Exercise 10

Due Sunday 11/22 by 11:59 pm

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 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

The government of small city is concerned that development along a nearby river has raised the risk that one of its buildings may be flooded. Historically, the risk has been 0.5% (half a percent) but the city believes there is a 20% chance that development has changed the city’s floodplain and the risk of a flood may now be 5%. If a flood occurs, the building would suffer $5 million of damage. However, the city could spend $150,000 to renovate the building to make it flood resistant. To keep things simple, you may assume that if the building is renovated, it will not be damaged at all by a flood. Finally, the city could also hire an engineering firm to determine whether the floodplain has changed before making a decision on the renovation. The firm’s determination would be infallible: the city would know for certain whether or not the building is in the floodplain (and thus whether or not the risk has increased).

Please determine the maximum the city would be willing to pay for the test. To keep things simple, you may assume that everything (decisions, renovation, possible flooding) happens in one period, and there is at most one flood.