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.) Break-Even Cost?

Answer 1

A 7- watt LED bulb lasts for 40,000 hours and hence save electricity in the long-term. However, it costs $2.25 per bulb, which is much costlier than incandescent bulbs

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 [(number of hours in life left) * watt] / 1000 (formula for calculating kwh)

or 500*60/1000 = 30 kilowatt hours (or kwh) per bulb. Kwh = (watts * time in hours) / 1000

Instead, if the incandescent bulbs were replaced by the LED bulbs, the next 500 hours will consume only 500*7/100 or 3.5 kwh (using the above formula)

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

(kilowatt hours of incandescent bulb * cost of electricity per kilowatt) + cost of purchasing incandescent bulb should be equal to [(kilowatt hours of LED bulb * cost of electricity per kilowatt ) + cost of purchasing LED bulb] *1.10 (which is the 10% rate extra saving that is required)

Let's say the cost of kilowatt hour is x.

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 of electricity at which the resident will make a 10% return on replacing her/his incandescent bulbs is $0.077438 . The breakeven cost with 10% return rate is still much lesser than the $0.121 per kwh electricity rate.

Hence, although LED bulbs are much more expensive compared to incandescent bulbs, they save a lot more in electricity costs in the long-term.