Question

A government agent considers three mutually exclusive project alternatives to rearrange the traffic in the metropolitan area. Capital investment costs and net annual benefits of each alternative are given in the following table. Assume that there will be no salvage value of the alternatives, and MARR is 10% per year.

ΕΟΥ O 1 A -$480,000 240,000 210,000 180,000 150,000 B -$735,000 360,000 300,000 240,000 180,000 C -$600,000 240,000 240,000 240,000 240,000 2 3 4

a) Using the B–C ratio method, determine which alternative is best. Justify your answer showing all your calculations.

b) If these alternatives were totally independent from each other, which ones do you suggest to the agency to go for? Explain your answer.

Answer 1

a) B-C ratio is calculated by finding the ratio between present benefits and present cost.

Net present benefits = B₁/1+i + B₂/(1+i)² + B₃/(1+i)³ + B₄/(1+i)⁴

For A,

i=10% = 0.1

The value of B1, B2, B3 and B4 are given in the table.

So, after calculation Net present benefits = 629,424.22

Costs = 480,000

So, B/C ratio= 629,424.22/480,000

= 1.31

Similarly For B,

i=0.1

Net present benefits = $878,464.59

Costs = $735,000

So, B/C = $878,464.59/$735,000

= 1.17

For C,

i=0.1

Net present benefits = $760,767.71

Costs = $600,000

So, B/C ratio = 1.27

Alternative A is chosen as it has the maximum B/C ratio of 1.31 amongst the 3 alternatives.

b)

If they are independent, firm can choose any alternative as the B/C ratio of all of them are above 1 meaning that the project is profitable owing to the higher present benefits compared to costs.

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