Jitters Coffee is considering expanding its business by investing in a new coffee bean roasting facility. The investment required today $($year t $=0)$ is $$5$ million. This investment can be depreciated using the straight$-$line method over the next two years $($to a value of zero at the end of year $2).$ In addition, Jitters will need to increase its net working capital by $$0\mathrm{.}3$ million per year in years $0,1,$ and $2,$ after which point its working capital will stay fixed.

The company expects that it will take a few years before the facility can begin production. Gross profit $($revenue $$ operating cost$)$ is expected to start at $$1$ million in year t $=3$ and grow by $3\mathrm{.}5\%$ per year thereafter.

Assume that the CAPM holds. The risk$-$free rate is $3\%,$ and the market's expected return is $11\%.$ Jitters has no cash or debt, and for now it plans on using all equity financing for this project. Its corporate tax rate is $35\%,$ and assume that its existing business is sufficiently profitable that it can always claim the full depreciation tax credit for the new project.

$($a$)$ Estimate Jitters's free cash flows for years $0,1,2,$ and $3.[3$ points$]$

$3$

$($b$)$ The CFO estimates that the company's unlevered equity beta is $1\mathrm{.}5,$ and she says that this is likely to be the relevant beta for this new project as well. Calculate the appropriate cost of capital for this project, and use this to calculate the project's NPV$.$ Would you recommend pursuing the investment? Note: You should assume that any free cash flows in year $0$ have not yet been distributed to investors. $[2$ points$]$

$4$

$($c$)$ You suggest that it might be advantageous to finance the new investment with a mix of debt and equity, rather than just equity. You suggest issuing enough debt that Jitters's debt$-$to$-$value ratio will be D$/$V $=1/3,$ and it will maintain this target ratio indefinitely. Assume that the cost of debt will be equal to the risk$-$free rate $(3\%).$ Calculate Jitters's levered cost of equity and WACC under this plan. Will the project's NPV be higher or lower than in part $($b$),$ and which investors will stand to gain or lose from this difference? $($For this part, you only need to calculate the new levered cost of equity and WACC; for the questions about the change in NPV$,$ you only need to provide brief answers in words.$)[3$ points$]$