Question

The following question comes from the end of Chapter 8 on Cost-Benefit Analysis regarding the "Big Dig" highway and bridge construction project. Assume that it is planned to take7 years to complete (from t-0 to t-6). . The project will require: $45 million in construction materials per year S20 million in labor costs per year Construction will disrupt transportation within the city for 7 years, which means longer commutes for 100,000 workers by 30 hours a year. These 100,000 workers are currently paid S15 per hour (which reflects each worker's per-hour valuation of leisure) . After 7 years (at t7), each of the 100,000 workers will have shorter commute time by 35 hours a year (compared to before the project started Part of the project is the creation of a park that each worker will value the park at $40 per year (assume that no one else will use the park) . The government uses a 5% discount rate. . The number of workers (100,000) will remain constant into the future indefinitely. (a) Should the project be approved? Formally show the cost- benefit analysis. (b) Suppose that some of the cost estimates mentioned above are uncertain. Specifically the construction materials estimate is $45 million with 50% probability and $100 million with 50% probability. Given these uncertainties, should the project proceed? (Assume that the government is risk neutral.)

Answer 1

Total cost in first year t0 Material Labor in project Labor loss by otal Interest in 4500000 4500000 1100000 grand total cost 2255000 Total bencfit in first ycar t7: Labor saving by Earning from park400000 Grand total 525000 100 565000 Payback yearotal cost in first year I-0)/(Total benefit in first year I-7) 225500000/56500000 3.99 around 4 year Answer-a:as we can see that payhack year is around 4 year which is much higher that 1 year Its imply that 1" year cost will be recover in 4 year after project completed. So according to cost-benefit analysis this project should not be approved now expected cost material in 1year-0.5-45+0.5 100-72.5mm now grand tatal cost 281875000 Payback year-4.98-around 5 year Project should not be proceed