Question

Light-emitting diode (LED) light bulbs have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent bulb costs $.45 and lasts for 1,000 hours. A 7-watt LED, which provides the same light, costs $2.25 and lasts for 40,000 hours. A kilowatt-hour of electricity costs $.121, which is about the national average. A kilowatt-hour is 1,000 watts for 1 hour. However, electricity costs actually vary quite a bit depending on location and user type (you can get information on your rates from your local power company). An industrial user in West Virginia might pay $.04 per kilowatt-hour whereas a residential user in Hawaii might pay $.25. You require a 10 percent return and use a light fixture 500 hours per year. What is the break-even cost per kilowatt-hour? (a negative number should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 6 decimal places).

Answer 1

Answer : 0.0068

Calculation :

For Break Even cost, make EAC of both light bulbs equal solve for cost.

EAC = NPV/PVAF

NPV= - (Initial Price + Cost per year @ PVF)

Cost per year = Kilowatts/Hour * total hours used in a year * cost/kilowatt

Incandescent bulb (t)= 1000/500 = 2

LED (t)= 40000/500 = 80

Kilowatts/hour = W/1000

EAC of 60-watt incandescent light bulb= - (Initial Price + Cost per year @ PVAF)/ PVAF

[- 0.45 - (60/1000*500*C) * (PVAF10%,2)]/(PVAF10%,2) = [-2.25- (7/1000*500*C)(PVAF10%,80)] / (PVAF10%,80)

{- 0.45 - [(60/1000)*500*C] *(1.7355) }/(1.7355) = {-2.25- [(7/1000)*500*C] * (9.9951)]}/ (9.9951)

Solving for C, break even cost per KW hour = $0.0068

Note : We have made two equations and then equated it to soive fir C.