Garrett Industries turns over its inventory six times each year; it has an average collection period of $35$ days and an average payment period of $30$ days. The firm$$s annual sales are $ $5$ million, costs of goods sold $ $1$ million while other operating costs excluding depreciation $ $2$ million.

Based on the data find the firm$$s cash conversion cycle and resource investment requirement if it makes the following changes simultaneously:

$(1)$ Shortens the average age of inventory by $3$ days.

$(2)$ Speeds the collection of accounts receivable by an average of $10$ days.

$(3)$ Extends the average payment period by $7$ days.

If the firm pays $13\%$ WACC, by how much, if anything, could it reduce annual costs of working capital financing?