In short, the stronger the company's internal cash flow, and in turn cash position, the less the need to draw on an external fund. If internal cash flow or the retention ratio increases, external fund requirements would decrease. If internal cash flow suffers, external fund requirements will climb.
Specifically, if a company reduces its payout ratio, it means that it is retaining more money in shareholders' equity, which can be used, in turn, to meet funding needs. With all other things remaining equal, such as internal liabilities, this reduced dividend payout ratio would lower the external fund requirement.
Conversely, a decline in profit margin, assuming overall revenue stays the same, would translate into less internal cash. This would increase the overall funding need and raise the external fund requirement.
Often these two actions are counterbalanced. Companies not wanting to increase their external fund requirements will often decrease their payout ratio in response to long-term declines in profit margin. Of course, a move such as this can raise shareholder fears and frustrations, putting a downward pressure on the overall price of a stock.
This question was answered by Ken Clark.