Question

Light emitting diodes (LED) light bulbs have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent light bulb costs $.39 and lasts 1,000 hours. A 15-watt LED, which provides the same light, costs $3.10 and lasts for 12,000 hours. A kilowatt-hour of electricity costs $.115. A kilowatt-hour is 1,000 watts for 1 hour. If you require a return of 11 percent and use a light fixture 500 hours per year, what is the equivalent annual cost of each light bulb? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Answer 1

Answer>

Equivalent annual cost is the cost of owning, maintaining and operating an asset over the due course of its life.It is used to compare the cost effectiveness of assets having unequal lifespans.

EAC = cost of life + cost of usage

Required rate of return = 11%

Considering the 60-watt incandescent light bulb

:Average use = 500 hours per year

Total life = 1000 hours = 2 years

Annuity factor = (1 - ((1/1+0.11)^2))/0.11 =

(1-((1/1.11)^2))/0.11

= (1-0.812)/0.11 = 1.709

Total cost of life = 0.39 / 1.709 = 0.228

total electricity usage = 60*500 =  30000 Watt hr per year = 30KWh per year

Cost per KWh = 0.115

Hence electricity cost = 30*0.115 per year = 3.45 per year

Hence total cost of usage of incandescent bulb = $3.45 + $0.228 = $3.678 per year

Considering the 15-watt LED

:Average use = 500 hours per year

Total life = 12000 hours = 24 years

Annuity factor = (1 - ((1/1+0.11)^24))/0.11 =

(1-((1/1.11)^24))/0.11

= (1-0.082)/0.11 = 8.345

Total cost of life = 3.10 / 8.345 = 0.371

total electricity usage = 15*500 = 7500 Watt hr per year = 7.5 KWh per year

Cost per KWh = 0.115

Hence electricity cost = 7.5*0.115 per year = 0.8625 per year

Hence total cost of usage of incandescent bulb = $0.8625 + $0.371 = $1.233 per year

Hence the EAC of light bulb is $3.68 while the EAC of LED is $1.23.

Hope this answers your question.