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 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 $______

Explanation / Answer

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.

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