Bauer Industries is considering purchasing a new machine, the XD$-750,$ which would allow it to expand its production capacity. The cost of the XD$-750$ is $$2\mathrm{.}75$ million. Unfortunately, installing this machine will take several months and will partially disrupt production. The firm has just completed a $$50,000$ feasibility study to analyze the decision to buy the XD$-750,$ resulting in the following estimates:

Marketing: Once the XD$-750$ is operating next year, the extra capacity is expected to generate $$10$ million per year in additional sales, which will continue for the $10-$year life of the machine.

Operations: The disruption caused by the installation will decrease sales by $$5$ million this year. Once the machine is operating next year, the cost of goods for the products produced by the XD$-750$ is expecte$4$d to be $70\%$ of their sales price. The increase production will require additional inventory on hand of $$1$ million to be added in year $0$ and depleted in year $10.$

Human Resources: The expansion will require additional sales and administrative personnel at a cost of $$2$ million per year.

Accounting: The XD$-750$ will be depreciated via the straight$-$line method over the $10-$year life of the machine. The firm expects receivables from the new sales to be $15\%$ of revenues and payables to be $10\%$ of the cost of goods sold. Billingham$$s marginal corporate tax rate is $35\%.$

a$.$ Determine the incremental earnings from the purchase of the XD$-750.$

b$.$ Determine the free cash flow from the purchase of the XD$-750.$

c$.$ If the appropriate cost of capital for the expansion is $10\%,$ compute the NPV of the purchase.

d$.$ Investigate the sensitivity of the NPV to fluctuations of the cost of capital. Allow cost of capital to increase from $8\%$ to $15\%$ with $1\%$ increment. Using $$Data Table$$ function, compute the value of the NPV for each value of the cost of capital and graph the NPV profile $($the NPV values $($on the Y$-$axis $)$ against the values of the cost of capital $($on the X$-$axis$)).$ Please use $$Data Table$$ function