Question

A firm is considering installing occupancy sensors in its eight conference rooms. Each room presently has four 4-lamp fluorescent fixtures with standard F40T12 (full spectrum 40-W, 1.5-inch in tube diameter) lamps. The fixture draws 188 watts (lamps plus ballasts). The lamps operate 10 hours/day, Monday through Friday. With the proposed system, sensors will automatically turn off the lights whenever the room is unoccupied for more than 5 minutes. The firm estimates that this will reduce the lamp operating hours to an average of 7 hours/day. Each conference room requires one occupancy sensor at a cost of $70 for materials plus $10 installation labor. The firm follows a "spot re-lamping policy" meaning that a burnt-out lamp is replaced immediately upon detection. It costs $2 for materials and $5 for labor to replace each burnt-out lamp. The firm believes that the use of occupancy sensors will not affect the average lamp lifetime of 20,000 hours. What is the payback period for the proposed system? Assume the cost of electricity consistent with that in your hometown (105.1 weeks or 2 years based on $0.06/kWh)

Answer 1

Power input, Po = 188 W
intiial working hours, To = 10 hours per day
final working hours, Tf = 7 hours/day
number of bulbs = 4
sensor cost, Cs = $80
repair cost, Cr = $7

Electricity cost = $0.06 kWh

now, savings in one day = Po(To - Tf) = 188*3 =564 Wh
for 4 bulbs, savings = 2.256 kWh / day
as life time opf bulbs does not change
sensor cost for one room = Cs
number of days requireed for coverign cost = n
n*2.256*$0.06 = $80
n = 591.01654 days = 1.61811512 years = 1 year 7 months 12.5214 days = 84.43093 weeks

including cost of lamps
n = 113.98176 weeks