If a firm pays its bills with a 30-day delay, what fraction of its purchases will be paid for in the current quarter? In the following quarter? What if its payment delay is 60 days?
It will pay 1/4 of its yearly bills each quarter -- no matter what its payment delay is.
With a 30-day delay, it will pay 2/3 of its current quarter's bills plus 1/3 of the previous quarter's bills.