Facey Corporation is considering changing its payment date from "net $45"$ to "net $30"$ as customers are currently paying in $60$ days on average. The company forecasts that this change will reduce the collection period to $40$ days $($use a $360-$day year$),$ free up $$10,000$ in idle cash balances, and reduce sales from $$6,000,000$ to $$5,400,000.$ Facey's variable costs are $65\%$ of sales, its tax rate is $35\%,$ and it has a $12\%$ cost of capital.

Reference: Ref $12-10$

Should Facey change its payment date?