Question

5. A number of intersections on an arterial in the City of Norcross in Metro Atlanta currently have a traffic count of 100,000 cars daily, expected to increase by 1,000 cars/day every year. A consultant for Georgia Department of Transportation has estimated that a new set of traffic signal systems for the intersections will cost $700,000 and save each car passing through an average of $0.005 in fuel, wear and tear, and time. It will cost $45,000/year to operate the systems. If the interest rate is 5% are expected to last for 15 years, what is the net present worth of the facility? Assume that costs and savings occur at the end of the year. Hint: The net present worth is the difference between the present worth of costs and the present worth of benefits. (10 points)

Answer 1

Working notes:

• Annual fuel savings = Q x $0.005 x 365, where Q: Number of cars per day and assuming 365 days a year
• Starting year 2, Q_N = Q_(N-1) + 1,000, where Q1 = 100,000 + 1,000 = 101,000
• Annual net benefit (NAB) = Annual fuel savings - Annual cost
• PV Factor in year N = (1.05)^-N.

Net present worth (NPW) of NAB is computed as follows.

Year	Q	Saving	Cost	NAB	PV Factor @5%	Discounted NAB
0			7,00,000	-7,00,000	1.0000	-7,00,000
1	1,01,000	1,84,325	45,000	1,39,325	0.9524	1,32,690
2	1,02,000	1,86,150	45,000	1,41,150	0.9070	1,28,027
3	1,03,000	1,87,975	45,000	1,42,975	0.8638	1,23,507
4	1,04,000	1,89,800	45,000	1,44,800	0.8227	1,19,127
5	1,05,000	1,91,625	45,000	1,46,625	0.7835	1,14,885
6	1,06,000	1,93,450	45,000	1,48,450	0.7462	1,10,776
7	1,07,000	1,95,275	45,000	1,50,275	0.7107	1,06,798
8	1,08,000	1,97,100	45,000	1,52,100	0.6768	1,02,947
9	1,09,000	1,98,925	45,000	1,53,925	0.6446	99,221
10	1,10,000	2,00,750	45,000	1,55,750	0.6139	95,617
11	1,11,000	2,02,575	45,000	1,57,575	0.5847	92,131
12	1,12,000	2,04,400	45,000	1,59,400	0.5568	88,760
13	1,13,000	2,06,225	45,000	1,61,225	0.5303	85,501
14	1,14,000	2,08,050	45,000	1,63,050	0.5051	82,351
15	1,15,000	2,09,875	45,000	1,64,875	0.4810	79,308
					NPW of NAB =	8,61,647