Bauer Industries is an automobile manufacturer. Management is currently evaluating a proposal to build a plant that will manufac ure lightweight trucks. Bauer plans to use a cost of capital of $12\mathrm{.}2\%$ to evaluate this project. Based on extensive research, it has prepared the incremental free cash flow projections shown in the following table $($in millions of dollars$)$:

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 lo examine the sensitivity of the NPV to the revenue assumptions. What is the NPV of this project if revenues are $10\%$ higher than forecast? What is the NPV if revenues are $10\%$ 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 $3\%$ 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 $3\%?$

d$.$ To examine the sensitivity of this project to the discount rate, management would like to compute the NPV for different discount rates. Create a grap. 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 ha a positive NPV$?$