Solar Power Arithmetic
By Arnold Kling
For a 3KW installation (about 275 sf of cells), the total cost to me would be approximately $18K.
Let us use my favorite asset valuation equation:
profitability = rental rate plus appreciation rate minus interest cost
The rental rate is the annual value of the solar energy provided by the system, divided by its cost. Danziger sees the system replacing 800 KWH per month of electricity from the power company. At ten cents a KWH (a reasonable ballpark estimate for competing electric power), this is $80 a month in savings, or $960 per year. The ratio of this to the installation cost is $960/$18,000 = 5.33 percent.
Suppose that average inflation will be 2 percent and that the cost of energy will rise 1 percent faster. That would suggest using an appreciation rate of 3 percent per year. However, the solar unit will have a physical depreciation rate of at least 2 percent per year. In addition, there will be economic depreciation, due to the fact presumably next year’s solar technology will be better than this year’s. But let’s ignore that, and just take 3 percent energy price inflation minus 2 percent depreciation, for a 1 percent appreciation rate.
Finally, we need an interest rate. Marc assumes 9 percent. That seems high to me. I might pick 7 percent. Overall, we get:
profitability = 5.33 + 1.0 – 7.0 = -0.67 percent
That is a pretty small loss, which could easily be offset by what Danziger calls the “feel-good” factor, or by government subsidies, although the latter would give me a “feel-bad” factor.
Nick Schulz of TCSdaily sent me an estimate for his home that looked worse. The company wanted $12,000 to $13,000 for an installation that would save only 110 KWH per month, or about $132 per year. That gives a rental rate of barely over 1 percent, which is a loser under almost any reasonable assumption.
UPDATE: In the comments below, Bob Knaus writes,
The great majority of solar panels manufactured today require more electricity to melt the silicon than they will produce over a 20-year lifespan. Bluntly, they are net carbon emitters.
Because they are manufactured in places where industrial electricity prices are much lower than US residential prices, they maybe in fact pencil out just on the plus side. But they are doing this because you are essentially buying 20 years worth of cheap Chinese electricity to replace your expensive US electricity.