Question

Light emitting diode (LEDs) light bulbs have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent light bulb costs $.51 and lasts for 1,000 hours. A 15-watt LED, which provides the same light, costs $3.70 and lasts for 12,000 hours. A kilowatt hour of electricity costs $.127. A kilowatt-hour is 1,000 watts for 1 hour. However, electricity costs actually vary quite a bit depending on location and user type. An industrial user in West Virginia might pay $.04 per kilowatt-hour whereas a residential user in Hawaii might pay $.25. You require a return of 10 percent and use a light fixture 500 hours per year. What is the break-even cost per kilowatt-hour? (Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.)

Answer 1

For solving the break even kilowatt hour cost, now the incandescent bulb has only 500 hours of useful life. In this case, the incandescent bulb has only one year of life left. The break even electricity cost under these circumstances is:

[–$0.51– (60 / 1,000 ×500 ×C)PVIFA10%,1] / PVIFA10%,1 = [–$3.70 – (15 / 1,000 ×500 ×C)PVIFA10%,24] / PVIFA10%,24

Here, PVIFA means Present value of interest factor of Annuity

C = –$0.007131

Unless the electricity cost is negative (Not very likely!), it does not make financial sense to replace the incandescent bulb until it burns out.