Question

7. A proposed bridge on the interstate highway system is being considered at the cost of $2 millin It is pring 2019 expected that the bridge will last 20 years. The federal and state governments will pay these construction costs. Operation and maintenance costs are estimated to be $180,000 per year. Benefits to the public are estimated to be $900,000 per year. The building of the bridge will result in an estimated cost of $250,000 per year to the general public. The project requires a 10% return. a) Determine the benefit-cost ratio for the project. State any assumptions made about benefits or costs b) Based on your result from Part A, would you proceed with the project? Why or why not? c) Determine the payback period (to the nearest year) for the project.

Answer 1

A) Benefit cost ratio = Annual benefit / Annual cost

Annual benefit = Annual benefit of public - Cost of the public per year

= $900000 - $250000

= $650,000

Annual cost = Initial cost of the project ( A/P, r, n) + Operating and maintenance cost

(A/P) = r ( 1 + r)ⁿ / ( 1 + r )ⁿ - 1

= $2000000 ( A/P, 10%, 20 ) +  $180000

= $2000000 ( 0.117 ) + $180000

= $414920

Benefit ratio = $650000 / $414920

= 1.57 times

B) Benefit ratio is calculated to identify the benefit receive from every dollar spend on the project . Project should be accepted if the ratio is more than 1. which means it gives return after recovering cost of the project.

In the above case benefit ratio is 1.57. it shows that after recovering the cost , project is given $0.57 for every dollar spend on the project. Hence it should be accepted. We should proceed with the bridge.

C

Payback period = Total cost of the project / Annual benefit

Total cost the project = $2,000,000

Annual benefit = Estimated benefit to the general public - ( Cost of the general public + Operating cost of the project )

= $900000 - ( $250000 + $180000 )

= $470000

Payback period = $2000000 / $470000

= 4.26 years