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 $.46 and lasts for 1,000 hours. A 15-watt LED, which provides the same light, costs $3.45 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.)

Answer 1

Solution :-

Required Return = 11%

Let Us assume the Break even Cost be X

In case of 60 Watt Bulb

A bulb used in a year = 500 hours

Total Hours = 1000

Now therefore total Life = 2 Years

Present Value of Cost = - $0.46 - ( 60 * C * 500 / 1000 ) * PVAF (11% , 2 )

= - $0.46 - 51.376 C

In case of 15 Watt Bulb

A bulb used in a year = 500 hours

Total Hours = 12000

Now therefore total Life = 24 Years

Present Value of Cost = - $3.45 - ( 15 * C * 500 / 1000 ) * PVAF (11% , 24 )

= - $3.45 - 62.611 C

Now Equivalent Annual Cost of 30 Watt bulb =

Present Worth / PVAF ( 11% , 2 ) = [ - $0.46 - 51.376 C ] / 1.7125 = - $0.2686 - 30C

Now Equivalent Annual Cost of 15 Watt bulb =

Present Worth / PVAF ( 11% , 24 ) = [ - $3.45 - 62.611 C ] / 8.348 = - $0.41327 - 7.5C

Now Take both Equivalent Annual Cost Equal =

- $0.2686 - 30C = - $0.41327 - 7.5C

0.144656 = 22.5C

C = $ 0.00643 Per Watt .

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