But since we have done many other things to reduce our consumption and bills, payback period has pushed out closer to 5 years.