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 $0.42 and lasts for 1,000 hours. A 15-watt CFL, which provides the same light, costs $3.25 and lasts for 12,000 hours. A kilowatt-hour is 1,000 watts for 1 hour. Suppose you have a residence with a lot of incandescent bulbs that are used on average 500 hours a year. The average bulb will be about halfway through its life, so it will have 500 hours remaining (and you can’t tell which bulbs are older or newer).

If you require a 11 percent return, at what cost per kilowatt-hour does it make sense to replace your incandescent bulbs today? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your final answer to 6 decimal places. (e.g., 32.161616))

Number should be negative.

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 $0.42 and lasts for 1,000 hours. A 15-watt CFL, which provides the same light, costs $3.25 and lasts for 12,000 hours. A kilowatt-hour is 1,000 watts for 1 hour. Suppose you have a residence with a lot of incandescent bulbs that are used on average 500 hours a year. The average bulb will be about halfway through its life, so it will have 500 hours remaining (and you can’t tell which bulbs are older or newer).

Explanation / Answer

At 500 hrs per year...
CFL:
500 hrs per year (usage) * 15 watts per hour = 7500 watts.../1000 = 7.5 kwh per year
7.5 kwh * $0.114 = $0.855 cost to "operate" per year
CFL lasts: 12,000hrs / 500 hrs used per year = 24 years
Annuity Factor: (1 - (1 / 1.09^24)) / 0.09] = 9.70661
EAC = (cost / annuity factor) + annual cost
= (3.05 / 9.70661) + 0.855
= 0.31422 + 0.855
= $1.16922, round to $1.17

Incandescent:
500 hrs per year * 60 watts per hour = 30,000 watts.../1000 = 30kwh
30kwh * $0.114 = $3.42 cost to "operate" per year...
Life: 1000hrs/ 500 hrs used per year = 2 years
Annuity factor: (1 - (1 / 1.09^2)) / 0.09
= 1.75911
EAC: (0.38 / 1.75911) + 3.42
= 0.21602 + 3.42
= $3.63

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