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What is the proper Financial Statement presentation of Dividend Payments made?

First you need to distinguish between dividends declared and dividend payments, because they may not happen at the same time. It's the dividends declared you're concerned with.

They come off retained earnings, so the retained earnings statement is the only place they would show up. You'd have your beginning balance of retained earnings, plus net income (or less net loss), less dividend declared, which gives you the ending balance.

That ending balance in retained earnings is taken to the balance sheet, but the dividends don't show up there.

They can also show up on a statement of stockholder's equity if such statement is done. Since retained earnings is part of stockholder's equity, anything affecting retained earnings would be on that statement also.