What happens when a company buys its own shares?

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Why does this reduce capital, and why does this reduce the company’s ability to pay creditors?

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Imagine a million people each own 1 share. The company makes a million in profit this yeah so each share holder gets a dollar. Then the company buys back 500,000 shares. Next year the company also makes a million in profit but since there are only 500,000 shares outstanding each shareholder gets 2 dollars.

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