Excelsior Industries is evaluating the purchase of a new manufacturing machine for its product line $($referred to as a "project" for the purpose of setting up the questions$).$ The machine has an estimated life of four years. The cost of the machine is $$250,000,$ and the machine will be depreciated using the straight$-$line method to a residual value of $$0.$

The machine is expected to generate additional sales of $10,000$ units in year $1,$ with sales growing by $8\%$ annually through year four. The selling price per unit will be $$120,$ and the cost of goods sold per unit will be $$75.$

To support the installation of the new manufacturing machine and the associated increase in production capacity, Excelsior Industries will need to invest in various net working capital components. The company estimates that it should hold $2\%$ of its annual sales in cash, $4\%$ of its annual sales in accounts receivable, $9\%$ of its annual sales in inventory, and $5\%$ of its annual sales in accounts payable.

Assume the marginal corporate tax rate is $21\%$ and the approximate cost of capital for this project is $10\%.$

$($a$)$ Construct a simple income statement showing the EBIT and unlevered net income from year $1$ to year $4$ of this project.

$($b$)$ Calculate the net working capital requirements for this project from year $1$ to year $4.$

$($c$)$ Calculate the free cash flow for this project from year $0$ to year $5.$

$($d$)$ Calculate the NPV of this project. Based on the NPV you calculated, do you recommend Excelsior Industries purchase the new manufacturing machine or not?