Problem $1(100$ marks$).$ Madison Manufacturing is considering a new machine that costs $$350,000$ and would reduce pre$-$tax manufacturing costs by $$110,000$ annually. Madison would use the $3-$year MACRS method to depreciate the machine, and management thinks the machine would have a value of $$33,000$ at the end of its $5-$year operating life. The applicable depreciation rates are $33\mathrm{.}33\%,44\mathrm{.}45\%,14\mathrm{.}81\%,$ and $7\mathrm{.}41\%.$ Net working capital $($NWC$)$ would increase by $$35,000$ initially, but it would be recovered at the end of the project$$s $5-$ year life. Madison$$s marginal tax rate is $25\%,$ and a $10\%$ cost of capital is appropriate for the project. Scenario Probability Cost Savings Salvage Value NWC Worst case $0\mathrm{.}35$ $$88,000$ $$28,000$ $$40,000$ Base case $0\mathrm{.}35$ $$110,000$ $$33,000$ $$35,000$ Best case $0\mathrm{.}30$ $$132,000$ $$38,000$ $$30,000$ a$)$ Calculate the project$$s NPV$,$ IRR, and MIRR. $[50$ marks$]$ b$)$ Assume management is unsure about the $$110,000$ cost savings$$this figure could de$-$ viate by as much as plus or minus $20\%.$ What would the NPV be under each of these extremes? $[20$ marks$]$ c$)$ Suppose the CFO wants you to do a scenario analysis with different values for the cost savings, the machine$$s salvage value, and the net working capital $($NWC$)$ requirement. She asks you to use the following probabilities and values in the scenario analysis. Calculate the project$$s expected NPV$.$ Would you recommend that the project be accepted?