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 worth of Benefit / Annual Cost

Operating and maintenance cost = $180,000

Benefit to the public = $900,000

Cost to the general public = $250,000

Cost of the project = $2 Million

Net benefit to the general public = ( $900000 - $250000 ) = $650000

Total cost of the project = $2,000,000 ( A/P, 10%, 20 ) + $180000

= $2,000,000 ( 0.117 ) + $180000

= $414920

Benefit cost ratio = $650000 / $414920

= 1.57

B)

Project should be accepted . Since benefit ratio is more than 1. Benefit ratio shows the earning for per dollar spend on the project. if it is more than 1 which means project gives earning more than its cost. Hence project should be accepted with benefit ratio more than 1.

C)

Payback period:- Time in which initial investment can be recovered from project benefits.

Total cost of the project = $2 million

Net benefit of the project = Benefit to the public - Cost to the public - Operating cost

= $900000 - $250000 - $180000

= $470000

Payback period = Initial investment / Net annual benefit =

=   $2,000,000 / $470,000

= 4.26 years

Payback period not consider the time value of money.