Question

Light emitting diodes (LED) light bulbs have become required in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent light bulb costs $.49 and lasts 1,000 hours. A 15-watt LED, which provides the same light, costs $3.60 and lasts for 12,000 hours. A kilowatt-hour of electricity costs $.125. A kilowatt-hour is 1,000 watts for 1 hour. If you require a return of 11 percent and use a light fixture 500 hours per year, what is the equivalent annual cost of each light bulb?

Answer 1

EAC of incandescent light bulb = - $ 4.04

EAC of LED light bulb = - $ 1.79

LED light bulb is preferable as it has lower EAC.

Explanation:

EAC = Asset price x Discount rate/ [1- (1+ Discount rate)^{-no. of years}] + Annual cost

Computation of EAC of incandescent light bulb:

Annual energy consumption = 60-watt hour x 500 hours

                                         = 30,000 watt- hours or 30 kilowatt-hours annually

1 kilowatt-hours = $ 0.125

Annual cost of energy = 30 x $ 0.125 = $ 3.75

Number of years to run = 1,000 hours/500 hours = 2 years

EAC = - $ 0.49 x 0.11 / [1 – (1+0.11)^-2] - $ 3.75

        = - $ 0.0539/ [1 – (1.11)^-2] - $ 3.75

       = -$ 0.0539/ (1 – 0.811622433244055) - $ 3.75

        = - $ 0.0539/0.188377566755945 - $ 3.75

        = - $ 0.286127488151659 - $ 3.75

        = - $ 4.036127488151659 or - $ 4.04

Computation of EAC of LED light bulb:

Annual energy consumption = 15-watt hour x 500 hours

                                         = 7,500 watt- hours or 7.5 kilowatt-hours annually

1 kilowatt-hours = $ 0.125

Annual cost of energy = 7.7 x $ 0.125 = $ 0.9375

Number of years to run = 12,000 hours/500 hours = 6 years

EAC = - $ 3.60 x 0.11 / [1 – (1+0.11)^-6] - $ 0.9375

        = - $ 0.396/ [1 – (1.11)^-6] - $ 0.9375

       = -$ 0.396/ (1 – 0.534640836088792) - $ 0.9375

        = - $ 0.396/0.465359163911208 - $ 0.9375

        = - $ 0.850955628920542 - $ 0.9375

        = - $ 1.788455628920540 or - $ 1.79