Next: We have Solar at Home Part 5.
Previously: We have Solar at Home Part 3.

How long will it take to pay off?

You may recall that we are assessing whether putting solar panels the roof of our house is worth it, with worth it narrowly defined as, will they pay for themselves in less than 10 years? We’ve collected the following information:

Question	Estimate from April 2022
How much electricity will we use between 2023 and 2032?	between 3217 and 5835 kW·h per year
How much will PG&E charge for that electricity?	$0.43 per kW·h, increasing 7.6 percent per year
How much will the system cost to install and operate?	$17,000 or $20,000
How much electricity will the system generate?	3915 kW·h or 6934 kW·h, decreasing 1% per year.

With this information, we can draw a chart with two lines, one for cumulative cost with solar, and one for cumulative cost without. Where the lines meet is when the system pays off. Since we have some uncertainty in some of our numbers¹, two our four questions have multiple answers. So I made three charts spanning the range of answers to “how much electricity will we use”, and each chart has two lines for the two sizes of system under consideration. We are thus looking at six scenarios, plus three null hypotheses. Let’s start with the scenarios most likely to disfavor solar.

Low Estimate

The No Solar scenario for the low usage estimate—a null hypothesis—comprises 3217 × $0.43 the first year, and then 7.6% more each year. Since the cost compounds, the line curves up.

In this scenario, we use the same amount of electricity as at the apartment, which seems very unlikely, but that’s why this is the most anti-solar scenario. We have more than enough solar with nine panels, so 12 is over-investment. We assume we don’t get any money back for over-generation. The solar lines start much higher, since we’ve just paid for solar. We don’t need any power from PG&E, but PG&E still charges a minimum monthly fee for connecting to the grid at all, so the lines slope (but don’t curve) up².

Pay-off is around 2035 or 2036.

Medium Estimate

A chart with 2023 to 2037 on the X axis and $0 to $60,000 on the Y. Title: Mid estimate (wild guess, 4300 kW·h/year). Legend shows a black box labeled No Solar, a blue box labeled 9 panels, and an orange box labeled 12 panels. The black line curves gently up from slightly above zero in 2023 to about $50,000 in 2037. The blue line is straight, starts below $20,000, and ends around $30,000. The orange line mirrors the blue line, several thousand dollars higher. The blue line intersects the black line just before 2035, and the orange line at 2036. — Forecast with medium usage

At the mid estimate, the 9-panel system doesn’t cover full usage, so the blue line includes the system, the minimum payments, and additional payments for more energy, so it slopes up faster than the 12-panel yellow line. They both pay off some time in 2032³, and the 9-panel system becomes a worse deal three years later.

High Estimate

In the high estimate, the No Solar case slopes up much faster, but the 9-panel and the 12-panel lines stay the same, since they cover all usage, so payoff is sooner. 2029 or 2030⁴.

Forecast conclusions

How long will it take to break even?

The solar system will pay off in 7 years in the best case, and 13 years in the worst case⁵.

The smaller system is better in some cases, worse in others. It’s a little better in the less probable cases, and much worse if usage is high. Solar panels are more likely than not to pay off in less than 10 years, and bigger is probably better.

Should we do it?

In Part 1 we defined a firm yes on purely financial terms to require a break-even of ten years or less. So, yes.

Appendix: The Story of the Dryer That Didn’t Get Used For Six Months, Part 1

This is all happening in April 2022, a few weeks after we closed on the house. It came with no laundry appliances. The laundry hookups in the wall only supported a gas dryer, not an electric one. We—meaning somebody with a license—would need to wire the space with 240V current. This was still in the thickest of the COVID-triggered supply chain problems⁶, so we figured that postponing the dryer purchase risked not getting a dryer for a long time, or not a matching one, so we bought both appliances. The existing electrical panel was on the other side of the wall, so we figured we’d just have the electrician add an outlet when they installed the solar stuff. So we had a working washing machine in our own owned home in April, a first for both my spouse and me as adults, and a useless dryer. But we had a backyard, and a greenhouse, and plenty of clothespins, and a laundromat at the end of our block, so we should be fine, right?

Thus began the story of The Dryer That Didn’t Get Used For Six Months.

Tune in next week when we’ll draw back the curtain on the last two years and see how the situation develops, including that next chapter in the story of … The Dryer That Didn’t Get Used for Six Months.

Next: We have Solar at Home Part 5.

All of the numbers are uncertain, since they are in the future, and we could express them all as ranges, but this is as far as we’ve gotten and this feels like an adequate amount of research to make an informed decision of this magnitude^א. ↩︎
This is about $11 per month; the number used in the estimate is $75, and I’m not sure what that’s based on. It makes solar look about $850 worse than we think I should have thought it. Remember that this also leaves out the tax rebate; together these make Solar look almost $7000 worse than I should have thought it would. If you correct for those, the breakeven points become about 2032 or 2033. That is to say, I should have thought that the worst-case scenario was around 10 years, not 13. ↩︎
As with the low estimate, had I correctly graphed the results of the original assumptions, this payoff would be a few years earlier. ↩︎
Wait, what? If we are using far more energy than the middle case, how can the panels cover everything? When I made this, I knew something was off, but I couldn’t put my finger on it, so I took the numbers at face value and we made our decision. Looking back two years later, let’s fix it. The 12-panel system will still cover everything, so it won’t change. In fact, it’s the same line on all three charts. But the 9-panel scenario is very different.

Corrected High Estimate forecast

Once we start paying PG&E for a big shortfall, the 9-panel system is more expensive than the 12-panel within 3 years. The 12-panel system pays for itself in 2030. The cheaper system takes longer to pay for itself, because it’s much smaller than what we need so it doesn’t cut our bills as much, but it’s still a better deal than nothing by 2033^ב. ↩︎
The worst case for buying solar, but the best case in the big picture of using less energy. I guess the worse it rains, the more valuable the umbrella. ↩︎
Triggered, not caused, because running Just In Time on a global scale with no margins for error was very good for shareholders, but when the SHTF, the system broke down. Which turned out to be even better for shareholders, but, and more or less by definition since monopoly capitalism is much more of a negative-sum activity, worse for everybody else. ↩︎

I worked on this data for about 3 hours over 3 days, I think. It's a low five figure investment, not novel, and the worst case, financially, is something like wasting a few thousand dollars over several years.
The rates go up so fast that the missing $7000 rebate only brings this back a year or so, to late 2031, and the 12-panel solution to maybe 2028.