First$-$Rate Cleaners is considering replacing one of its tired cleaning machines for a new model that can dry$-$clean clothes in half the time of the old machine. Both the book value and the salvage value of the current machine are $$2,500$; the current machine would be sold if the new machine is purchased. The new machine would cost $$20,000$ and is expected to last $15$ years, at which point it would be sold for its salvage value of $$2,000.$ It would generate additional net operating cash flows of $$4,500$ each year of its useful life. First$-$Rate Cleaners estimates its tax rate to be $25\%,$ while its required rate of return is $8\%.$

Required

a$.$ Using the format below, outline the appropriate cash flows$$including the depreciation tax shield, timing, adjustment for taxes, and appropriate PV factor for each component of this equipment$-$replacement scenario.

Item

$$

Cash Flow $($B$)$

$$

When $($C$)$

$$

Tax Rate $($D$)$

$$

PV Factor $($E$)$

$$

Present Value $($B $\backslash$times D $\backslash$times E$)$

b$.$ Calculate the NPV of this potential investment. Should First$-$Rate Cleaners purchase this new asset? Provide both quantitative and qualitative reasons for your conclusion.

c$.$Would your answer to part $($b$)$ change if First$-$Rate requires a return of $12\%?$

d$.$ Would your answer to part $($b$)$ change if the additional annual net operating cash flows are only $$2,800$ using the $8\%$ discount rate? Using the $12\%$ discount rate?