Lululemon is considering a new project that improves inventory management for the next $5$ years. The project has similar risks as the overall firm. The new technology will require an investment in computer and robotic equipment of $$4$ million $($t$=0).$ The machines will be depreciated on a straight$-$line basis to $0$ over $5$ years. At the end of the project, the company expects that they will be able to sell the used machines for $$0\mathrm{.}7$ million. To operate the machines, each year there will be a fixed cost of $$100,000.$ The benefit of these machines is that they will reduce the inventory $($ie Net Working Capital$)$ of the company by $$8$ million dollars during the time that the machines are in use $($starting at year $1).$ There is no gain in operating revenues from these new machines. The tax rate for the company is $20\%.$

Based on historical company information, you estimate that the cost of equity for Lululemon is $14\%$ and the cost of debt is $6\%.$ The company has maintained a debt$-$to$-$equity ratio of $1$:$2.$

Q$1)$ What are the FCFs for the project for years $0$ through $5?[$If you have trouble with FCF$,$ make up FCF for each year then continue with the other questions.$]$

Q$2)$ If the project is financed using the same capital structure as the firm, what is the NPV of this project?

Q$3)$ If the project is all equity financed, what is the NPV of this project?

Q$4)$ Instead of maintaining a constant capital structure for the project, the company chooses to finance the initial cost of the investment with debt $($$$5$ million$)$ and will keep this debt for the duration of the project $($it will be paid off in year $5).$ Assume the cost of debt and interest rate on debt are both $6\%.$ What is the NPV of this project under this alternative financing option?

Q$5)$ Another alternative option is to finance the project at the debt$-$to$-$equity ratio of $1$:$1.$ Assuming they maintain this debt ratio for the duration of the project, what is the NPV under this financing option?

Input FCF$\_0$ in the answer prompt.