Discounting and CBA Exercises for Excel: A. Consider a project with initial costs of $150,000 that yields $40,000 annually in revenue over five years. At the end of year five there is a cost of $30,000. At a discount rate of 10% should the project be undertaken? If the discount rate is 5%?

B. A new highway lane is under consideration. The highway would take two years to build. The costs and benefits of the road as follows:

1. Reductions in accidents valued initially at $2.5 million in the first year of operation (year 2), and increase by 2% annually. 2. $1,000,000 initial time-savings starting in year 2, increases by 3% annually 3. $10,000,000 in construction costs expended at the start of the project (year 0) 4. $5,000,000 in construction costs expended in second year of the project (year 1) 5. $4,000,000 for relocation of displaced households in year 0

6. Maintenance expenses for the highway will increase by $300,000 when the lane is completed (year 2) and increase at an annual rate of 3% Should this project go forward? Base your analysis on a 15-year time frame. What happens if the time-frame is 10 years? 20 years? Use a discount rate of your choice and justify your selection.

C. The city of Xanadu is considering a congestion pricing system. The program would cost an initial $100 million to implement (year 0) and an additional $20 million the following year. The plan will yield estimated benefits (through charging drivers $7 for entry/exit into the city) of $50 million in year 1, $45 million in year 2 and $40 million in year 3, then diminishing by 2% annually through year 10. Calculate the Net Present Value of the proposed project, assuming a discount rate of 5%. Should it go forward? Does your decision change if the discount rate is 8%? 3%? Why or why not?

D. The City of Zydyxa wants to lease out its parking meter revenue for the next 50 years. The city is projected to earn $3.5 million in parking meter revenue in year 1, and revenue has consistently increased at an annual rate of 3.5%. Three investors, each from different countries, have expressed interest in leasing the citys parking meter revenue. Investor A uses a discount rate of 12%, Investor B a discount rate of 8%, and Investor C a discount rate of 15%. How much are the three investors willing to pay for the lease? How much would they pay now if revenues increase by 5% annually? 1%?

E. [Optional] The state of Florida is considering two options for reducing homelessness:

1: Increasing the capacity of the shelter system by 1,000 beds for homeless single adults. This option would involve $3,000,000 in construction costs, and $850,000 in personnel costs (increasing by 3% annually). The provision of additional shelter beds is estimated to reduce the street homeless population by 3,000. Each homeless person on the street is estimated to cost, on average $2,000 in hospital costs, $500 in EMS costs, and $750 in court and jail costs. These costs increase by 2% annually.

2: Providing short-term rental subsidies to prevent evictions. Today, it is estimated that this assistance would prevent 2,000 families with children and 500 single individuals from becoming homeless. Each homeless family costs $2,000 a month in shelter costsand the average duration of family shelter stay is 4 months. In addition, each month in the homeless system is estimated to cost society $750 per individual in remedial education, and $500 per individual in social services (including the housing itself). Individuals stay in shelters for an average of 2 months. The rental subsidy level remains fixed at $5 million a year. It is estimated that the number of families and individuals who benefit would decline by 1% annually. Which option has the highest net benefit (Net Present Value)? Calculate the net present value over five years, and use a 6% discount rate.