Question

The estimates shown are for a bridge under consideration. Use the B/C ration method at an interest rate of 6% per year to determine which bridge, if either , should be built.

East Location West Location

Initial Cost, $ 11,000,000 27,000,000

Annual M&O, $/year 100,000 90,000

Benefits $/year 990,000 2,400,000

Disbenefits $/year 120,000 100,000

Life, years infinity infinity

Answer 1

East Location:

Annual worth of net costs = 11,000,000(A/P, 6%, infility) + 100,000

                                   = 11,000,000 * 0.06 + 100,000

                                 = 660,000 + 100,000

                                   = 760,000

Annual worth of net benefits = 990,000 - 120,000 = 870,000

B/C ratio = Annual worth of net benefits / Annual worth of net costs

              = 870,000 / 760,000

              = 1.14

West Location:

Annual worth of net costs = 27,000,000(A/P, 6%, infility) + 90,000

                                   = 27,000,000 * 0.06 + 90,000

                                 = 1,620,000 + 90,000

                                   = 1,710,000

Annual worth of net benefits = 2,400,000 - 100,000 = 2,300,000

B/C ratio = Annual worth of net benefits / Annual worth of net costs

              = 2,300,000 / 1,710,000

              = 1.34

Since the B/C ratio of West Location is greater than East Location, therefore, West Location bridge should be built.