Question

the benefits are also per year

The city of Ottawa is considering to build a new toll highway that spans from Orleans to Kanata, the project cost is estimated to be $90,000,000 and is to be paid in 3 equal payments (Payment 1 before commencement, Payment 2 at the end of the 1t year and Payment 3 at the end of 2nd year when the construction is done). The feasibility assessment of this project is 25 years after construction. This highway benefits the city a total of $5,000,000 by reducing travel times and safety improvements and would generate toll revenues of $7,000,000 per year. The O & M costs for the proposed highway is expected to be $2,100,000 per year. ** The revenues in terms of toll fares are to be treated as negative costs not benefits, i.., there is no direct benefit to the society by charging the motorists. If the social discount rate for this project is chosen to be 5.5%. Calculate the benefit/cost ratio of this project and comment on its feasibility.

Answer 1

Benefit-to Cost Ratio is the comparison of the benefit arising from the project to the cost incurred on the project.

Benefit-to-Cost Ratio= PV of Benefits to be earned / PV of Cost of Project; If the ratio is > 1, the project is feasible and if the ratio is < 1, the project is not feasible

Discounting Rate = 5.5%

PV of Benefits

Toll Revenues = $7,000,000 per year

Highway Benefits = $5,000,000 per year

PV of Benefits = $(7,000,000+5,000,000)* (5.5%,25 years) (Discounting)

= $12,000,000*13.4139 [to calculate 13.1439-> 1/1.055, 25 times] (rounded off to 4 decimals)

= $160,966,800

PV of Cost of Project

O&M cost = $2,100,000 per year

PV of O&M Cost = $2,100,000* (5.5%, 25 years)

= $2,100,000 * 13.4139

= $28,169,190

Loan Installment = $90,000,000/ 3 Installments = $30,000,000

PV of Loan = $30,000,000* 1 (Yr 0) + $30,000,000 * (5.5%, 2 years)

= $30,000,000 + $30,000,000*1.8463 [To calculate 1.8463-> 1/1.055, 2 times]

= $85,389,000

PV of Cost of Project = PV of O&M Cost + PV of Loan

= $28,169,190 + $85,389,000

= $113,558,190

Benefit-to-Cost Ratio = $160,966,800/$113,558,190 = 1.4175 (rounded off to 4 decimals)

Comment: Since the ratio is greater than 1, the project is feasible.