Question

Light-emitting diode (LED) light bulbs have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incadescent light 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. Suppose you have a residence with a lot of incandescent bulbs that are used on average 500 hours a year. The average bulb will be about halfway through its life, so it will have 500 hours remaining (and you can’t tell which bulbs are older or newer). If you require a 10 percent return, at what cost per kilowatt-hour does it make sense to replace your incandescent bulbs today? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 6 decimal places, e.g., 32.161616.)

FIND BREAK-EVEN COST PER KWH

Answer 1

In order to calculate the cost per kilowatt hour for replacing first we must know the 60 watt incandescent bulb present cost value

Given the average usage is 500 hours and the 60 watt bulb will have a normal duration of 2 years as per the average usage so this is the last year for its usage

The cost incurred in using them is [-$.45-(60/1000*500)*$1.21] = -$36.75

So inorder to replace them will 7 watt bulbs with a return 10% will be [-$2.25-(7/1000*500)*c*PVIFA(10%,80)]/PVIFA(10%,80) which will be equal to 10.435683

Here c = cost per kwh

PVIFA(10%,80) refers to return of 10% for a period of 80 years (40000/500) as the average usage per year is 500 hours and the life time of 7 watt bulb is 40000 hours.

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