Question

A city council considers to construct a new toll bridge across the river. Investment cost of the bridge is estimated to be $7,000,000 with an annual operating and maintenance costs of $130,000 per year. In addition, the bridge must go through a comprehensive maintenance in every fifth year of its 30-year expected life at a cost of $500,000 per occurrence (no cost in year 30). It is expected 200,000 vehicles per year to cross the bridge. The city plans to set the toll-fee as $5 in its first year of operation, and increases it by $0.25 every year. Assume that market value for the bridge at the end of 30 years is zero and a MARR is 10% per year.

a) Should the toll bridge be constructed? Justify your answer using B-C ratio method and show all your calculations.

b) In order to have a B-C ratio of 1 (Break even point), how many vehicle should across the bridge per year?

c) Write down the meaning of B-C ratio calculated in (a) using your own words.

Answer 1

a)

Benefit cost ratio = Annual worth of Benefits / Annual worth of cost

Benefit cost ratio = [1000000 + 5000(A/G,10,30)] / [7000000(A/P,10%,30) + 130000 + 500000(A/F,10%,30)]

Using DCIF Tables

Benefit cost ratio = [1000000 + 5000(8.7262)] / [7000000(0.1061) + 130000 + 500000(0.0061)]

Benefit cost ratio = 1043601 / 875750

Benefit cost ratio = 1.19

b)

In order to estimate the break even number of vehicles(X) we need to consider Benefit cost ratio = 1

1 = [5X+ 0.25X(A/G,10,30)] / [7000000(A/P,10%,30) + 130000 + 500000(A/F,10%,30)]

1 = [5X+ 0.25X(8.7262)] / [7000000(0.1061) + 130000 + 500000(0.0061)]

875750 = 7.1815X

X = 121945.3

The break even number of vehicles(X) must be 121946.

c)

The benefit cost analysis calculated is the ratio of annual worth of benefits to annual worth of cost, In the problem the benefit cost analysis is greater than 1. The same indicates that the benefits overweigh the costs,therefore the project is profitable.