Question

A city govt. is planning to run bus service on a new route. A total of 8 buses will be purchased at a price of $25,000 each. The city has made a contract with maintenance agency for the upkeep of the fleet at the cost of $1,500 annually. Every two years (including the last year), the buses will be repainted at the cost of $1,000 for the whole fleet. If the service life of the bus is 8 years, and each year the number of passengers using the service will be 12,000. Using AE analysis, how much should be the fare charged per passenger to cover the cost of the bus service given that the MARR is estimated to be 6%. (select the closest answer)

$4.4

$3.9

$5.2

$2.9

$6.2

Answer 1

Solution :-

Interest Rate Per Year = 6%

Interest Rate for 2 Years = ( 1 + 0.06 )² - 1 = 0.1236 = 12.36%

Now Initial Cost = $25,000 * 8 = $200,000

Present Value of Annual Maintenance Cost = $1,500 * PVAF ( 6% , 8 ) = $1,500 * 6.2098 = $9,314.69

Present Value of Repainted Cost = $1,000 * PVAF ( 12.36% , 4 ) = $1,000 * 3.0144 = $3,014.46

Present Value of Total Cost in 8 Years = $200,000 + $9,314.69 + $3,014.46 = $212,329.15

Now Equivalent Annual Cost = Present Worth / PVAF ( r , n )

= $212,329.15 / PVAF ( 6% , 8 )

= $212,329.15 / 6.2098

= $34,192.63

Now Number of Passengers per year = 12,000

Therefore Now Cost Charged Per Passenger = $34,192.63 / 12,000 = $2.9

Therefore Correct Answer is (d)

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