# Exercise 9

Due Monday 4/23

### Part A, Expected Value

For each of the following projects, please draw an appropriate decision tree, calculate any relevant expected values, and indicate whether a risk-neutral agent would undertake the activity. Please note that all costs must be paid up front before any of the uncertainties have been resolved, and all benefits listed in the problems are gross (that is, costs have not been deducted).

1. Project A costs $1 million to undertake. There is a 70% probability it will fail completely and produce$0 of benefits, a 20% probability it will produce $1 million of benefits, and a 10% chance it will produce$12 million of benefits.
2. Project B costs $12 million and is subject to two uncertainties which can be called the "preliminary" and "final" stages. If the preliminary stage goes badly (40% chance), the project will have to be terminated and the gross benefit will be$2 million. If the preliminary stage goes well (60% chance), the project can move to final stage. In the final stage, the project will either be modestly successful and produce $10 million (80% chance), or it will be highly successful and produce$50 million (20% chance).

### Part B, Expected Net Present Value

A city is considering building a new convention center on a "brownfield" -- an old, abandoned industrial site that is in a desirable location but 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?

URL: http://wilcoxen.maxwell.insightworks.com/pages/2575.html
Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 07/09/2018