$251$ point

A company is launching a new sales initiative and expects sales of $$446,838$ during the first year, and the gross profit margin to be $25\%.$ To prepare for this, they plan to acquire $49$ days worth of inventory. Their vendor will allow $48$ days to pay its invoices. The company plans to sell only on account to its customers, so sales will be entirely credit based, and the average invoice is expected to take $44$ days to collect. What amount of net working capital should be included in the initial investment?

Enter your answer as a monetary amount rounded to four decimal places, but without the currency symbol. For example, if your answer is $$90\mathrm{.}1234,$ enter $90\mathrm{.}1234$