How do slower inventory turnovers, slower receivables collections, or faster payments to suppliers influence the numbers produced by a cash budget?
This is a great question. All three points that you mention have an important effect on all companies.
First, if a company has a slow turnover rate in terms of inventory, then that company will not have as much money on hand. The reason for this is because the company bought the inventory and so they are out of cash. So, they will need to replenish their cash through selling their inventory. Also you might want to keep in mind that storing inventory takes money.
Second, the speed with which money is received also plays an important role. Faster payments mean faster liquidity. In other words, when a company gets faster payments, then that company will have more money on hand to invest in other things. If they get money slowly, they might run out of cash.
Finally, if a company pays their suppliers quickly, then they will be out money. So, ideally a company that pay suppliers quickly should have a mechanism to get money quickly as well.