Bauer Industries is an automobile manufacturer. Management is currently evaluating a proposal to build a plant that will manufacture lightweight trucks. Bauer plans to use a cost of capital of $12\mathrm{.}4\%$ to evaluate this project. Based on extensive$$ research, it has prepared the following incremental free cash flow projections$($in millions of$$ dollars$)$: See picture

a$.$ For this$$ base$-$case scenario, what is the NPV of the plant to manufacture lightweight$$ trucks?

b$.$ Based on input from the marketing$$ department, Bauer is uncertain about its revenue forecast. In$$ particular, management would like to examine the sensitivity of the NPV to the revenue assumptions. What is the NPV of this project if revenues are $12\%$ higher than$$ forecast? What is the NPV if revenues are $12\%$ lower than$$ forecast?

c$.$ Rather than assuming that cash flows for this project are$$ constant, management would like to explore the sensitivity of its analysis to possible growth in revenues and operating expenses.$$ Specifically, management would like to assume that$$ revenues, manufacturing$$ expenses, and marketing expenses are as given in the table for year $1$ and grow by $2\%$ per year every year starting in year $2.$ Management also plans to assume that the initial capital expenditures$($and therefore$$ depreciation$),$ additions to working$$ capital, and continuation value remain as initially specified in the table. What is the NPV of this project under these alternative$$ assumptions? How does the NPV change if the revenues and operating expenses grow by $5\%$ per year rather than by $2\%?$

d$.$ To examine the sensitivity of this$($base$-$case scenario$)$ project to the discount$$ rate, management would like to compute the NPV for different discount rates. Create a$$ graph, with the discount rate on the x$-$axis and the NPV on the y$-$axis, for discount rates ranging from $5\%$ to $30\%.$ For what ranges of discount rates does the project have a positive$$ NPV$?$