Question

Compact fluorescent lamps (CFLs) have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent lightbulb costs $.47 and lasts for 1,000 hours. A 15-watt CFL, which provides the same light, costs $3.50 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 9 percent return, at what cost per kilowatt-hour does it make sense to replace your incandescent bulbs today? (Negative amount 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

Power consumed by an incandescent bulb per hour= 60/1000 kWh = 0.06 kW

Power consumed by CFL per hour= 15/1000 = 0.015 kW

Average life remaining for an incandescent bulb = 500 hours

So, power saved by replacing a bulb with a CFL= 500*(0.06-0.015)= 22.5 kWh

Let the cost of electricity at which it would make to sense to replace bulb with CFL be x

So, amount saved by replacing each bulb= 22.5/x

Cost of each CFL= $3.50

For 9 percent return, (22.5/x - 3.5)/3.5=0.09

So, x= $ 5.897772/kWh