Parramore Corp has $$18$ million of sales, $$1$ million of inventories, $$2$ million of receivables, and $$1$ million of payables. Its cost of goods sold is $65\%$ of sales, and it finances working capital with bank loans at an $8\%$ rate. Assume $365$ days in year for your calculations. The current cash conversion cycle is $40\mathrm{.}56$ days.

$1.$if Parramore could lower its inventories and receivables by $9\%$ each and increase its payables by $9\%,$ all without affecting sales or cost of goods sold, what would be the new CCC$?$

$2.$ How much cash would be freed up$,$ If Parramore could lower its inventories and receivables by $9\%$ each and increase its payables by $9\%,$ all without affecting sales or cost of goods sold?

$3.$ How much would pretax profits change, If Parramore could lower its inventories and receivables by $9\%$ each and increase its payables by $9\%,$ all without affecting sales or cost of goods sold?