Question

Compact fluorescent lamps (CFLs) have become more popular in recent years, but do they make financial sense? Suppose a typical 60-watt incandescent light bulb costs $0.37 and lasts 1,000 hours. A 15-watt CFL, which provides the same light, costs $3.00 and lasts for 12,000 hours. A kilowatt-hour of electricity costs $0.113, 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 light bulb?

(Negative amounts should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places. (e.g., 32.16))

	Equivalent annual cost
60-watt incandescent light bulb	$
Compact fluorescent lamps

Answer 1

Answer : Calculation of Equivalent Cost

---> 60-watt incandescent light bulb

Given thet 60-watt incandescent light bulb last for 1000 hours

If use of Light fixtures is 500 hours per year

Then Number of year = 1000 / 500

= 2 years

Power Usage per years = 60 watts * 500 per years = 30,000 watts per year

Since Electricity cost is given as Kilowatt hours therefore 1 Kilowatt = 1000 watts

Therefore 30000 watts = 30 kilowatt

therefore Total Annual cost = 30 * $0.113 = $3.39

Now we will calculate NPV

NPV = -0.37 (Initial cost) - [3.39 ( Annual cost )* Present value annuity factor for 2 years @ 10 %]

= -0.37 - [ 3.39 * 1.73554]

= -0.37 - [5.8835]

= - 0.37 - 5.8835

= - 6.2535

Equated Annual Cost = NPV / (Present value annuity factor for two years @ 10%)

= -6.2535 / 1.73554

= - $3.6032

---> Compact Fluorescent

Given thet Compact Fluorescent last for 12000 hours

If use of Light fixtures is 500 hours per year

Then Number of year = 12000 / 500

= 24 years

Power Usage per years = 15 watts * 500 per years = 7500 watts per year

Since Electricity cost is given as Kilowatt hours therefore 1 Kilowatt = 1000 watts

Therefore 7500 watts = 7.5 kilowatt

therefore Total Annual cost = 7.5 * $0.113 = $0.8475

Now we will calculate NPV

NPV = -3 (i.e.Initial cost) - [0.8475(i.e. Annual cost )* Present value annuity factor for 24 years @ 10 %]

= - 3 - [ 0.8475 * 8.984744]

= - 3 - [7.614571]

= - 3 - 7.614571

= - 10.614571

Equated Annual Cost = NPV / (Present value annuity factor for 24 years @ 10%)

= -10.614571 / 8.984744

= - $ 1.1814