Consider a project that costs $$100,000$ and yields a return of $$30,000$ for five years. At the end of the fifth year, there is a cost of $$30,000$ to dispose of the waste from the project.

a$.$ Should the project be undertaken if the discount rate is $0?10\%?15\%?$

b$.$ Assume there is uncertainty about the costs of disposing of the waste: there is a $50-50$ chance that the costs will be $$10,000$ or $$50,000.$ Discuss how this uncertainty affects the cost$-$benefit calculation if the government is: $(1)$ risk neutral $($i$.$e$.$ is indifferent about taking on risk$),(2)$ risk averse $($i$.$e$.$ must be compensated for taking on risk$).$