A bicycle manufacturer currently produces $257$ comma $000$ units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of $ $2\mathrm{.}20$ a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct in$-$house production costs are estimated to be only $ $1\mathrm{.}50$ per chain. The necessary machinery would cost $ $268$ comma $000$ and would be obsolete after ten years. This investment could be depreciated to zero for tax purposes using a ten$-$year straight$-$line depreciation schedule. The plant manager estimates that the operation would require $ $54$ comma $000$ of inventory and other working capital upfront $($year $0),$ but argues that this sum can be ignored since it is recoverable at the end of the ten years. Expected proceeds from scrapping the machinery after ten years are $ $20$ comma $100.$

If the company pays tax at a rate of $20\%$ and the opportunity cost of capital is $15\%,$ what is the net present value of the decision to produce the chains in$-$house instead of purchasing them from the supplier?

$($a$)$The annual free cash flows for years $1$ to $10$ of buying the chains is $?$

$($Round to the nearest dollar. Enter a free cash outflow as a negative number.$)$

$($b$)$compute the NPV of buying the chains from FCF$.$

$($c$)$ Compute the initial FCF of producing the chains.

$($d$)$Compute the FCF in years from $1$ through $9$ of producing the chains.

$($e$)$ Compute the FCF in year $10$of producing the chains

$($f$)$ Compute the NPV of producing the chains from the FCF

$($G$)$ Compute the difference between the NPV found above.