I don\'t understand the formula 15. Compact fluorescent lamps (CFLs) have become

Question

I don't understand the formula

15. Compact fluorescent lamps (CFLs) have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent lightbulb costs $.49 and lasts for 1,000 hours. A 15-watt CFL, which provides the same light, costs $3.60 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 ulbs 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 -0,005007 1 % Explanation: We are again solving for the breakeven kilowatt hour cost, but now the incandescent bulb has only 500 hours of useful life. In this case, the incandescent bulb has only one year of life left. The breakeven electricity cost under these circumstances is: [-$49-(60 / 1,000x 500x C)PVI FA11% 1] / PVI FA11%,1 -|-$3.60-(15 / 1,000x 500x C)PVIFA 11%,24] / PVIFA11%.24 C--$.005007 Unless the electricity cost is negative (Not very likely!), it does not make financial sense to replace the incandescent bulb until it burns out.

Explanation / Answer

the question is trying to find the annual equivalent cost for both-incandescent bulb and CFL

incandescent bulb:

number of kilo watt hours used for incandescent=60*500 as the bulb is running for 500 hours

number of kilo watt hours used =60*500/1000

let c be the cost per kilowatt hour

cost of running the bulb for 1 year=60*500/1000*C

hence, annual equivalent cost=0.49/PVIFA(11%,1)+(60*500/1000*C)=(0.49+(60*500/1000*C)*PVIFA(11%,1))/PVIFA(11%,1)

cfl:

number of kilo watt hours used for cfl=15*500 as the cfl is running for 500 hours

number of kilo watt hours used =15*500/1000

let c be the cost per kilowatt hour

12000 watts will be used in 12000/500=24 years

cost of running the cfl for 24 years=15*500/1000*C

hence, annual equivalent cost=3.6/PVIFA(11%,24)+(15*500/1000*C)=(3.6+(15*500/1000*C)*PVIFA(11%,24))/PVIFA(11%,24)

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