$1$A$).$ Calculate the firm$$s cash conversion cycle given annual sales are $$660,000$ and cost of goods represent $90\%$ of sales. Assume a $365-$day year, inventory turnover $10\mathrm{.}8,$ collection period $45\mathrm{.}6$ days, and payable deferred period is $30$ days

$1$B$)$ If the company reduces its inventory without adversely affecting sales, what effect should this have on free cash flow: $(1)$ in the short run and $(2)$ in the long run?

$1$C$).$ If the company reduces its DSO without seriously affecting sales, what effect would this have on its free cash flow $(1)$ in the short run and $(2)$ in the long run?

$1$D$).$ Cash doesn$$t earn interest, so why would a company have a positive target cash balance?