Start-up firm and net working capital financing

Consider a firm planning to expand sales by $36 million/year.

It requires additional facilities of $ 2 million.

Typically, the firm produces with 90 days of inventory (largely raw material).

The firm offers its customers an average of 90 days credit (Average Collection Period), and gets 30 days credit from suppliers.

Purchases account for 50% of every dollar sold. Other expenses are 20% of sales.

Assume that purchases occur at the beginning of the month, and sales at the end of the month.

The firm currently has excess cash balances of $ 5 million. It needs to keep cash balances of 10% of monthly sales.

How much additional financing does the firm need and when? Hint: calculate the monthly cash flows of the start-up.