Question

Bill rides the subway at a cost of $.75 per trip but would switch if the price were any higher. His only alternative is a bus that takes five minutes longer, but costs only $.50. His only alternative is a bus that takes five minutes longer but costs only $.50. He makes 10 trips a year. The city is considering renovations of the subway system that will reduce the trip by 10 minutes, but fares would rise by $.40 per trip to cover the costs. The fare increase and reduced travel time both take effect in one year and last forever. The interest-rate is 25%.

a. As far as Bill is concerned, what are the present values of the project benefits and costs?

b. The city’s population consists of 55,000 middle-class people, all of whom are identical to Bill, and 5000 poor people. Poor people are either unemployed or have jobs close to their homes, so they do not use any form of public transportation. What are the total benefits and costs of the project for the city as a whole? What is the net present value of the project?

c. Some members of the city Council propose an alternative project that consists of an immediate tax of $1.25 per middle-class person to provide free legal services for the poor in both of the following two years. The legal services are valued by the poor at a total of $62,500 per year. (Assume this amount is received at the end of each of the two years.) What is the present value of the project?

d. If the city must choose between the subway project and the legal services project, which should select? What is the “distribution of weight” of each daughter received by a person that would make the present values of the two projects just equal? That is, how much must each dollar of income to report person be waited relative to that of the middle-class person? Interpret your answer.

Answer 1

a. Bill is willing to pay 25 cents extra to save 5 minutes and his value for each minute of commute time is 5 cents. Now after the proposed renovation and reduction in time - Bill will save 10 minutes valued at 50 cents and his cost will increase by 40 cents. At 10 trips a year, his total benefit from the project will be $ 5 and total cost increase will be $4 . Since these changes are forever, we will calculate the PV using the perpetuity formula:

PV of benefits = 5/25% = $20

PV of costs = 4/25% = $16

Net benefit = $ 4

b. For the city as a whole, with 55000 people who will have same cost & benefits as above, the net present value of the project benefits less cost will be = 55000 * 4 = $ 220000

c. The middle class will be taxed at $1.25 per person or total of (55000 * 1.25) = 68750 which is value lost or reduction for the middle class folks. The poor people value the legal help from this tax at $62500 ony per year, which means that for the city as a whole there is value loss of (68750-62500) = $6250. Hence the cost in this case is more than the benefit