Question

25) You are comparing LED and CFL bulbs. A 100 watt CFL bulb costs $1.00 and lasts 1,500 hours, while a comparable LED bulb of 15 watts costs $3.00 and lasts 4,000 hours. There are 1,000 watt in a kilowatt and a unit of electricity (1,000 watts-hour) costs 12 cents. If you use each bulb for 500 hours in a year and require a return of 15% what are the equivalent annual cost of each bulb?

Please show the calculations. Thank you in advance :)

Answer 1

Annual Cost of a bulb = No. of hours used * Cost per unit / (No. of units consumed per hour)

Annual cost of CFL = 500*0.12*100/1000 = $6

Life of CFL bulb at the current rate of consumption = 1500/500 = 3 years

Annual cost of LED = 500*0.12*15/1000 =$0.9

Life of LED bulb at the current rate of consumption = 4000/500 = 8 years

PV of future cash-flows =

where n is the number of future cash-flows

A is the amount of annual cash-flow

I is the rate of interest

NPV of Cash-flows = Initial investment + PV of future cash-flows

NPV of CFL Cash-flows = -1 + -6*[(1.15^3 -1)/(0.15*(1.15^3)]

NPV of CFL Cash-flows = -$14.70

NPV of LED Cash-flows = -3 + -0.9*[(1.15^8 -1)/(0.15*(1.15^8)]

NPV of LED Cash-flows = -$7.04

Equivalent annual cost =

Equivalent annual cost  of CFL = (-14.70*0.15)/(1-(1+0.15)^(-3))

Equivalent annual cost  of CFL = -$6.44

Equivalent annual cost  of LED = (-7.04*0.15)/(1-(1+0.15)^(-8))

Equivalent annual cost  of LED = -$1.57