$.$ A group of farmers in the western U$.$S$.$ considers building a dam in a scenic canyon to

provide more irrigation water to crops and protect agricultural production from climatic risk.

Assume the dam costs $$1$ billion to build and that it can be completely built during the first

year. However, there is uncertainty about benefits and costs over the following decades. The

net present value of the stream of ensuing benefits is $$1\mathrm{.}2$ billion with a $90\%$ probability.

With a $10\%$ probability the loss of the natural resource is a real bummer and the 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 they 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. Environmental advisors

suggest that in a year it will be clear if we really need the scenic canyon. What is the net

benefit today of deferring the decision to build the dam until next year?