A bicycle manufacturer currently produces $262,000$ units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of $$$$2\mathrm{.}00$ a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct$$ in$-$house production costs are estimated to be only $$$$1\mathrm{.}60$ per chain. The necessary machinery would cost $$$$217,000$ and would be obsolete after $10$ years. This investment could be depreciated to zero for tax purposes using a $10-$year $$straight$-$line depreciation schedule. The plant manager estimates that the operation would require $$$$26,000$ of inventory and other working capital upfront$($year $0),$ but argues that this sum can be ignored since it is recoverable at the end of the $10$ years. Expected proceeds from scrapping the machinery after $10$ years are $$$$16,275.$ If the company pays tax at a rate of $20\%$ and the opportunity cost of capital is $13\%,$ what is the net present value of the decision to produce the chains$$ in$-$house instead of purchasing them from the$$ supplier?

$1.$ First, we project the annual free cash flows of buying the chains and then compute the$$ project's NPV$.$

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.$)$

$2.$ The NPV of buying the chains is $$$$\_\_\_($Round to the nearest dollar. Enter a negative NPV as a negative$$ number.$)$

$3.$Next$,$ we project the annual free cash flows of producing the chains and then compute the$$ project's NPV$.$

The initial FCF of producing the chains is $$$ $\_\_\_($Round to the nearest dollar. Enter a free cash outflow as a negative$$ number.$)$

$4.$ The FCF in years $1$ through $9$ of producing the chains is $$$ $\_\_\_($Round to the nearest dollar. Enter a free cash outflow as a negative$$ number.$)$

$5.$ The FCF in year $10$ of producing the chains is $$$$\_\_\_($Round to the nearest dollar. Enter a free cash outflow as a negative$$ number.$)$

Part $6$

$6.$ The NPV of producing the chains is $$$ $\_\_\_($Round to the nearest dollar. Enter a negative NPV as a negative$$ number.$)$

$7.$ Then, we compute the difference between the net present values found above.

The net present value of producing the chains$$ in$-$house instead of purchasing them from the supplier is $$$$\_\_\_($Round to the nearest$$ dollar.$)$