# Exercise 10

Due Monday 4/22

### Part A, Expected Net Present Value

A city is considering building a new convention center on a brownfield that might be contaminated with hazardous waste. The cost of constructing the center is $25 million, which the city would have to pay in year 1 if it decides to go ahead with the project. The actual construction process would take three years (no additional payments) and the center could be used beginning in year 4. Once it begins operating, the center will generate$2 million per year in revenue every year forever.

However, there is a 50% chance the site is contaminated, which would add a lot of additional costs and time to construction of the center. If construction goes ahead, the city will discover whether or not the site is contaminated in year 1 (only after the $25 million has been paid). If contamination is found, the city will need to abandon the project or pay an extra$25 million in year 1 in order to remediate (clean up) the site. If it decides to remediate, the process will delay completion of the center by 3 years and the first revenue payment will arrive in year 7 instead of year 4.

Assuming the city is risk-neutral and uses a 5% interest rate in all present value calculations, calculate the expected present value of the project. Should the city build the convention center?

### Part B, Value of Information

Suppose a city is considering developing a brownfield site but believes there is a 50% chance the site is contaminated with hazardous waste. If the site is clean (call that state "C"), the net present value of development will be $10 million. However, if the site is discovered to be contaminated during the construction process (call that state "D" for "dirty"), the site will have to be remediated and the net present value will be -$20 million.

It is possible to test the site for contamination prior to making the decision to develop. However, the test costs $1 million and is imperfect: when contamination is present, the test will fail to detect it 20% of the time. Moreover, the test has a 10% chance of falsely indicating that a clean site is contaminated. What is the expected present value of the test? Should the city buy it? In doing your calculations, you should assume that if the city chooses not to develop, it does not have to pay any remediation costs -- it only has to pay for the test itself. Please note that since all costs and payoffs are already expressed in present value terms, you do not need to do any present value calculations in this problem. ### Part C, Risk Aversion An individual saving for retirement has a choice of three investments. Option A would have a 20% chance of producing$1 million and an 80% chance of producing $10,000. Option B would have a 30% chance of producing$250,000 and a 70% chance of producing $60,000. Option C would produce$100,000 for certain.  The person is risk averse and will choose the option that maximizes his expected utility.  The person's ordinary (ex post) utility from a payoff of x dollars is u(x) = x^0.5 (that is, the square root of x).

Please evaluate each of the options: calculate its expected value, its expected utility, and its certainty equivalent.  Which option would the individual choose?  Would a risk neutral agent choose a different alternative?

URL: http://wilcoxen.maxwell.insightworks.com/pages/4867.html
Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 04/15/2019