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 $13\%$ cost of capital is appropriate for the project.

a$)$ Calculate the project's NPV$,$ IRR, MIRR, and payback. Do not round intermediate calculations. Round the monetary value to the nearest dollar and percentage values and payback to two decimal places. Negative values, if any, should be indicated by a minus sign.

NPV: $X

IRR: X$\%$

MIRR: X$\%$

The project's payback $\_\_\_$ years

b$.$ Assume management is unsure about the $$110,000$ cost savings $-$ this figure could deviate by as much as plus or minus $20\%.$ Do not round intermediate calculations. Round your answer to the nearest dollar. Negative values, if any, should be indicated by a minus sign.

b$1.$ Calculate the NPV if cost savings value deviate by plus $20\%.$ $X

b$2.$ Calculate the NPV if cost savings value deviate by minus $20\%.$

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 working capital $($WC$)$ requirement. She asks you to use the following probabilities and values in the scenario analysis:

Scenario; Probability; Cost Savings; Salvage Value; WC

Worst case; $0\mathrm{.}25$; $ $88,000$; $$28,000$; $$40,000$

Base case; $0\mathrm{.}45$; $110,000$; $33,000$; $35,000$

Best case; $0\mathrm{.}30$; $132,000$; $38,000$; $30,000$

Calculate the project's expected NPV$,$ its standard deviation, and its coefficient of variation. Do not round intermediate calculations. Round the monetary values to the nearest dollar and a coefficient of variation to two decimal places. Negative values, if any, should be indicated by a minus sign.

The project's expected NPV: $X

Standard deviation: $X

Coefficient of variation: X