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 $.47 and lasts 1,000 hours. A 15-watt LED, which provides the same light, costs $3.50 and lasts for 12,000 hours. A kilowatt-hour of electricity costs $.123. A kilowatt-hour is 1,000 watts for 1 hour. If you require a return of 9 percent and use a light fixture 500 hours per year, what is the equivalent annual cost of each light bulb? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) 60-watt incandescent light bulb LED light bulb

Answer 1

To get the equivalent annual cost for each bulb we need to first find the NPV of each bulb and then annualize it.

The NPV of each bulb is calculated using excel, we have been given the initial cost and have calculated the annual electricity cost for each bulb based on 500 hours usage in year.

Calculation in excel

A B C D F 1 2 Particulars 3 Watt 4 Life span in hours 5 Initial cost 6 Light bulb LED Bulb 601 15 1000 12000 S 0.47 $ 3.50 7 0.123 S 0.123 8 Eletricity cost per KWH S 9 10 Conversion in KWH 11 KWH used in 1 year 500 hours/year 12 Electricity cost per year 13 0.06 30 3.69S 0.015=B5/1000 7.5 =B12*500 0.92 =B13-B10 C5/1000 =C12.500 =C13 C10 S

For calculating the Equivalent Annual Cost we need to convert the net present value to annual terms which we can do by treating the net present value obtained as the present value of an ordinary annuity of duration equal to the life of each bulb.

Equivalent Annual Cost =NPV × r/(1 − (1 + r)^-n )

We have calculated the NPV using excel formula of NPV

14 15 Rate of return 16 Life of bulb in years =C6/500 18 24 25 26 27 28 24 =B6/500 Light bulb LED Bulb Year 0 S 0.47S 3.50 Year 1 s 3.691 S 0.92 Year 21 $ 3.69 $ 0.92 Year 3 $ 0.92 Year 4 0.92 Year 51 0.92 Year 6 0.92 Year 7 $ 0.92 Year 8 S 0.92 Year 9 $ 0.92 Year 10 S 0.92 Year 11 $ 0.92 Year 12 S 0.92 Year 13 $ 0.92 Year 14 S 0.92 Year 15 $ 0.92 Year 16 $ 0.92 Year 17 IS 0.92 Year 18 0.92 Year 19 $ 0.92 Year 20 $ 0.92 Year 21 IS 0.92 Year 22 S 0.92 Year 23 S 0.92 Year 24 0.92 6.39 11.43'NPV(B17,B20:B22) wwwwwwwww NPV ENPV(B17,C20:044) A $ 3.63 $ 1.18 =B45*(B17/(1-(1+B1714-B18)) =C45*(B17/(1-(1+B17C18) 45 Equivalent Annual Cost 46

So the Equivalent Annual Cost for 60 – Watt incandescent light bulb is $ 3.36 and for LED Light bulb is $ 1.18