Multiple changes in cash conversion cycle Garrett Industries turns over its inventory $7$ times each year; it has an average collection period of $37$ days and an average payment period of $26$ days. The firm's annual sales are $$3\mathrm{.}2$ million. Assume there is no difference in the investment per dollar of sales in inventory, receivables, and payables; and a $365-$day year.

a$.$ Calculate the firm's cash conversion cycle, its daily cash operating expenditure, and the amount of resources needed to support its cash conversion cycle.

b$.$ 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 $12$ days.

$(3)$ Extends the average payment period by $8$ days."

c$.$ If the firm pays $17\%$ for its resource investment, by how much, if anything, could it increase its annual profit as a result of the changes in part b$?$

d$.$ If the annual cost of achieving the profit in part $c$ is $$32,000,$ what action would you recommend to the firm? Why?

a$.$ The firm's cash conversion cycle, $CCC,$ is $63\mathrm{.}14$ days. $($Round to the nearest whole day.$)$

The firm's daily cash operating expenditure is $$8767.($Round to the nearest dollar.$)$

The amount of resources needed to support the firm's cash conversion cycle is $$553556.($Round to the nearest dollar.$)$

b$.$ 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 $12$ days.

$(3)$ Extends the average payment period by $8$ days.

The new cash conversion cycle, CCC$,77\mathrm{.}14$ days. $($Round to the nearest whole day.$)$