A$-$for$-$Alpha Shop is considering is considering a new project which requires a new machine. The project will last for $4$ years. The price of the machine is $$60,000,$ and an additional installation cost of $$6,000$ is required. In four years, the machine can be sold for $$5,000.$ Assuming the tax rate is $20\%,$ the appropriate discount rate for the project is $10\%,$ and the machine applies five$-$year MACRs for tax purpose. To start the project, it also requires $$30,000$ net working capital, and this amount will be recovered when the project is terminated in four years. If the project is accepted, the increase of cash sales is estimated at $$22,000$ each year during the project life.

The following table shows the depreciation rates.

$\backslash$table$[[$Year$,3-$year MACRS $(\%),5-$year MACRS $(\%),7-$year MACRS $(\%)],[1,33\mathrm{.}33,20\mathrm{.}00,14\mathrm{.}29],[2,44\mathrm{.}45,32\mathrm{.}00,24\mathrm{.}49],[3,14\mathrm{.}81,19\mathrm{.}20,17\mathrm{.}49],[4,7\mathrm{.}41,11\mathrm{.}52,12\mathrm{.}49],[5,,11\mathrm{.}52,8\mathrm{.}93],[6,,5\mathrm{.}76,8\mathrm{.}92],[7,,--,8\mathrm{.}93],[8,,--,4\mathrm{.}46]]$

a$)$ Calculate the depreciation expense for each year from year $1$ to year $4.$

$(5$ marks$)$

b$)$ Calculate the operating cash flows for each year from year $1$ to year $4.$

$(5$ marks$)$

c$)$ Calculate the net capital spending for each year from year $0$ to year $4.$

$(4$ marks$)$

d$)$ Calculate the net present value of the project, and decide whether the company should take the project or not.

$(8$ marks$)$