Question

Compact fluorescent lamps (CFLs) have become more popular in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent light bulb costs $0.65 and lasts 1,040 hours. A 15-watt CFL, which provides the same light, costs $3.50 and lasts for 13,000 hours. Assume a kilowatt-hour of electricity costs $0.103. A kilowatt-hour is 1,000 watts for 1 hour. Required: If you require a 10 percent return and use a light fixture 520 hours per year, what is the equivalent annual cost of each light bulb? (Do not include the dollar signs ($). Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16)) EAC Compact fluorescent lamps $ _____ 60-watt incandescent light bulb $______

Answer 1

Solution:
		Equivalent annual cost
	60 watt incandescent light bulb $	-3.59
	Compact Fluorescent Lamps        $	-1.19
Working Notes:
	Particulars	60 watt incandescent light bulb	Compact Fluorescent Lamps
		1Bulb x 60 (Watts Each) = 60 Watt	1CFL x 15 (Watts Each) = 15 Watt
	Q	60 Watts / 1000 = 0.06 kw (Kilowatt)	15 Watts / 1000 = 0.015 kw (Kilowatt)
	W	0.06 kw x 520 hrs per year = 31.2 kwh (Kilowatt/Hour)	0.015 kw x 520 hrs per year = 7.8 kwh (Kilowatt/Hour)
a.	Per Annum Operating Cost ( Q x W)	31.2 kwh x $0.103 = $3.2136	7.8 kwh x $0.103 = $0.8034
I	Cost Per CFL/bulb	$0.65	$3.50
	Life (as per use 520 hrs a year)	1040/520 = 2 year	13000/520=25 year
	Cost of Capital	10%	10%
II	Cumulative PVF @ 10 %
	2 year	1.735537190
	25 year		9.077040018
	Equivalent Annual Cost ( a + (I/II) )	($3.2136 + (0.65 / 1.73553719)) = $ 3.59	($0.8034+ ($3.50/ 9.0770400182)) = $1.19
	Equivalent Annual Cost	$3.59	$1.19
	Hence, Equivalent Annual cost is negative as it shows cash out flows.
	Equivalent Annual Cost	-3.59	-1.19
Notes:	Equivalent Annual Cost = Per Annum Operating Cost + (Cost Per CFL/bulb /Cumulative PVF @ 10 %)
	Cumulative PVF @ 10% for 1 to 2th is calculated = (1 - (1/(1 + 0.10)^2) ) /0.10 = 1.73553719
	Cumulative PVF @ 10% for 1 to 25th is calculated = (1 - (1/(1 + 0.10)^25)) /0.10 = 9.077040018
Please feel free to ask if anything about above solution in comment section of the question.