Compact fluorescent lamps (CFLs) have become required in recent years, but do th

Question

Compact fluorescent lamps (CFLs) have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent light bulb costs $.51 and lasts 1,000 hours. A 15-watt CFL which provides the same light, costs $3.70 and lasts for 12,000 hours. A kilowatt-hour of electricity costs $.127, which is about the national average. A kilowatt-hour is 1,000 watts for 1 hour. If you require a return of 10 percent and use a light fixture 500 hours per year, what is the equivalent annual cost of each light bulb? (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Equivalent annual cost 60-watt incandescent light bulb Compact fluorescent lamps References eBook & Resources Learning Objective: 10-04 How to evaluate the equivalent annual cost of a project. Worksheet Section: 10.6 Some Special Cases of Discounted Cash Flow Analysis Difficulty: Intermediate 725

Explanation / Answer

Solution: Equivalent annual cost 60-watt incandescent light bulb $ -4.10 Compact fluorescent lamps          $ -1.36 minus sign shows it cash outflows there is cash outflows only annual cost + purchase cost 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 60 Watts / 1000 = 0.06 kw (Kilowatt) 15 Watts / 1000 = 0.015 kw (Kilowatt) 0.06 kw x 500 hrs per year = 30 kwh (Kilowatt/Hour) 0.015 kw x 500 hrs per year = 7.5 kwh (Kilowatt/Hour) a. Per Annum Operating Cost 30 kwh x $0.127 = $3.81 7.5 kwh x $0.127 = $0.9525 I Cost Per CFL/bulb $0.51 $3.70 Life (as per use 500 hrs a year) 1000/500 = 2 year 12000/500=24 year Cost of Capital 10% 10% II Cumulative PVF @ 10 % 1000 hours/500 hours =2 year 1.735537190 12,000 hours/500 hours =24 year 8.984744020 Equivalent Annual Cost ( a + (I/II) ) [$ 3.81 + (0.51 / 1.7355371901)] = $4.10 [$ 0.9525 + ($ 3.70 / 8.9847440201)] = $1.36 Equivalent Annual Cost -4.10 -1.36 Notes: Cumulative PVF @ 10% for 1 to 2th is calculated = (1 - (1/(1 + 0.10)^2) ) /0.10 = 1.7355371901 Cumulative PVF @ 10% for 1 to 24th is calculated = (1 - (1/(1 + 0.10)^24)) /0.10 = 8.9847440201 Please feel free to ask if anything about above solution in comment section of the question.

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