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Compact fluorescent lamps (CFLs) have become required in recent years, but do they make financial sense?...

Compact fluorescent lamps (CFLs) have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent lightbulb costs $.36 and lasts for 1,000 hours. A 15-watt CFL, which provides the same light, costs $2.95 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 answer to 6 decimal places, e.g., 32.161616.)

Break-even cost $?

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Expert Solution

Existing Bulb:(incandescent )
Life remaining of bulb=500 hours
Average life of a bulb=1000 hours
Cost of bulb =$0.36
Capital cost of remaining life=0.36/2= $0.18
Cost of CFL bulb $2.95
Total initial cost for replacement $3.13
Life of CFL bulb in hours 12000
Number of years of use =(12000/500) 24
Present Value of savings of $1 per year for 24 years at 11% discount $8.35 (Using PV function of excel with Rate=11%,Nper=24, Pmt=-1$,)
Required present value of savings to break even $3.13
Required annual savings in dollar 0.37493397 (3.13/8.35) 0.37493397
Saving in electricity per year per bulb=(60-15)*500 Watt Hour 22500 Watt hour 22500
Saving in electricity per year= 22.5 Killowatt hour (22500/1000)
Assume Breakeven cost per killowatt hour= X
Annual savings=22.5X=0.37493397
X=0.374934/22.5= 0.016664 Dollar per Killowatt hour
Cost per kilowatt-hour that makes sense to replace incandescent bulbs today 0.016664 Dollar per Killowatt hour
Cost per kilowatt-hour that makes sense to replace incandescent bulbs today(Rounded to nearest cent) $       0.02 Dollar per Killowatt hour
Breakeven Annual Cost =(15watts*500 hours*0.016664)/1000 0.124978 dollar
Breakeven Annual Cost per bulb(Rounded to nearest cent) $       0.12

jeff jeffy answered 2 years ago
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