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.)

Answer 1

One 7- watt LED bulb lasts for 40,000 hours but costs $2.25 per bulb.

Meanwhile, the average incandescent bulb at the residence halfway through its life and has 500 hours of its life remaining.

If incandescent bulbs are kept, they will need 500*60/1000 = 30 kilowatt hours (or kwh) per bulb. Kwh = (watts * time in hours) / 1000

If the incandescent bulbs were replaced by the LED bulbs, the next 500 hours will consume only 500*7/100 or 3.5 kwh

If 10% rate of return is required, the following equation could be used to find out the breakeven cost per kilowatt hour:

Let's say the cost of kilowatt hour is x. Since 10% return is required

Hence, 30x + $0.45 =  (3.5x + $2.25) * 1.1

30x + $0.45 = 3.85x +$2.475

26.15x = 2.025

x= 2.025/26.15 = $0.077438

Hence the cost per kilowatt-hour at which make the resident will make a 10% return on replacing her/his incandescent bulbs is $0.077438