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Tutorial on Capital Costs: Light Bulbs

RoyLatham
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9/21/2011 11:08:22 PM
Posted: 5 years ago
Debates on the costs of alternative energy recently have shown that many people are perplexed by the calculations, particular of capital costs. I've tried here to provide a relatively simple example. It gets complicated enough.

The idea is to compare the costs of three light bulbs including the purchase price, capital costs, and electricity. Here are three products I found on amazon.com. Each claims to produce 400 lumens, like a 60 watt incandescent bulb:

cost power life (hrs)
LED $15.00 7 25000
CFL $1.00 14 10000
Incandescent $0.46 60 1000

So the LED unit costs $15, draws seven watts, and is claimed to last 25,000 hrs.
To start with, assume the national average price for a kilowatt hour of electricity and the utility bond interest rate. These are:

Cost / kwh $0.11
Interest Rate4.00%

Okay. Which is cheapest if the light is to be on about 3 hours per day -- 1000 hrs per year. The LED will cost $1.98 to run. It uses 77 cents worth of electricity. 1/25 of the bulbs 25,000 hour life is consumed, 60 cents. To those costs, the cost of having money tied up in a light bulb rather than invested must be added. The bond interest rate of 4% is one investment possibility, and a year of that at $15 costs 60 cents.

However, if the person has credit card debt costing 16%, then paying off that debt would yield a saving of $2.40. The cost of capital depends on what alternatives are available. With the higher cost of capital, the LED unit would cost $3.77 for the year, rather than $1.98.

Using 4% interest rate, the CFL comes in at $1.68 and old fashioned incandescent at $7.70.

Now suppose the bulb is on 24/7 for the year. The LED wins at $12.80, with the CFL at $14.41, and the incandescent at $61.86. Low power consumption beats the higher capital cost of the LED.

Finally, suppose the bulb is in the closet with the Christmas ornaments, and is used only 2 hours a year. Now the incandescent wins $0.033, to $0.043 (CFL) and $0.60 (LED). Actually, would anyone figure on keeping a light bulb for 5000 years -- the life of the CFL in the application? It would be more reasonable to assume that after 50 years you'll give up on it. The CFL and LED are then more expensive relative to the incandescent, the LED 22 times as much.

I live in California where electric rates quickly soar to 42 cents, a punishment for sin. Then the costs for 1000 hr/year usage favor LED lamps, even at $15 apiece.

It's also worth thinking about maintenance costs. A company must pay someone to change the bulb, which might cost $15 or most in labor. That's effectively added to the bulb cost.

I haven't figured other attributes into the calculation. A $1 CFL has in my experience an annoying flicker. LEDs are usually more beautiful. We just did cost here.

If anyone would like to play with the spreadsheet for this problem, it's here:
factspluslogic.com/LightingCosts.xls
F-16_Fighting_Falcon
Posts: 18,324
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9/22/2011 2:31:08 AM
Posted: 5 years ago
Mostly, it makes sense, but you are assuming a guaranteed rate of return on your investment which you then add to the cost of the light bulb. In reality, you never know how much you are going to get from an investment. Adding it to the price will obviously inflate the cost. A better alternative would be to include the time value of money for long-term calculations.
RoyLatham
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9/22/2011 1:32:21 PM
Posted: 5 years ago
At 9/22/2011 2:31:08 AM, F-16_Fighting_Falcon wrote:
Mostly, it makes sense, but you are assuming a guaranteed rate of return on your investment which you then add to the cost of the light bulb. In reality, you never know how much you are going to get from an investment. Adding it to the price will obviously inflate the cost. A better alternative would be to include the time value of money for long-term calculations.

The 4% interest rate is for a long term bond, so the rate is locked in for 20 or 30 years. Interest rates are near a historical low, so locking up money in a long term fixed asset is actually less attractive than supposed. Historical stock market returns are around 9%, which is probably a better number.

There is nothing to "time value of money" other than expected rates of return. For cost estimates on Government contracts, the Government provides a table of expected inflation rates to use in estimating the contract. Point is that something has to be projected, and there is no certainty.
darkkermit
Posts: 11,204
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9/22/2011 2:21:20 PM
Posted: 5 years ago
Well If your going to consider the capital cost of the light bulb, how much it costs compared to the alternative of investing, why not consider fuel as a capital cost as well?
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RoyLatham
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9/22/2011 2:39:30 PM
Posted: 5 years ago
At 9/22/2011 2:21:20 PM, darkkermit wrote:
Well If your going to consider the capital cost of the light bulb, how much it costs compared to the alternative of investing, why not consider fuel as a capital cost as well?

I don't understand. Fuel is bought and consumed. The cost of electricity is in the cost equation, and it's true that the future cost is uncertain. Electricity, corrected for inflation, was stable for several decades until about the past decade, when government started insisting on using uneconomical green energy. An equation for future electricity costs could be used instead of the fixed cost, but that's not a capital cost.
sadolite
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9/22/2011 2:48:25 PM
Posted: 5 years ago
All subsequent arguments against the original post are samantics and make no difference. The short term and long term have been covered. Return on investment? On a light bulb? Please. You are going to forced to buy what ever light bulb the light bulb Nazi's are going to make you buy or face fines or possible imprisonment. No matter whether it serves your purposes or not or whether it is cost effective to you or not. It is one size fits all, don't like it to bad. The gov't and the EPA don't give a damn what you think. You will get that pile of crap fluorescent "made only in china" light build and you will like it. (Now an EPA bureaucrat slaps you in the face)
It's not your views that divide us, it's what you think my views should be that divides us.

If you think I will give up my rights and forsake social etiquette to make you "FEEL" better you are sadly mistaken

If liberal democrats would just stop shooting people gun violence would drop by 90%
darkkermit
Posts: 11,204
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9/22/2011 2:52:36 PM
Posted: 5 years ago
At 9/22/2011 2:39:30 PM, RoyLatham wrote:
At 9/22/2011 2:21:20 PM, darkkermit wrote:
Well If your going to consider the capital cost of the light bulb, how much it costs compared to the alternative of investing, why not consider fuel as a capital cost as well?

I don't understand. Fuel is bought and consumed. The cost of electricity is in the cost equation, and it's true that the future cost is uncertain. Electricity, corrected for inflation, was stable for several decades until about the past decade, when government started insisting on using uneconomical green energy. An equation for future electricity costs could be used instead of the fixed cost, but that's not a capital cost.

You stated: "To those costs, the cost of having money tied up in a light bulb rather than invested must be added. The bond interest rate of 4% is one investment possibility, and a year of that at $15 costs 60 cents."

However, you do not state the "the cost of having money tied up in fuel than must be added".

Do you not consider that cost because the costs apply equally to both?
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RoyLatham
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9/22/2011 3:44:03 PM
Posted: 5 years ago
At 9/22/2011 2:52:36 PM, darkkermit wrote:
However, you do not state the "the cost of having money tied up in fuel than must be added".

Do you not consider that cost because the costs apply equally to both?

There is no money "tied up" in fuel because that money cannot be reallocated. It's used up. It's an expense, but not a cost of capital. If the capital were invested, the earnings could be used to buy electricity, but there is no way to use the money spent on electricity to buy anything else. I think it's just the semantics of how costs are classified.
Ore_Ele
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9/22/2011 3:59:54 PM
Posted: 5 years ago
You cannot go to a bond broker and ask to invest $1 or $15, and you would need to look at fee associated with investing in that manner.

When it comes to labor for changing bulbs, most large companies already have custodians on hand that have that as one small part of their job desrciption. And since every employee slacks off a certain degree, every employee has the capacity to "pick up the slack" on little things like changing light bulbs (unless you are in a large plant that needs large ladders or special equipment).

As for the "annoying flicker" it goes at 60 htz, your TV does 30.
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darkkermit
Posts: 11,204
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9/22/2011 4:18:56 PM
Posted: 5 years ago
At 9/22/2011 3:44:03 PM, RoyLatham wrote:
At 9/22/2011 2:52:36 PM, darkkermit wrote:
However, you do not state the "the cost of having money tied up in fuel than must be added".

Do you not consider that cost because the costs apply equally to both?

There is no money "tied up" in fuel because that money cannot be reallocated. It's used up. It's an expense, but not a cost of capital. If the capital were invested, the earnings could be used to buy electricity, but there is no way to use the money spent on electricity to buy anything else. I think it's just the semantics of how costs are classified.

Alright, so we are assuming that in the example, money can only be allocated to either electricity or bonds? Surely I can use money for more then just electricity :p.
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RoyLatham
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9/22/2011 4:38:03 PM
Posted: 5 years ago
At 9/22/2011 3:59:54 PM, Ore_Ele wrote:
You cannot go to a bond broker and ask to invest $1 or $15, and you would need to look at fee associated with investing in that manner.

Capital costs are computed as if you are making transactions in groups. You might put the money in a 401K or use it to pay off a credit card debt or put it in savings awaiting a larger investment opportunity. The example what we call "an example."

When it comes to labor for changing bulbs, most large companies already have custodians on hand that have that as one small part of their job desrciption. And since every employee slacks off a certain degree, every employee has the capacity to "pick up the slack" on little things like changing light bulbs (unless you are in a large plant that needs large ladders or special equipment).

No, its an incremental cost that is reasonably accounted for incrementally. At one time Disney had a staff of more than 25 people devoted to changing light bulbs. A guy who one the NY lottery had a full time job changing flourescent lamps in the Empire State Building. Perhaps it's easier to relate to McDonalds installing drink machines that shut off automatically when the cup is filled, a response to n increase in the minimum wage. They could reduce the staff of a dozen in a large restaurant by one person using the automatic machine. Its a mistake to think that incremental costs don't count because they can always be absorbed at "no cost." It a proportionate percentage of the time, someone will be eliminated.

As for the "annoying flicker" it goes at 60 htz, your TV does 30.

American TV is 60Hz, usually interlaced like 1080i. Old British TV is 50Hz, and it is annoying to me if it's in my peripheral vision. (Has Britain moved to 1080i? I dunno.) Peripheral vision is more sensitive to flicker for more people. Standards now forbid 60Hz computer monitors in workplaces. Whether flicker is annoying depends upon the brightness, the brightness change between frames, and the individual. 72 Hz seems safe for nearly all circumstances. I'm guessing cheap CFLs have a 60 Hz flicker, whereas better flourescents have the rectified 120 Hz frequency that doesn't bother anyone. Good CFLs or tube flourescents don't bother me.
RoyLatham
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9/22/2011 4:53:17 PM
Posted: 5 years ago
At 9/22/2011 4:18:56 PM, darkkermit wrote:
Alright, so we are assuming that in the example, money can only be allocated to either electricity or bonds? Surely I can use money for more then just electricity :p.

Sure, you can consume electricity to make light, or you can consume something else. The example assumes you want 400 lumens worth of light by some controllable means. You might also compare the economics of candles or a gas powered Coleman lantern. The assumption is that you want those 400 lumens, and the question is what it costs.

The cost of capital converts the lost opportunity to spend the capital on something else to a monetary cost. What that is worth depends upon interest rates and investment opportunities, but it is always a cost. The early Soviets suffered economically by failing to account for capital costs. It's a law of nature that cannot be ignored any more than than conservation of energy can be repealed.

Islam forbids paying interest. They have developed permitted practices that accomplish the same thing.
darkkermit
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9/22/2011 6:46:26 PM
Posted: 5 years ago
At 9/22/2011 4:53:17 PM, RoyLatham wrote:
At 9/22/2011 4:18:56 PM, darkkermit wrote:
Alright, so we are assuming that in the example, money can only be allocated to either electricity or bonds? Surely I can use money for more then just electricity :p.

Sure, you can consume electricity to make light, or you can consume something else. The example assumes you want 400 lumens worth of light by some controllable means. You might also compare the economics of candles or a gas powered Coleman lantern. The assumption is that you want those 400 lumens, and the question is what it costs.

The cost of capital converts the lost opportunity to spend the capital on something else to a monetary cost. What that is worth depends upon interest rates and investment opportunities, but it is always a cost. The early Soviets suffered economically by failing to account for capital costs. It's a law of nature that cannot be ignored any more than than conservation of energy can be repealed.

Islam forbids paying interest. They have developed permitted practices that accomplish the same thing.

Alright, thanks for the clarification.
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