Compact fluorescent lamps (CFLs) have become required in recent years, but do th
ID: 2716138 • Letter: C
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 $.43 and lasts 1,000 hours. A 15-watt CFL, which provides the same light, costs $3.30 and lasts for 12,000 hours. A kilowatt-hour of electricity costs $.119, 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.)please show calculations and formulas.
Explanation / Answer
Annual cost CFL Annual cost Incandescent Light CFL 15 watt Incandescent Light 60 watt Yearly hours 500 Yearly hours 500 Yearly KWH 7.5 Yearly KWH 30 Electricity cost/KWH 0.119 Electricity cost/KWH 0.119 Annual electricity cost 0.8925 Annual electricity cost 3.57 Incandescent Light EAC Year Investment Annual electricity cost Total Cost Discount factor @10% PV of costs Year 1 0.43 3.57 4.00 1.000 4.00 Year 2 3.57 3.57 0.909 3.25 Year 3 0.43 3.57 4.00 0.826 3.31 Year 4 3.57 3.57 0.751 2.68 Year 5 0.43 3.57 4.00 0.683 2.73 Year 6 3.57 3.57 0.621 2.22 Year 7 0.43 3.57 4.00 0.564 2.26 Year 8 3.57 3.57 0.513 1.83 Year 9 0.43 3.57 4.00 0.467 1.87 Year 10 3.57 3.57 0.424 1.51 Year 11 0.43 3.57 4.00 0.386 1.54 Year 12 3.57 3.57 0.350 1.25 Year 13 0.43 3.57 4.00 0.319 1.27 Year 14 3.57 3.57 0.290 1.03 Year 15 0.43 3.57 4.00 0.263 1.05 Year 16 3.57 3.57 0.239 0.85 Year 17 0.43 3.57 4.00 0.218 0.87 Year 18 3.57 3.57 0.198 0.71 Year 19 0.43 3.57 4.00 0.180 0.72 Year 20 3.57 3.57 0.164 0.58 Year 21 0.43 3.57 4.00 0.149 0.59 Year 22 3.57 3.57 0.135 0.48 Year 23 0.43 3.57 4.00 0.123 0.49 Year 24 3.57 3.57 0.112 0.40 90.84 9.883 37.509 Annuity factor for discount@100% =9.883 PV of costs = 37.509 EAC = PV of cost/Annuity factor =37.509/9.883 $ 3.80 so EAC of Incandescent Light $ 3.80 CFL EAC Year Investment Annual electricity cost Total Cost Discount factor @10% PV of costs Year 1 3.3 0.8925 4.1925 1.000 4.19 Year 2 0.8925 0.8925 0.909 0.81 Year 3 0.8925 0.8925 0.826 0.74 Year 4 0.8925 0.8925 0.751 0.67 Year 5 0.8925 0.8925 0.683 0.61 Year 6 0.8925 0.8925 0.621 0.55 Year 7 0.8925 0.8925 0.564 0.50 Year 8 0.8925 0.8925 0.513 0.46 Year 9 0.8925 0.8925 0.467 0.42 Year 10 0.8925 0.8925 0.424 0.38 Year 11 0.8925 0.8925 0.386 0.34 Year 12 0.8925 0.8925 0.350 0.31 Year 13 0.8925 0.8925 0.319 0.28 Year 14 0.8925 0.8925 0.290 0.26 Year 15 0.8925 0.8925 0.263 0.24 Year 16 0.8925 0.8925 0.239 0.21 Year 17 0.8925 0.8925 0.218 0.19 Year 18 0.8925 0.8925 0.198 0.18 Year 19 0.8925 0.8925 0.180 0.16 Year 20 0.8925 0.8925 0.164 0.15 Year 21 0.8925 0.8925 0.149 0.13 Year 22 0.8925 0.8925 0.135 0.12 Year 23 0.8925 0.8925 0.123 0.11 Year 24 0.8925 0.8925 0.112 0.10 24.72 9.883 12.121 Annuity factor for discount@100% =9.883 PV of costs = 12.121 EAC = PV of cost/Annuity factor =12.121/9.883 = $ 1.23 so EAC of CFL $ 1.23
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