$8.$ Use the following information for the problem.

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Year MACRS Depreciation Allowances for $3-$year Property Class

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$133\mathrm{.}33\%$

$244\mathrm{.}44\%$

$314\mathrm{.}82\%$

$47\mathrm{.}41\%$

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Your company just bought a new distillation unit for $$6,000,000.$ Such equipment has a $3-$year modified accelerated cost recovery system $($MACRS$)$ classification.

a$)$ What is the book value of the distillation unit at the end of year $3?$ Use the $$6,000,000$ cost of the unit and the MACRS table above to find the book value.

b$)$ If the distillation unit will be sold in $3$ years for $$900,000($before taxes$),$ what is the after$-$tax cash flow $($i$.$e$.,$ after$-$tax salvage value or after$-$tax resale value$)$ from the sale? The tax rate is $25$ percent.

c$)$ The distillation unit is used in a project that has a three$-$year life. The project is expected to generate the following operating cash flows. The initial investment required for the project is the cost of purchasing the distillation unit of $$6,000,000.$ The project also requires an initial net working capital cash flow of $$350,000,$ which is fully recoverable when the project ends in year $3.$ It has no other cash flows besides the operating cash flows, the initial net working capital requirement, and the cash flow from selling the equipment at the end of the project in $($b$).$ If the required rate of return on the project is $14$ percent, what is the net present value of the project? Should it be accepted? Why?

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Year Operating cash flow $($OCF$)$

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$1$ $$2,000,000$

$22,500,000$

$33,000,000$

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