Compact fluorescent lamps (CFLs) have become more popular in recent years, but d
ID: 2736563 • Letter: C
Question
Compact fluorescent lamps (CFLs) have become more popular in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent light bulb costs $.40 and lasts for 1,000 hours. A 15-watt CFL, which provides the same light, costs $3.15 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 10 percent return, at what cost per kilowatt-hour does it make sense to replace your incandescent bulbs today?
Explanation / Answer
Let the cost per kilowatt hour be C
1. For light Bulb
Kilowatt hour user per year for bulb = (60 / 1000) * 500 = 30
Electricity cost per year = 30C
The bulb will last for 1000 hours i.e. two years
Present value of annual cost = 30C * (1 – 1.10-2)/0.10 = 1.7355 * 30C = 52.065C
NPV = -Cost of bulb – Present value of annual cost = -$0.40 - $52.065C
Equivalent annual cost of bulb = NPV/Present value of annuity = (-$0.40 - $52.065C)/1.7355
2. For CFL
Kilowatt hour user per year for bulb = (15 / 1000) * 500 = 7.5
Electricity cost per year = 7.5C
The bulb will last for 12000 hours i.e. 24 years
Present value of annual cost = 7.5C * (1 – 1.10-24)/0.10 = 7.5C*8.9847 = 67.3853C
NPV = -Cost of CFL – Present value of annual cost = -$3.15 - $67.3853C
Equivalent annual cost of CFL = NPV/Present value of annuity = (-$3.15 - $67.3853C)/8.9847
At the indifference level, both EAC should be equal
(-$0.40 - $52.065C)/1.7355 = (-$3.15 - $67.3853C)/8.9847
- $3.59388 - $467.7884C = -$5.4668 - $116.9472C
$350.8412C = $1.8729
C = $1.8729/$350.8412 = $0.005338
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