Lifetime Costs Of Light Bulbs

Huddler Bobkart developed a formula for computing the total (tangible) cost of ownership of light bulbs that takes into account the initial cost of the bulb, its energy consumption, its light output, its lifetime length, and the cost of electricity. The full analysis and explanation is below, but we’ll start with the comparison of an incandescent, CFL, and LED lamp each with identical 800 Lumen output capabilities, but with vastly different initial cost, energy consumption, and lifetime length:

Up-front cost: $1

Lifetime cost: $8.75/megalumen-

15W/800 Lumen CFL

Up-front cost: $5.00

Lifetime cost: $3.43/megalumen-hour

7.5W/800 Lumen LED

Up-front cost: $100

Lifetime cost: $4.04/megalumen-hour
While CFL is the most cost-effective under current conditions, if the cost of an 800 lumen LED comes down even to $75, it makes economic sense.
How the Formula is Calculated
The formula gives dollars/megalumen-hour, and takes into account:

* initial-dollars: the initial cost of the bulb in dollars
* watts-consumed: how much power the bulb consumes in watts
* average-lumens: how much light it produces at any given time, on average over its lifetime, in lumens
* thousand-hours-lifetime: how long it lasts in thousands of hours
* dollars-per-kilowatt-hour: the cost of electricity in dollars per kilowatt-hour

If you understand that a kilowatt-hour is the consumption of one thousand watts for one hour, or one hundred watts for ten hours, etc., then you’ll understand the megalumen-hours concept too, it’s the generation of one million lumens for one hour, or one thousand lumens for one thousand hours, etc. In other words, its a way of measuring the total light output of the bulb over time, just as kilowatt-hours is a way of measuring the total energy consumed by the bulb over time.

dollars/megalumen-hour = ( initial-dollars + watts-consumed * dollars-per-kilowatt-hour * thousand-hours-lifetime) / ( average-lumens * thousand-hours-lifetime / 1000 )

Because both CFLs and LEDs slowly lose their brightness over their lifetime, “average lumens” were used assuming a 30% loss of brightness over a bulb’s lifetime. Thus, in the examples below, for CFLs and LED lamps, an average-lumens value of 85% of the so-called “initial-lumens” is used.

Here are some examples (all assuming $0.10/kilowatt-hour):

60-watt incandescent bulb, 800 lumens, 1,000 hours lifetime, $1.00 initial cost:

( $1.00 + 60 * $0.10 * 1 ) / ( 800 * 1 / 1000 ) = ( $1.00 + $6.00 ) / 0.8 = $8.75 / megalumen-hour

15-watt CFL bulb, 800 lumens (680 average), 6,000 hours lifetime, $5.00 initial cost:

( $5.00 + 15 * $0.10 * 6 ) / ( 680 * 6 / 1000 ) = ( $5.00 + $9.00 ) / 4.08 = $3.43 / megalumen-hour

7.5-watt LED lamp, 800 lumens (680 average), 50,000 hours lifetime, $100.00 initial cost:

( $100.00 + 7.5 * $0.10 * 50 ) / ( 680 * 50 / 1000 ) = ( $100.00 + $37.50 ) / 34 = $4.04 / megalumen-hour

Note that the CFL does come out a little better than the LED lamp in this case, but if the initial cost were dropped to more like $75.00, the LED lamp would start to have a better bottom line.

Note also that this formula does not consider less tangible factors like the cost of frequent changing of bulbs in difficult-to-access locations, or the cost to the environment of mercury escaping from improperly-disposed-of CFLs, or the additional CO2 that is put into the atmosphere to generate the extra electricity used by both incandescent bulbs and CFLs compared to LED lamps.

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