Light Bulb Math

I should probably come clean right at the start of this and admit that I have a thing about energy saving light bulbs. You might call it a pet peeve. WhatLight Bulb KMJ bothers me about them is not that they give off light of a slightly different hue than I am used to. Nor do I have any reason to believe that they do not use less energy, as advertized.

What drives me up the wall is the pious focus on them as a great green savings of energy and/or money. A focus which some years ago resulted in the federal government actually banning the old-fashioned Edison bulb.

Do not get me wrong. I agree that switching to energy saving bulbs will save energy. My point is that it will save only a tiny amount of energy. An amount that really only works as a symbolic act, and symbolism is in the eye of the beholder. What some may see as a visible sign that we love the planet is for me a sign we are governed by innumerate twits. I am here referring to both our politicians and the citizens who elect them.

What pressed this hot button of mine is a minor non-news item bouncing around the web. Apparently, last August the Department of Energy, the one Gov. Perry could not remember, awarded a $10 million prize to Philips for a new LED light bulb. This “L Prize” was intended to “substantially accelerate America’s shift from inefficient, dated lighting products to innovative, high-performance products.”

Philips has recently started selling the things, which prompted a piece in the Washington Post that, among other things, pointed out that at $50 each, these bulbs do not quite satisfy the stated L prize goal of affordability.

Indeed, it is hard to see how these particular LED bulbs are a prize-worthy improvement on the existing offerings. Yes, they produce the light of a 60 watt incandescent with only 10 watts, but that only sounds impressive until you learn that the old LEDs did it with 12.5 watts. And the old ones cost less than half as much money.

Why does the prize winning bulb cost so much? Well, one reason could be that the prize rules required that it be made (mostly) in the USA. The $50 bulb will be assembled in Wisconsin. Philips’ not-quite-as-good $25 version is made in China. (Of course, Philips is a Dutch company, so the L Prize Bulb is American in the same way an iPhone is Chinese.)

A round up of eco-friendly bulbs in the Wall Street Journal says the new bulb “works pretty well” and then recommends an $8 CFL instead.  This is proudly linked to on the L Prize website.

Philips was the only entrant in the prize competition.

The bottom line is that our government gave a cash prize to a foreign company for producing something that no consumer in his right mind would ever buy. The Post article makes it pretty clear that retailers would prefer not to waste shelf space on this turkey, but may do so just as a face-saving favor to Philips.

The L Prize strikes me as an example of Obamaism at its worst: a cutesy dinner-party-friendly solution to a problem we do not really have.

Needless to say, others disagree. Right Wingers Attack Innovative $50 Light Bulb Because They Can’t Do Math is a typically shrill response to the Post item. It focused on a since-removed info graphic not prepared by the article’s author that attempted to compare the lifetime cost of the L Prize bulb to the equivalent number of incandescent bulbs.

This graphic was fundamentally flawed for several reasons. 1) It used a much too low estimate of electricity cost. 2) In the context of the article, comparing the $50 L Prize bulb to existing $25 LED bulbs would have made more sense. 3) It is an academic question, as Americans will not be able to buy incandescent bulbs in the future. 4) Totaling expenditures over 30 years is not how you decide which is cheaper.

#4 bothers me the most. This is a simple time value of money problem that comes up in consumers lives with some frequency and that everybody ought to be able to solve. In the forlorn hope it will do some good, permit me to walk through the proper way to do the math.

I will start with the L Prize bulb vs. incandescents comparison. LEDs last a long time. Indeed, they never really burn out at all. When Philips says the bulb will last 30 years, what they mean is that after 30,000 hours of use (1 year = 1000 hours apparently being the standard assumption) it will have faded to 70% of its original brightness, which will be annoying enough for the consumer to want to replace it.

So if we assume the L Prize bulb will last 30,000 hours, and the incandescent alternative will last 1000 hours, then you will need 30 of the old style bulbs to match one L Prize. You can get the incandescent ones for about 50 cents each, at least the cheap ones that only last 1000 hours. To make the calculation both realistic and simpler, let us assume that you will buy all 30 bulbs today, while they are still available. That would set you back $15, $35 less than the L Prize bulb.

And what do you get for your $35 in additional outlay if you spring for the L Prize bulb? Why, a lower electric bill, of course. You will be using 50 watts less of power over 30,000 hours, which is 1500 kilowatt hours. At $0.10/kWh, that is a total 30 year savings of $150, which you only paid $35 for. Hooray.

Not so fast. $150 dribbled out over 30 years, at $5 a year, is not worth $150 today. To find out what it is worth, you need a discount rate, essentially your expected return on investment. To price the $5 payment in 2020, you need to work out how much you would need to invest to have $5 in 2020.

I will assume (very arbitrarily) a discount rate of 8%. And based on that rate, $5 a year for 30 years is worth a grand total of $56.29 today. So buying the L Prize bulb nets you $21.29 in present value. How very exciting.

Just for fun, let’s imagine that you lived in a country so permissive that it actually allowed you to buy 60 watt incandescent bulbs during this 30 year period. In that case, going old school would cost you $5.50 a year, $5 in extra electricity and $0.50 for a new bulb. The present value of that cost is $61.91, but you have to pay $50 out of pocket today to avoid it, for a net savings of $11.91. So almost half of the $21.29 savings is due to the government created constraint on buying incandescent bulbs.

Furthermore, there are a few unlikely assumptions baked into this calculation. First, 1000 hours a year is about 2 3/4 hours a day of use, which is probably more work than most of the bulbs in your house get. Second, the analysis only makes sense if you are going to stay in your house for 30 years or are the kind of person who would pack up the light bulbs when they move out.

And what about the comparison that should have gone with the Post article? Which is cheaper, the $50 Wisconsin-made L Prize bulb or the $25 Chinese-made no prize bulb? The prize winner gets the job done for 2.5 fewer watts, which over the course of a year would save 2.5 kWh, or $0.25. 30 annual payments of a quarter, assuming an 8% discount rate, comes to $2.81 in today’s money.

And what is that worth? $10 million, apparently.

[Photo: KMJ]

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