Question

ompact fluorescent lamps (CFLs) have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent light bulb costs $.35 and lasts 1,000 hours. A 15-watt CFL, which provides the same light, costs $2.90 and lasts for 12,000 hours. A kilowatt-hour of electricity costs $.111, which is about the national average. A kilowatt-hour is 1,000 watts for 1 hour. If you require a return of 9 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 $

Answer 1

Incandescent Light Bulb
Typical life	1000 hours
Annual usage	500 hours
Life of 1 bulb	2 years	=1000/500
Requirement over 1 year	0.5	=500/1000
Cost of 1 bulb	0.35
Cost over 1 year	0.175	=0.5*0.35
Electricity / watt	0.000111	=0.111/1000
Electricity / hour	0.00666	=0.111/1000*60
Annual electricity consumption	3.33	=0.111/1000*60*500
Annual cost	3.505	=3.33+0.175
Compact fluorescent lamps
Typical life	12000 hours
Annual usage	500 hours
Life of 1 bulb	24 years	=12000/500
Requirement over 1 year	0.041667	=500/12000
Cost of 1 bulb	2.9
Cost over 1 year	0.120833	=0.04167*0.29
Electricity / watt	0.000111	=0.111/1000
Electricity / hour	0.001665	=0.111/1000*15
Annual electricity consumption	0.83	=0.111/1000*15*500
Annual cost	0.953333	=0.83+0.1208

RoR   9%

Year	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
Incandescent Light Bulb
Cost	-0.35		-0.35		-0.35		-0.35		-0.35		-0.35		-0.35		-0.35		-0.35		-0.35		-0.35		-0.35
Electricity usage	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33	-3.33
Total cost	-3.68	-3.33	-3.68	-3.33	-3.68	-3.33	-3.68	-3.33	-3.68	-3.33	-3.68	-3.33	-3.68	-3.33	-3.68	-3.33	-3.68	-3.33	-3.68	-3.33	-3.68	-3.33	-3.68	-3.33	-3.33
Discounted present value of cost	-3.68	-3.05505	-3.09738	-2.57137	-2.607	-2.16427	-2.19426	-1.82162	-1.84687	-1.53322	-1.55447	-1.29048	-1.30837	-1.08617	-1.10123	-0.91421	-0.92688	-0.76947	-0.78014	-0.64765	-0.65663	-0.54511	-0.55267	-0.45881	-0.42093
Total discounted cost	-37.5843
Compact fluorescent lamps
Cost	-2.9
Electricity usage	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83	-0.83
Total cost	-3.7325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325	-0.8325
Discounted present value of cost	-5.12542	-1.08324	-1.0872	-1.03901	-1.04221	-1.00319	-1.00579	-0.97401	-0.97613	-0.9501	-0.95184	-0.93043	-0.93186	-0.91419	-0.91538	-0.90074	-0.90173	-0.88958	-0.89039	-0.88029	-0.88097	-0.87254	-0.87311	-0.86608	-0.86325
Total discounted cost	-27.7487

Hence, we see that, effective annual cost of ILB is $3.5050 while that of a CFL is $0.9533. If we compare the total cost over the life of the instruments, the ILB costs $37.5843 while the CFL costs $27.7487. Note, we compared the life over 24 years since the minimum common life multiple of a ILB (2 years life) and a CFL (24 years life) is 24 years.