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.) Please find break even cost

Answer 1

SOLUTION:

Given That data 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.

So

Annual cost:

incandescent light bulb:

500 hours per year * 60 watts = 30000 watts

= 30000 watts / 1000 hours

= 30kwh.

operating cost = 30kwh * $0.121

= $3.63

life = 1000 hours / 500 hours

= 2 years

annuity = [1-(1/ (1+9%)²)] / 9%

= 1.71

EAC = ($0.45 / 1.7127) + $3.63

= $3.893.

LED light bulb:

500 hours * 7 watts = 3500 watts

3500 watts / 1000 watts

= 3.5 kwh

operating cost = 3.5 * $0.121

= 0.4235

life = 4000 hours / 500 hours

= 8 years

annuity = [1-(1/(1+9%)²⁴] / 9%

= $9.711

EAC = ($2.25 / $9.711) + $0.915

= $12.876