A traffic intersection currently has a vehicle count of 10,000 cars daily, expected to increase by...

A traffic intersection currently has a vehicle count of 10,000 cars daily, expected to increase by 1,000 per day each year(i.e., it is expected that there will be 11,000 cars per day in 2012, 12,000 cars per day in 2013, etc.). A new traffic signal system being installed at the intersection is estimated to cost $200,000. It is expected to save each car passing through an average of $0.02 worth of fuel, wear and tear, and time. If the system has a 10-year life, at a nominal interest of 5%, compare the present worth of the savings versus the cost of the proposed system. Both annual costs and savings occur at the end of the year. Is this a worthwhile project?

Expert Solution

Formula used,

Where, PV is the present value, FV is the future value, r is the nominal interest rate, n is the number of years

Answer

Present value of the cost,

Year 1

Number of cars per day = 10,000

Number of cars in an year = 3,650,000 (assuming 365 days)

Savings in the year = 73000 (number of cars x 0.02)

Present value of savings = 69523 (73000/1.05)

Similar calculation for all years are done and values are shown below,

The total PV of savings is $794746. This is greater than the present value of costs.

Hence the project is worthwhile.

Rahul Sunny answered 1 year ago

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