Consider Sarah's bright idea to build a dam in the scenic Grand Canyon of the western US to provide electricity to the nearby urban area of Las Vegas. To make things simple, suppose the dam costs \(\$ 1\) billion to build and that it can be entirely built in the first year. A stream of benefits and costs ensue over the following decades. However, there is uncertainty about those costs and benefits. With an \(90 \%\) probability the net present value of the stream of ensuing benefits is \(\$ 1.2\) billion. With a \(10 \%\)

probability the loss of the natural resource is a real bummer and net present value of the stream of ensuing benefits is 0 . The discount rate is \(5 \%\) per year.

a. What is the expected value of the ensuing benefits? What is the net benefit of building the dam today (benefits less costs)?

b. Suppose we could wait a year to build the dam. In a year's time, all the costs and benefits will be the same, except pushed one year into the future. You are told by your environmental advisors that in a year it will be clear if we really need the Grand Canyon. What is the net benefit today of deferring the decision to build the dam until next year?