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 $$33,000$ at the end of its $5-$year operating life. The applicable depreciation rates are $33\mathrm{.}33\%,44\mathrm{.}45\%,14\mathrm{.}81\%,$ and $7\mathrm{.}41\%.$ Working capital would increase by $$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.

Calculate the project's NPV$,$ IRR, MIRR, and payback.

Assume management is unsure about the $$110,000$ cost savings $-$ this figure could deviate by as much as plus or minus $20\%.$ What would the NPV be under each of these extremes?

Suppose the CFO wants you to do a scenario analysis with different values for the cost savings, the machine's salvage value, and the working capital $($WC$)$ requirement. She asks you to use the following probabilities and values in the scenario analysis:

$\backslash$table$[[$Scenario$,$Probability,Cost Savings,Salvage Value,WC$],[$Worst case,$0\mathrm{.}35,$$$88,000,$$$28,000,$$$40,000$