Compact fluorescent lamps (CFLs) have become more popular in recent years, but d
ID: 2778782 • 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 $0.46 and lasts for 1,000 hours. A 15-watt CFL, which provides the same light, costs $3.45 and lasts for 12,000 hours. A kilowatt hour of electricity costs $0.122, 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 11 percent and use a light fixture 500 hours per year. What is the break-even cost per kilowatt-hour? (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 = $ 0.460
Total wattage over the life of the bulb = 60 * 1000 = 60,000 watts or 60000/1000 = 60 kilowatts
Cost per kilowatt hour = 0.46/60 = $0.007667
CFL Bulb
No of watts per hour = 15
Life of a Bulb = 12000 hours
Cost of the bulb = $3.45
Total wattage over the life of the bulb = 12000 * 15 = 180,000 watts or 180,000/1000 = 180 kilowatts
Cost per kilowatt hour = $3.45/180 = $0.019167
Cost of electricity per kilowatt hour = $0.122
Let x be the cost of electricity per kilowatt hour
Total cost of electricity and incandescent bulb for 500 hours = 500 * $0.007667 * 0.122
= $0.467687
Present value of the cost = 0.467687/ 1.11 = 0.4213396
Total cost of electricity and CFL bulb for 500 hours = 500 * $0.019167 * x = 9.5835 *x
Present value of the cost = 9.5835 *x /1.11 = 8.633784 *x
Break-even cost when the present value of cost per kilowatt hour of incandescent bulb equals present value of cost per kilowatt hour of CFL bulb
0.4213396 = 8.633784 *x
X = 0.4213396/8.633784 = $ 0.0488
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