A state highway department is planning the construction of a 50 mile, four lane

Question

A state highway department is planning the construction of a 50 mile, four lane toll road. It estimates that the construction cost (t=0) will be $200,000,000 and annual maintenance costs will be $1,000,000 per year forever. In addition, every 10 years in perpetuity, a major resurfacing will have to be carried out at a cost of $10,000,000. It is estimated that $6,000,000 cars and $600,000 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. Interest rate is 7%. Determine what the toll should be for each car and truck to cover all expenses over an infinite planning period. Note: The toll does not vary year-to-year. The answers are Tollcar = $1.87 Tolltruck = $7.48. I keep getting numbers that are too high using capitalized cost formulas I have found. I am looking for an explanation/workout of this problem.

Explanation / Answer

at t=0

$200,000,000 intial cost

total cost per year =$1,000,000(maintainence costs)+$10,000,000/10 (per year it is given here that it costs 10years so divided by 10 )+4*$6,000,000 (becausecharged to a truck will be four times that of a car.) +$6,000,000

=$32,000,000

total cost per year =$32,000,000

interest rate for total cost =$32,000,000*0.07 =$2,240,000

for calculating the tll for each car

$200,000,000+$32,000,000 =$232,000,000

for car it is =232,000,000/224,000,000 =$1.82

for truck = it is 4 times of car =4*$1.82 =$7.28

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