A two-lane highway between two cities, 10 miles apart, is to be converted to a f

Question

A two-lane highway between two cities, 10 miles apart, is to be converted to a four-lane divided freeway. The average daily traffic (ADT) on the new freeway is forecast to average 20,000 vehicles per day over the next 20 years. Trucks represent 5% of the total traffic. Annual maintenance on the existing highway is $1,500 per lane-mile. The existing accident rate is 4.58 million vehicle-miles (MVM). Three alternate plans are under consideration.

Plan A: Improve along the existing development by adding two lanes adjacent to the existing lanes at a cost of $450,000 per mile. This will reduce auto travel time by 2 minutes and truck travel time by 1 minute. The estimated accident rate is 2.50 per MVM. Annual maintenance is $1,250 per lane-mile.

Plan B: Improve the highway along the existing alignment with grade improvements at a cost of $650,000 per mile. Plan B adds two lanes and would reduce auto and truck travel time by 3 minutes each. The accident rate of this improved road is estimated to be 2.40 per MVM. Annual maintenance is $1,000 per lane-mile.

Plan C: Construct a new freeway on a new alignment at a cost of $800,000 per mile. This plan would reduce auto ravel time by 5 minutes and truck travel time by 4 minutes. Plan C is 0.3 miles longer than Plan A or Plan B. The estimated accident rate for C is 2.30 per MVM. Annual maintenance is $1,000 per lane-mile. Plan C also includes abandoning the existing highway with no salvage value.

Incremental Operating Cost

Autos Trucks

Time saving

Autos Trucks

$0.06 per mile $0.08 per mile

$0.03 per minute $0.15 per minute

average incident cost $1,200 per incident
If a 5% interest rate is used, which of these three plans should be adopted?

Explanation / Answer

Solution:

Existing Plan A Plan B Plan C
Length (miles) 10 10 10 10.3
Number of Lanes 2 4 4 4
Average ADT 20,000 20,000 20,000 20,000
Autos 19,000 19,000 19,000 19,000
Trucks(5%) 1,000 1,000 1,000 1,000
Time Savings(minutes)  
Autos 2 3 5
Trucks 1 3 4
Accident Rate/MVM 4.58 2.50 2.40 2.30
Initial Cost per mil (P) - $450,000 $650,000 $800,000
Annual Maintenance per $1,500 $1,250 $1,000 $1,000
lane per mile
Total Annual Maintenance $30,000 $50,000 $40,000 $41,200
EUAC of Initial Cost=(P $0 $360,900 $521,300 $660,850
x miles) (A/P, 5%, 20)
Total Annual Cost of $30,000 $410,900 $561,300 $702,050
EUAC + Maintenance

Annual Incremental Operating Costs due to distance
None for Plans A and B, as they are the same length as existing road.

Plan c Autos 19,000 x 365 x 0.3 mi x $0.06 = $124,830
Trucks 1,000 x 365 x 0.3 mi x $0.18 = $19,710
Total = $144,540/yr

Annual Accident Savings compared to Existing Highway
Plan A: (4.58 — 2.50) X (10^-6) X ( 10 mi) X (365 days) X (20,000 ADT) X ($1,200)
= $182,200

Plan B: (4.53 — 2.40) X (10^-6) X ( 10 mi) X (365 days) X (20,000 ADT) X ($1,200)
= $190,790

Plan c: (4.53 — 2.30) X (10^-6) X ( 10.3 mi) X (365 days) X (20,000 ADT) X ($1,200)
= $205,720

Time Savings Benefits to Road Users compared to Existing Highway

Plan A:

Autos 19,000 x 365 days x 2 min x $0.03 = $416,100

Trucks 1,000 x 365 days x 1 min x $0.15 = $54,750
Total = $470,850

Plan B:

Autos 19,000 x 365 days x 3 min x $0.03 = $624,150

Trucks 1,000 x 365 days x 3 min x $0.15 = $164,250
Total = $788,400

Plan C:

Autos 19,000 x 365 days x 5 min x $0.03 = $1,040,250

Trucks 1,000 x 365 days x 4 min x $0.15 = $219,000

Total = $1,259,250

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