Question

Two routes are under consideration for new highway. The northerly route X would be located about 5 miles from the central business district and would require longer travel distance by local commuter traffic. The southerly route Y would pass directly trough the downtown area and, although its construction cost would be higher, it would reduce the travel time and distance for local commuter. Assume the cost for two route are as follow : Route X Route Y Initial cost Maintenance cost per year Road user cost per year $ 10.000.000 35.000 450.000 $ 15.000.000 55.000 200.000 if the roads are assumed to last 30 year, which route should be accepted using interest rate of 5% per year?

Answer 1

Let us use annual worth method of comparision.

AW of route X = 10,000,000(A/P, 5%, 30) + 35,000 + 450,000

                       = 10,000,000(0.0651) + 35,000 + 450,000

                       = 651,000 + 35,000 + 450,000

                       = $1,136,000

AW of route Y = 15,000,000(A/P, 5%, 30) + 55,000 + 200,000

                       = 15,000,000(0.0651) + 55,000 + 200,000

                       = 976,500 + 55,000 + 450,000

                       = $1,231,500

Since AW of route X is less than route Y, therefore, route X should be accepted.