A state highway department is planning the construction of a toll road. Construc
ID: 2638877 • Letter: A
Question
A state highway department is planning the construction of a toll road. Construction cost will be $200M (at period=year 0). Annual maintenance is estimated to be $1M every year and forever. In addition, every 10 years in perpetuity (=forever), a major resurfacing will have to be carried out at a cost of $10M. It is estimated that 6M cars and 600K trucks will use the road each year and it is decided that the toll charged to a truck will be four times that of a car. MARR is 10%. Determine what minimum toll should be charged to each car and truck to cover all expenses over an infinite planning horizon. [Note: the toll is constant and does not vary year-to-year]
Explanation / Answer
Calculation of all cost incurred at T0:
Total spending at T0 = Construction cost + PV of maintenance cost + PV of refsurfacing cost
Construction cost = 200 M
PV of maintenance cost = A / i = 1 / .10 = 10 M
PV of resurfacing cost:
PV at T1 = A / (1+i)^n = 10000000 / (1+.10)^9 = 4240976
PV at T0 = 4240976 / .10 = 42409762
Total cost at T0 = 200,000,000 + 10,000,000 + 42,409,762 = 252,409,762
Calculation toll collection:
Required annual collection = 252409762 * 10% = 25,240,976
No of cars = 6000000
No of truck = 600,000
Ratio of freight = 1 : 4
Weighted ratio = 6000,000*1 : 600,000*4
Total no of weighted vehicle = 6000,000 + 2400,000 = 8400,000
Toll charge per weighted vehicle = 25240,976 / 8400,000 = 3
Toll charge for car = 3 per car
Toll charge for truck = 3 * 4 = 12 per truck
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