Exercise 1

Due Thursday 1/31.

The US EPA administers a program of grants and loans to help state and local governments identify and eliminate brownfield sites.   Imagine that the City of Chicago has been awarded such a grant and is considering what to do about Roosevelt and California, a site described in more detail below:

• Estimated damages from the site in its brownfield state: $40,000 per year. The damages are the total value to the city from having the site in its current brownfield condition, including increased crime, reduced property values, lost tax revenue and so on.
• Whether or not the site is contaminated is unknown.  However, the probability of contamination is 60 percent. 
• If the site is contaminated, cleaning it up is prohibitively expensive given the City's current budget.
• If the probability of contamination could be shown to be less than 1 percent, the EPA would issue a "No Further Remediation" (NFR) letter for the site. An NFR letter absolves buyers from any future liability for cleaning up contamination subsequently discovered at the site. 
• If an NFR letter were issued, the site would be developed and brownfield damages would drop to zero in period 1.
• The site could be tested for contamination at a cost of $20,000 per sample. If the site is contaminated, the test will reveal that 75 percent of the time. The test never generates false positives: it never indicates contamination when the site is not contaminated.
• If contamination is discovered, the site remains a brownfield but it does not become worse: the damages do not increase.
• The City has enough money in its budget to cover a testing program for the site, including multiple tests, but would only proceed if the testing program had a positive expected net present value.
• If multiple tests are done, they could all be performed in year 0, and the results of any given test would be available when deciding whether or not to do a subsequent test.
• The City uses an interest rate of 5 percent in present value calculations.

Imagine you have been hired as a consultant to decide what to do about the site.  Please design an appropriate testing program, explain how it would be implemented and calculate the program's expected net present value.  Also indicate the maximum possible cost of testing and the probability that an NFR letter would be issued.