Question

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Bill rides the subway at a cost of 75 cents per trip, but would switch is the price were any higher. His only alternative is a bus that takes 5 minutes longer, but costs only 50 cents. He makes 10 trips per year. The city is considering renovations on the subway that would reduce Bill’s travel time by 10 minutes, but fares would raise by 40 cents per trip to cover costs. The fare increase and the reduction in travel time both take place after one year and last forever. The interest rate is 25%. a) As far as Bill is concerned, what are the present values of the projects benefits and costs? b) The city’s population consists of 55,000 middle-class people, identical to Bill, and 5,000 poor people. The poor do not use bus or subway. What are the projects benefits and costs for the city as a whole? What is the NPV, the internal rate of return and the benefit/cost ratio? c) Consider an alternative project: an immediate tax of 1.25 euro per middle-class person to provide free legal services to the poor, in both of the following two years. The legal services are valued by the poor at a total of 62,500 euro per year (to be received at the end of each of the two years). What is the NPV, the internal rate of return and the benefit/cost ratio of this project? d) If one of these projects must be chosen, which would you select? e) One might argue that the value to the poor should be weighed heavier, because their marginal utility of income is higher. How much must each dollar of income to a poor person be weighted relative to that of a middle-class person in order to end up at the same NPV for both projects?

Answer 1

a. Bill is eager to pay 25 pennies extra to spare 5 minutes and his incentive for every moment of drive time is 5 pennies. Presently after the proposed remodel and decrease in time - Bill will spare 10 minutes esteemed at 50 pennies and his cost will increment by 40 pennies. At 10 outings every year, his all out advantage from the undertaking will be $ 5 and all out cost increment will be $4 . Since these progressions are perpetually, we will compute the PV utilizing the ceaselessness recipe:

PV of advantages = 5/25% = $20

PV of expenses = 4/25% = $16

Net advantage = $ 4

b. For the city in general, with 55000 individuals who will have same expense and advantages as over, the net present estimation of the task benefits less cost will be = 55000 * 4 = $ 220000

c. The working class will be burdened at $1.25 per individual or aggregate of (55000 * 1.25) = 68750 which is esteem lost or decrease for the white collar class people. The needy individuals esteem the lawful assistance from this duty at $62500 ony every year, which implies that for the city overall there is esteem loss of (68750-62500) = $6250. Consequently the expense for this situation is more than the advantage.

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