Light emitting diode(LED) light bulbs have become required in recent years, but do they make financial sense?

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Light emitting diode (LED) light bulbs have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent light bulb costs $.42 and lasts for 1,000 hours. A 15-watt LED, which provides the same light, costs $3.25 and lasts for 12,000 hours. 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 return of 11 percent, 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.)

 

To determine the cost per kilowatt-hour at which it makes financial sense to replace incandescent bulbs with LED bulbs, we need to compare the costs of operating the two types of bulbs over their respective lifetimes.

Let’s calculate the costs for both types of bulbs:

1. Incandescent bulb:
The cost of a 60-watt incandescent bulb is $0.42, and it lasts for 1,000 hours. We’re assuming that the average bulb has 500 hours remaining. Therefore, the cost of operating the incandescent bulb over its remaining life is:
Cost of operating = Cost of bulb + (Energy consumption per hour * Remaining hours * Cost per kilowatt-hour)

The energy consumption per hour for the incandescent bulb is 60 watts, which is 0.06 kilowatts.

2. LED bulb:
The cost of a 15-watt LED bulb is $3.25, and it lasts for 12,000 hours. We’re assuming that the average bulb has 500 hours remaining. Therefore, the cost of operating the LED bulb over its remaining life is:
Cost of operating = Cost of bulb + (Energy consumption per hour * Remaining hours * Cost per kilowatt-hour)

The energy consumption per hour for the LED bulb is 15 watts, which is 0.015 kilowatts.

Now, we can set up an equation to determine the cost per kilowatt-hour at which the two options have the same cost:

Cost of operating incandescent bulb = Cost of operating LED bulb

($0.42) + (0.06 * 500 * Cost per kilowatt-hour) = ($3.25) + (0.015 * 500 * Cost per kilowatt-hour)

Now we can solve this equation for the cost per kilowatt-hour.

$0.42 + 30 * Cost per kilowatt-hour = $3.25 + 7.5 * Cost per kilowatt-hour

22.5 * Cost per kilowatt-hour = $3.25 – $0.42

22.5 * Cost per kilowatt-hour = $2.83

Cost per kilowatt-hour = $2.83 / 22.5

Cost per kilowatt-hour ≈ $0.126044

Therefore, at a cost per kilowatt-hour of approximately $0.126044 or lower, it makes financial sense to replace incandescent bulbs with LED bulbs, assuming a required return of 11 percent.