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Two traffic signal systems are being considered for an intersection. One system

ID: 2719899 • Letter: T

Question

Two traffic signal systems are being considered for an intersection. One system costs $32,000 for installation and has an efficiency rating of 81%, requires 27 kW power (output), incurs a user cost of $0.25 per vehicle, and has a life of 9 years. A second system costs $46,000 to install has an efficiency rating of 88%, requires 34 kW power (output has a user cost of $0.22 per vehicle, and has a life of 14 years Annual maintenance costs are $80 and $100 respectively. MA-12% per year. How many vehicles must use the intersection to Justify the second system when electricity costs $0.07/kWh? Assume salvage value for each system equals zero. Project the difference in the user cost as savings for the second system. There are approximately 8,760 hours/year. Click the icon to view the interest and annuity table for discrete compounding when the MARR is 12% per year. At leastvehicles per day must use the intersection to justify the second system. (Round up to the nearest whole number.)

Explanation / Answer

Unit cost=$0.07/KWh

Let number of vehicles per year be “n”

Total Electricity Cost=0.07*Power*efficiency*hours/year*Number of years

For System 1

P.V of Total cost=Installation cost+ (user cost*N*+Maintenance cost)*AnnuityFactor (12% for 9 years)

P.V of Total cost=32000+(0.25*N+80)*5.328

Total Electricity cost=0.07*0.81*27*8760*9=120696.156

For intersection to justify the system

Total Electricity cost= P.V of Total cost

32000+(0.25*N+80)*5.328=120696.156

N=(((120696.156-32000)/5.328)-80)/0.25=66268.7 vehicle per year

For System 2

P.V of Total cost=Installation cost+ (user cost*N*+Maintenance cost)*AnnuityFactor (12% for 14 years)

P.V of Total cost=46000+(0.22*N+100)*6.628

Total Electricity cost=0.07*0.88*34*8760*14=256857.216

For intersection to justify the system

Total Electricity cost= P.V of Total cost

46000+(0.22*N+100)*6.628=256857.216

N=(((120696.156-46000)/6.628)-100)/0.22=50771.7 vehicle per year

Since the 2nd system requires less vehicle per year for intersection to justify the system

Number of less vehicle required by system 2=66268.7-50771.7=15497 vehicle

Cost saving=Vehicle Saving*cost=15497*0.22 per year=$3409 per year