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I will use all my knowledge and schooling in accounting to try and clear up this confusion for you.

1) The equity section of the balance sheet represents the amount of ownership in a company by the owners. For instance, common stock and paid-in-capital represent the investments by the owners. Retained earnings represent all earnings since the foundation of the business that have not been distributed to the owners. This is reported in the equity section because, ultimately, the owners have the right to the profits of their company.

2) You wrote: "It appears some of the components of the Additional Paid-In Capital(e.g. re-purchase of stock) also tie the balance sheet(via equity) to the cash flow statement"

Actually, additional paid in capital results from the issuance of stock, not the repurchase. Most common stock has a legal par value (usually very low, like, around $1). Any price paid for stock above this par value is recorded as additional paid in capital. For instance, if a company issues 1 share of $1 par common stock for $50, it would show in the equity section of the balance sheet common stock for $1 and additional paid in captial for $49.

3) You wrote: "Isn't there a bit of a double dipping going on though? Specifically, Earnings are the result of the income statement and the cash flow statement uses these same earnings to arrive at a new cash and equivalents"

Yes, the income statement reports earnings. However, as was stated already, these earnings are not all cash. Therefore, in the cash flow statement, there must be a reconciliation from accrued earnings to cash income or outflow. The purpose of the cash flow statement is to show how the company is using its cash. One of the most important numbers in the entire financial statements is the cash flow from operations. If this number is negative, it means that the company is using more cash than it is bringing in through operations. This means that a company will eventually need to turn to outside financing unless that number becomes positive.

The reconciliation from beginning cash to ending cash at the bottom of the cash flow statement is just to prove that the company has accounted for all the use or receipt of cash during the period.

4) Finally, you wrote: "Where I get left in the dust is when I remember that the equity section of the balance sheet can be separately developed by adding common stock(at par value) with paid in capital and retained earnings" In accounting, there is a balance sheet equation, where assets=liabilities + equity. This is true because, if our hypothetical company is liquidated, it would sell its assets, then pay its liabilities. What is left would then be for the owners, so it is reported as equity. As I stated earlier, equity is made up of investments by owners (common stock and paid in capital), and the cumulative earnings (less distributions).

Hope I have helped out a little.

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