A DOT is performing a benefit-cost analysis of a new highway using an analysis p

Question

A DOT is performing a benefit-cost analysis of a new highway using an analysis period of 40 years as part the required environmental impact assessment of the project. The section of highway is estimated to have a construction cost $210 million dollars. The public benefit in reduced travel time and economic development around the highway is estimated to be $17 million per year for the first 5 years, then decrease by 3% per year for the remainder of the 40 year analysis period as congestion grows and economic development slows. The public disbenefit is estimated to be $1.9 million dollars in year 0 due to additional congestion and pollution during construction, then average $140,000 per year over the 40-year project life in environmental costs due to increased runoff and vehicle emissions. Using an interest rate of 4%, determine the benefit-cost ratio for this project using public/government version of the B/C ratio. Express your answer to two decimal places.

Explanation / Answer

Step1: Computation of the present value of benifits.We have,

Step2: Computation of the present value of cost.We have,

Step3: Computation of the B/C ratio.We have,

B/C ratio =Present value of total benifits / Present value of Total costs

B/C ratio = 252.37/214.59 = 1.18

Hence, the B/C ratio is 1.18.

Year Benifits( In million $) PVIF@4% Present value 1 17 0.961 16.34 2 17 0.924 15.71 3 17 0.889 15.11 4 17 0.855 14.53 5 17 0.822 13.97 6 16.49 0.790 13.03 7 15.99 0.760 12.15 8 15.51 0.731 11.34 9 15.05 0.702 10.56 10 14.60 0.675 9.85 11 14.16 0.650 9.20 12 13.74 0.625 8.59 13 13.32 0.600 7.99 14 12.92 0.577 7.45 15 12.53 0.555 6.95 16 12.16 0.534 6.49 17 11.79 0.513 6.05 18 11.44 0.494 5.65 19 11.10 0.475 5.27 20 10.76 0.456 5.00 21 10.44 0.439 4.58 22 10.13 0.422 4.27 23 9.82 0.406 3.99 24 9.53 0.390 3.72 25 9.24 0.375 3.46 26 8.97 0.361 3.24 27 8.70 0.347 3.02 28 8.44 0.333 2.81 29 8.18 0.321 2.62 30 7.94 0.308 2.44 31 7.70 0.296 2.28 32 7.47 0.285 2.13 33 7.24 0.274 1.98 34 7.03 0.263 1.85 35 6.82 0.253 1.72 36 6.61 0.244 1.61 37 6.41 0.234 1.50 38 6.22 0.225 1.40 39 6.04 0.216 1.30 40 5.85 0.208 1.22 Present value $ 252.37

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