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))

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

For incandescent,total kilowatt-hour=1000*60/1000=60KWh, cost/KWh=.42/60= .007$/KWh

The total kilowatt-hour consumed by end of the year for remaining 1/2 year=500*60/1000=30KWh

The cost of above 30KWh consumed at year end=30KWh*.007$/KWh= .21$

The cost of above 30KWh consumed today=.21$/(1.055)

Let x be the cost per kilowatt-hour does it make sense to replace your incandescent bulbs today,

The cost of above 30KWh consumed with new bulbs=30KWh*x $/KWh= 30x $

Thus , 30x <=.21$/(1.055)

=>x<=$ .21/(1.055*30)=0.006635 $/KWh

at 0.006635 $/KWh  does it make sense to replace your incandescent bulbs today.

For CFLs,total kilowatt-hour=12000*15/1000=180KWh, cost/KWh=3.25/180= .018$/KWh

As .018$/KWh>0.006635$/KWh required cost,Thus it does not make a financial sense to replace  your incandescent bulbs today.

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