$22.(16$ points$)$ Your new employer, Freeman Software, is considering a new expansion project. The new project requires the purchase of a new machine for $$10,000$ at t$-0.$ The incremental sales are expected to be $$20,000$ each year and the incremental costs are expected to be $$15,000$ each year. The machine will be depreciated over $4$ years using the MACR method and the allowed depreciation rates for the equipment are $33\mathrm{.}33\%,44\mathrm{.}45\%,14\mathrm{.}81\%,$ and $7\mathrm{.}41\%$ for Years $1$ through $4.$ The project requires an increase of NOWC of $83,000$ in year $0,$ which will be fully recovered when the project is ended. The project has a $3-$year life. At the end of Year $3,$ the equipment can be sold for $$2,000.$ The marginal corporate tax rate is $25\%.$

a$)$ What are the depreciation expenses for year $1$ to year $4?(4$ points$)$

b$)$ What is the project's cash flow in year $0,$ i$.$e$.$ CFo? $(4$ points$)$

c$)$ What is the project's cash flow in year $1?(4$ points$)$

d$)$ What is the project's cash flow in year $3?($Hint: Do not forget the ATSV of the machine$)(4$ points$)$

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