Compact fluorescent lamps (CFLs) have become more popular in recent years, but d
ID: 2778826 • 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 lightbulb costs $0.50 and lasts for 1,000 hours. A 15-watt CFL, which provides the same light, costs $3.65 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 9 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))
Break-even cost $________?
Explanation / Answer
Incandescent Bulb
No of watts of an incandescent bulb per hour = 60
Life of a Bulb = 1000 hours
Cost of the bulb = $ 0.50
Total wattage over the life of the bulb = 60 * 1000 = 60,000 watts or 60000/1000 = 60 kilowatts
Cost per kilowatt hour = 0.50/60 = $0.008333
CFL Bulb
No of watts per hour = 15
Life of a Bulb = 12000 hours
Cost of the bulb = $3.65
Total wattage over the life of the bulb = 12000 * 15 = 180,000 watts or 180,000/1000 = 180 kilowatts
Cost per kilowatt hour = $3.65/180 = $0.020278
Break-even cost when the cost per kilowatt hour of incandescent bulb equals the present value of the cost per kilowatt hour of CFL bulb
Cost per kilowatt hour of incandescent bulb = cost per kilowatt hour of CFL bulb / 1.09
0.0833333 = x /1.09
X = 0.083333 * 1.09 = $ 0.09083297
Average time for which an incandescent bulb is used per annum = 500 hours
Average life of the bulb = 500 hours
That is the bulb needs to be replaced in one year time.
Per-bulb kilowatts based on average remaining life = 60 * 500 hours /1000 hours
= 60 * 0.5 = 30 kilowatts
Cost for incandescent bulb over the remaining life of the bulb = 30 * $ $0.0083333
= $ 0.249999
Present value of the cost = $ 0.249999/1.09 = $0.229357
If the bulb is replaced today, CFL bulb will be used for 500 hours
Total wattage of CFL bulb over the 500 hour period = 180 * 500/12000 = 180 * 0.041667
= 7.5 Kilowatts
Cost for CFL bulb for the same period of 500 hours as incandescent bulb = 7.5 * $0.020278
= $ 0.152085
Present Value of the cost = $0.152085/1.09 = $0.139527
Present value of savings = $0.229357 - $0.139527 = $0.08983
Cost of the CFL Bulb = $3.65
Net Present Value of replacing = -$3.65 + $0.08983
= -$3.56017
That is over a one year horizon it is not profitable to replace an incandescent bulb with a CFL bulb. However if you calculate the total life of the bulb one needs to replace 12 incandescent bulbs over the life of one CFL bulb which makes a CFL bulb profitable over the entire life.
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