$09\mathrm{.}02-$PR$001$ An air purifier for use in manufacturing semiconductors is placed in service with a first cost of $$50,000.$ It will be used for $8$ years, have an annual gross income

less operating expenses of $$14,000$ and will have no salvage value. Corporate income$-$tax rate is $25\%.$

a$.$ Determine the after$-$tax cash flows for years $0-8$ if depreciation allowances are $$10,000,$$$16,000,$$$9,600,$$$5,760,$$$5,760,$$$2,880,$$$0,$ and $$0$ during the $8$ years

$($MACRS$-$GDS $5-$year property class$).$

b$.$ Determine the after$-$tax cash flows for years $0-8$ if depreciation allowances are $$10,000$ for years $1-5$ and $$0$ in years $6-8($SLN depreciation over only the first $5$ years$).$