5

Problem Set #6. Due Thursday 10/25 at 5 pm.

1. The initial cost of constructing a permanent dam (i.e., a dam that is expected to last forever) is $425 million. The annual net benefits will depend on the amount of rainfall: $18 million in a “dry” year, $29 million in a “wet” year, and $52 million in a “flood” year. Meteorological records indicate that over the last 100 years there have been 86 “dry” years, 12 “wet” years, and 2 “flood” years. Assume the annual benefits, measured in real dollars, begin to accrue at the end of the first year. Using the meteorological records as a basis for prediction, what are the net benefits of the dam if the real discount rate is 5 percent?

2. A city with a population of 328,500 persons is considering introducing a recycling program that would require residents to separate paper from their household waste so that it can be sold rather than buried in a landfill like the rest of the town’s waste. The major benefit is revenue from the sale of waste paper. The program will involve capital costs of specialized collection equipment, household containers, and a sorting facility, and higher collection costs. The planning period for the project has been set at eight years, the expected life of the specialized equipment (t = 0, ..., 7).

The following information has been collected by the town’s sanitation department:

Quantities: Residents currently generate 400 pounds of waste paper per person per year. Based on the experience of similar programs in other towns, it is estimated that 56% of paper included in the program will be separated from other waste and suitable for sale. But, the percentage might range from a low of 48% to a high of 64%.
Prices: The current local market price for recycled paper is $28/ton but has fluctuated in recent years between a low of $12 per ton and a high of $32 per ton.
Capital Costs: The program would require an initial capital investment of $844,000.
Annual Costs: The department estimates that the separate collection of paper will add an average of $6/ton to the cost of collecting household waste (2000 pounds = 1 ton).
Discount Rate: The sanitation department has been instructed by the budget office to discount at the town’s real borrowing rate of 6 percent.

For these questions use the NPV formula in Excel. Check your work by hand with a calculator and the shortcut method for calculating the present value of an annuity:

PV = NB_t=0 + [NB_n(1 - (1 + i)^-n]/i

where n = 7 (i.e., n = t - 1). See equations 6A.1 and 6A.2 on page 156 of the textbook for more detail.

Calculate a base case estimate of the present value of net benefits for the program.
Conduct a best-case or worst-case NPV analysis (whichever is the most appropriate).
From your base case, conduct a breakeven analysis over the price of recycled paper. Present your results in a table and a graph using Excel.
Implement a Monte Carlo analysis of the present value of net benefits of the program. Present your results in a Histogram.

Submit your answers to #2 via e-mail in a spreadsheet with your answers to a-d clearly labeled.