The City of Washington is considering adding new buses for its current mass-tran
ID: 1221260 • Letter: T
Question
The City of Washington is considering adding new buses for its current mass-transit system that links from the Tacoma International Airport to clustering city destinations on non-stop basis. The total investment package is worth $10 million and expected to last 10 years with a salvage value of $850, 000. The annual operating and maintenance costs for buses would be $5 million during the first year and will grow by 5% each year over the previous year's O&M; costs thereafter. If the system is used for 800, 000 trips per year, what would be the fair price to charge per trip? Assume that the City of Washington uses 5% interest rate for any city-sponsored project. Assume the fare will be the same for all destinations.Explanation / Answer
We first find the present worth (PW) of costs, and then the equivalent uniform annual cost (EUAC).
PW of costs is computed as follows.
Note that salvage value is deducted from year 10 O&M costs.
So, EUAC ($) = PW of costs x A/P(5%, 10)**
= 57,097,221 x 0.13
= 7,422,634
Price per trip = EUAC ($) / Trips per year = $7,422,634 / 800,000
= $9.28 per trip
Year Cost ($) Discount factor @5% Discounted cost ($) (A) (B) (A) x (B) 0 100,00,000 1.0000 100,00,000 1 50,00,000 0.9524 47,61,905 2 52,50,000 0.9070 47,61,905 3 55,12,500 0.8638 47,61,905 4 57,88,125 0.8227 47,61,905 5 60,77,531 0.7835 47,61,905 6 63,81,408 0.7462 47,61,905 7 67,00,478 0.7107 47,61,905 8 70,35,502 0.6768 47,61,905 9 73,87,277 0.6446 47,61,905 10 69,06,641 0.6139 42,40,078 PW ($) = 570,97,221