Compact fluorescent lamps (CFLs) have become more popular in recent years, but d

Question

Compact fluorescent lamps (CFLs) have become more popular in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent lightbulb costs $0.47 and lasts for 1,000 hours. A 15-watt CFL, which provides the same light, costs $3.50 and lasts for 12,000 hours. A kilowatt hour of electricity costs $0.123, which is about the national average. A kilowatt-hour is 1,000 watts for 1 hour. However, electricity costs actually vary quite a bit depending on location and user type. An industrial user in West Virginia might pay $0.04 per kilowatt-hour whereas a residential user in Hawaii might pay $0.25. You require a return of 9 percent and use a light fixture 500 hours per year. What is the break-even cost per kilowatt-hour?

Explanation / Answer

Per year, with 500 hours of use we divide cost of each lamp by the number of years it would work the expense would be:

1 watt = 1/1000 kilowatt

Incandescent: 0.55*500/1000 + R* (60/1000) * 500

CFL: 3.90*500/12000 + R*(15/1000)*500

where R is the breakeven rate per kilowatt hour.

So, dividing both by 500:

0.55/1000 + 60*R/1000 = C1

3.9/12000 + 15*R/1000 = C2

and multiplying by 1000 we have:

0.55 + 60*R = C1

0.325 + 15*R = C2

C1 - C2 = 45R + 0.225

For a 11% return, or 89% discount,

45R + 0.225 = C1*11/100 = (0.55 + 60*R)*11/100

So, 45R + 0.225 > 0.0605 + 6.6R

So, 38.4R > -0.1645

So, R > -0.004284

R = $0.0 per unit for breakeven.

This implies that since the CFL lasts 12 times as long, it is financially better irrespective of cost of electricity.

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