AAI specializes in production of music equipment. The firm incurred $$3\mathrm{.}2$ million to do a feasibility study on new equipment $($implant$).$ The firm plans to replace three existing pieces of equipment with one, more efficient, technologically advanced piece of equipment to meet all its production needs. The projected sales volume of a new seven$-$octave voice emulation implant is as follows.

Year $12345$

Sales Volume

$($$M$)1216101413$

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Production of the implants will require $$30$ million in working capital $($NWC$)$ immediately. Thereafter, WC will equal to $20\%$ of projected sales revenue

Each implant is priced to sell at $$38$ with a variable cost of $$23$ per unit. Annual total operating fixed costs amount to $$32$ million. The production of the implants will require acquisition of a computerized machine at a cost of $$292$ million excluding $$8$ million transportation and installation cost. The acquisition of the machine is partly financed with a $5-$year, $4\mathrm{.}8\%,$ $$150$ million amortizable loan. The machine is industrial machinery which qualifies as a seven$-$year MACRS property.

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The introduction of the music equipment will reduce before$-$tax cash flows of existing music equipment by $$15$ million per year for the first three years and $$10$ million per year for the last $2$ years.

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In five years, the firm projects that it will sell the computerized machine at a price approximately equal to about $30\%$ of depreciable cost $($initial cost of the machine subject to depreciation$).$ The firm is in the $25\%$ marginal tax rate. The cost of capital is $13\%.$

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Required

$($i$)$ Compute the depreciation per year and after$-$tax salvage value of the machine $(5$ points$)$

$($ii$)$ Compute investment in NWC each year and recovered$/$terminal cash flows of NWC $(5$ points$)$

$($iii$)$ Derive the CFO and unlevered FCF or FCF to the firm $($FCFF$)$ of the project. $(20$ points$)$

$($iv$)$ Prepare a loan amortization schedule showing annual interest charges and principal $(5$ points$)$

$($v$)$ Derive the levered FCF or free cash flow to equity $($FCFE$)(5$ points$)$

$($vi$)$ Suppose the NPV of the project is positive, state $5$ qualitative factors you may consider before making the final decision based on the information provided in the question. $(10$ points$)$