The Metropolitan Transit Authority (MTA) has just opened a new subway line (the
ID: 1216540 • Letter: T
Question
The Metropolitan Transit Authority (MTA) has just opened a new subway line (the Orange Line) in its underground transportation network. The Orange Line had a capital investment of $20 million, expected operating and maintenance expenses are $3 million per year, and the final salvage value at the end of a 40-year life is negligible. If the revenue generated by each customer is $3, how many customers per day will be required before the Orange Line can break even? The MTA’s hurdle (interest) rate is 5% compounded annually. Assume there are 365 days in a year
Explanation / Answer
Time = 40 years
R = 5%
Present worth of the new subway line = initial investment + present value of O&M cost - present value of salvage value
Present worth of the new subway line = 20000000 + 3000000*(1-1/(1+R)^40)/R – 0
Present worth of the new subway line = 20000000 + 3000000*(1-1/1.05^40)/.05
Present worth of the new subway line = $71477259.06
Now, we have to calculate the equivalent daily cost (EDC) to calculate the number of customers per day.
Time = 365*40 = 14600 days
Daily Interest rate = 5%/365
Thus,
Present value of all cost = EDC*(1-1/(1+ 5%/365)^14600)/( 5%/365)
71477259.06 = EDC*6311.917
EDC = equivalent daily cost = 71477259.06/6311.917
EDC = $11324.176
Revenue generated per customer = $3
Thus, No. of customers required to achieve break even = 11324.176/3
No. of customers required to achieve break even = 3774.72 or 3775 approx.