Compact fluorescent lamps (CFLs) have become required in recent years, but do th
ID: 2561511 • Letter: C
Question
Compact fluorescent lamps (CFLs) have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent lightbulb costs $.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 answer to 6 decimal places, e.g., 32.161616.)
Break-Even cost = ?
Compact fluorescent lamps (CFLs) have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent lightbulb costs $.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).
Explanation / Answer
Watts per hour used
Watts per hour = watts of bulb/1000
60-watt bulb = 60/1000 = 0.06
15-Watt bulb = 15/100 =0.015
Total kilowatt hour per year
Kilowatts per year = watts per hour * used hours per year
60-watt bulb = 0.06*500 = 30
15-Watt bulb = 0.015*500 = 7.5
Electricity cost per year
Yearly electricity = kilowatts per hour*cost per kilowatt hour
60-watt bulb = 30* cost
15-Watt bulb = 7.5*cost
Number of years that each light bulb will last
Number of years = total hours/annual consumption
60-watt bulb = 1000/500 = 2 years
15-Watt bulb = 12000/500 = 24years
Annuity factor
Annuity factory = (1-(1+r)^-n))/r
60-watt bulb = (1-(1.09^-2)/0.09 = 1.759111
15-watt bulb = (1-(1.09^-24)/0.09 = 9.706612
NPV
NPV = price of bulb*(yearly electricity cost * annuity factor)
60-watt bulb = -0.50+(30*cost*1.759111)
15-watt bulb = -3.65+(7.5*cost*9.706612)
EAC
EAC = NPV/annuity factor
60-watt bulb = -0.50+(30*cost*1.759111)/ 1.759111
15-watt bulb = -3.65+(7.5*cost*9.706612)/ 9.706612
Breakeven point =
EAC of 60-watt bulb = EAC of 15-watt bulb
-0.50+(30*cost*1.759111)/ 1.759111= -3.65+(7.5*cost*9.706612)/ 9.706612
-0.50+(30*cost*1.75911)* 9.706612 =-3.65+(7.5*cost*9.706612)* 1.75911
1.567449 = 439.4506 cost
Cost = 1.567449/439.4506 = 0.04
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