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 $0.48 and lasts for 1,000 hours. A 15-watt CFL, which provides the same light, costs $3.55 and lasts for 12,000 hours. A kilowatt hour of electricity costs $0.124, 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 10 percent and use a light fixture 500 hours per year. What is the break-even cost per kilowatt-hour?

Explanation / Answer

To solve the EAC algebraically for each bulb, we can set up the variables as follows:
W = light bulb wattage
C = cost per kilowatt hour
H = hours burned per year
P = price the light bulb
The number of watts use by the bulb per hour is:
WPH = W / 1,000
And the kilowatt hours used per year is:
KPY = WPH × H
The electricity cost per year is therefore:
ECY = KPY × C
The NPV of the decision to but the light bulb is:
NPV = - P - ECY(PVIFAR%,t)
And the EAC is:
EAC = NPV / (PVIFAR%,t)
Substituting, we get:
EAC = [-P - (W / 920 × H × C)PVIFAR%,t] / PVIFAR%,t
We need to set the EAC of the two light bulbs equal to each other and solve for C, the cost per kilowatt hour. Doing so, we find:

[-$0.48 - (60 / 1000 × 500 × C)PVIFA10%,2] / PVIFA10%,2 = [-$3.55 - (15 / 1000 × 500 × C)PVIFA10%,24] / PVIFA10%,24]

C = $0.00566

So, unless the cost per kilowatt hour is extremely low, it makes sense to use the CFL

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