Question

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 $.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. If you require a 10 percent return and use a light fixture 500 hours per year, what is the equivalent annual cost of each lightbulb?

Answer 1

The equivalent annual cost of the incandescent bulb is $3.30 and the equivalent annual cost of the LED bulb is $2.14.

Step-by-step explanation:

The equivalent annual cost of each lightbulb can be calculated by considering the initial cost, operating cost, and lifespan of the bulbs.

For the 60-watt incandescent bulb:

• Initial cost = $0.45
• Operating cost = (0.06 kWh/hour × $0.121/kWh × 500 hours/year) = $3.03/year
• Lifespan = 1000 hours

Using the formula for Equivalent Annual Cost (EAC):

EAC = (Initial cost + Annual operating cost) / (1 + Discount rate)
EAC = ($0.45 + $3.03) / (1 + 0.10) = $3.30

For the 7-watt LED bulb:

• Initial cost = $2.25
• Operating cost = (0.007 kWh/hour × $0.121/kWh × 500 hours/year) = $0.04/year
• Lifespan = 40,000 hours

EAC = ($2.25 + $0.04) / (1 + 0.10) = $2.14

Therefore, the equivalent annual cost of the incandescent bulb is $3.30 and the equivalent annual cost of the LED bulb is $2.14.