Arnold Kling  

Solar Power Arithmetic

More on the Trouble with Minar... Ancient Rome, etc....

Marc Danziger writes,

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.

Comments and Sharing

COMMENTS (16 to date)
Buzzcut writes:

Hmm, I take issue with 10 cents per killowatt hour. Should you be taking the wholesale price or the retail price? Are you including taxes?

10 cents is on the low end of the retail price of energy in this country. And in the blue states, where this type of solar energy might be a little more popular, the retail price of energy is much higher than 10 cents, especially when you include any and all taxes.

Even here in Red Indiana, the first kilowatt of electricity costs a staggering 36 cents a kilowatt hour. It quickly falls from there, and the lowest you can possibly pay (after using 700 kWhrs) is 9 and change, plus taxes.

So... I think that for a good number of people, solar makes very good financial sense!

Armed Liberal writes:

Thanks for the link; one fact and one assumption need challenging, however. We have a tiered pricing system, and we bump into the highest tier, which is closer to $0.40/KwH than $0.10; and a 1% assumption for electricity cost increases over inflation is radically low, in my estimation...


Stefano writes:

Even in the sunniest locales, insolation is never above about 6 hours per day, that is about 2000 hours per year. Therefore a 3 kW installation should provide around 6000 kWh per year, or 500 kWh per month.

Also, expected active life for photovoltaics is around 20 years, implying a 5% depreciation.

I would use a lower interest rate than 7%, though, since solar panels are a less risky investment than stock. Let's make it 4%.

Using 30 cents/kWh as "marginal" rate, the profitability computation becomes:

p = 6000 * 30 / 18000 + 1 - 5 - 4 = 2 %

Stefano writes:

BTW, $18,000 for a 3 kW installation is a very good price, pratically at cost.

The panels alone should cost around $14,000 (see for a price index), to which you have to add inverters, cabling and labor.

Ironman writes:

Ooo - new tool project! Thanks, Arnold!

Floccina writes:

For me here in Gainesville Forida it is getting close:
Nanosolar is on track to make solar electricity:
cost-efficient for ubiquitous deployment
mass-produced on a global scale
available in many versatile forms.
Nanosolar has developed proprietary process technology that makes it possible to produce 100x thinner solar cells 100x faster.

Watch videos by CNN, KQED, CNBC to see how we can simply roll-print thin-film solar cells.

Our first product, the Nanosolar Utility Panel™, is the industry's first panel specifically designed for optimal utility-scale systems economics.

The result sets the standard for cost-efficient solar power.

Solar Power at Half the Cost
A new roof-mounted system that concentrates sunlight could cut the price of photovoltaics

Floccina writes:

BTW a better way to go would be super efficent heating and cooling see Hallowell's product and better insulation and windows etc.

Buzzcut writes:

One more thing. At least in Indiana, net metering does pay you back at retail rates in the case that you make more power than you are using, but you can't produce more power in a month than you use.

Well, you can produce more, but you don't get paid for it.

bwv writes:

The potential benefit of Solar is that it is a purely technological problem. There has been great success in the past dramatically lowering the cost and increasing the efficiency of semiconductors, so if there is an equivalent to Moore's law for solar cells then a good part of our energy problems are solved. Plus the economic impact if a significant portion of GDP spent on buying raw materials from state oil suppliers was redirected to R&D and complex manufacturing activity would have significant effects for the overall wealth of society.

Bob Knaus writes:

There's one inconvenient fact which features even easier math. 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.

The problem is not permanent; lowering energy usage during the manufacturing process is the prime goal of new technologies. Evergreen Solar (ESLR) in Massachussetts has been making panels commercially for a few years now using a lower-energy silicon melting process. They claim their panels are, in fact, net energy savers over a 20-year life.

When Huricane Wilma blew the solar panel off my boat 3 years ago, I replaced it with an ESLR model. I feel much better!

Bob Knaus:

It might have been true 20 years ago that it took more energy to produce solar cells than they returned over their lifetime, but it isn't the case today by a large factor. This article produced by the U.S. Department of Energy estimates the energy payback time of current (as of 2004) solar systems as 3-4 years, and expects the energy payback time to drop to 1-2 years in the near future.

So if the functional lifespan of a solar module is around 30 years, a solar system manufactured today will return 8x to 10x the energy required to manufacture it over its lifetime.

Bob Knaus writes:

Shivering Timbers:

Good paper, as I said the problem is temporary and not permanent.

Here are the key paragraphs from the paper:

Today’s PV industry generally recrystallizes any of several types of “off-grade” silicon from the microelectronics industry, and estimates for the energy used to purify and crystallize silicon vary widely. Because of these factors, energy payback calculations are not straight-forward. Until the PV industry begins to make its own silicon, which it could do in the near future, calculating payback for crystalline PV requires that we make certain assumptions. To calculate payback, Dutch researcher Alsema reviewed previous energy analyses and did not include the energy that originally went into crystallizing microelectronics scrap.

If you take a marginal view of silicon production costs, then the current production scheme can escape the initial costs of melting the silicon. But this scheme will not ramp up to the volumes needed to replace significant portions of electric generation.

ESLR makes its own crystalline silicon. The cost of its panels (which in true efficient market fashion are identical to its competitors) fully incorporates the cost of producing the raw materials.

I own 100 shares of the company's stock. It has been less than satisfying as an investment. The board includes academics from MIT who act like primadonnas. I still feel good about the company. Hopefully their superior technology will overcome their management deficiencies.

Dr. T writes:
Hopefully their superior technology will overcome their management deficiencies.
Surely you jest. When has superior technology ever overcome bad management?

Here's my take on solar power: If you have high electricity costs, live in a sunny area, have $20,000 or so to invest, and don't mind making your roof look ugly, then solar electricity roof panels might be a good investment. I do not believe the useful lifespan claims of 20-30 years: the technology hasn't been in use long enough to confirm those claims. Also, I think that owners will encounter high maintenance costs: even if the solar panels don't fail, other components will, and the panels must be cleaned regularly or they will lose efficiency.

In Memphis I'm paying $0.116 per kwh (averaged cost including taxes). Solar power is not yet economical here.

L. Burke Files writes:

I spent many years working on the financing of alternate energy, solar, power, wind etc... What became clear to me is that alternate energy can supplement traditional energy in urban and suburban environments and do so in a cost effective method, mostly just heating hot water or preheating it.

Stand alone systems or being "unplugged" from the grid made economic sense when the cost of electricity begins to hit about 11 cents per kwh or the cost of brining power to where you live "wheeling" is prohibitive.

The idea that photovoltaic will make a meaningful contribution to the very efficient power generation systems in our urban or suburban areas is many years off. On the other hand they make an excellent contribution for places where power is very expensive. Small Islands throughout the Caribbean rely on diesel generated power, at nearly 18 cents for kwh. In these environments all forms of power generation and power consumption reducing technology are used.

For the general homeowner in the US - we can save 20% or more by, using solar to preheat our hot water or in some regions heat the water without assistance from the grid. Use more efficient lighting, I like for low light long-term outdoor use LED's lights, buying more efficient appliances and HVAC units, and remember to maintain them well, and reducing the involuntary air exchanges with the outside - leaky house. That alone can save $200 to $300 per house per year.

mpower writes:

Neither the author nor the comments has considered the possibility of producing MORE kWh than that being used in the home. Combine that 3kW system with a smaller, more efficient homestead... the excess power is sold back to the utility, and the homeowner is receiving monthly checks - not sending them.

If a 3kW system has only a fractional impact on your energy bill, then I would argue that your homestead is too big and/or too inefficient to attempt any real "green' savings in the first place. Downsize first, and then try all of this math again...

Yet another reason why so many brand new 6br McMansions will stand empty for decades to come.

Mark Fitz writes:

You also left out the appreciating value of a long term cost for power in a world seeing inflation and rapidly rising energy costs.

For a smaller home based business to take profits today and invest them in a longterm fixed cost that sunsets would probably turn that rate or return you show into a positive.

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