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> There is no change in the value of the company. There are fewer shares outstanding though which means each existing share is worth more.

The company's value decreases by the buyback amount. Share price (ignoring positive signalling impact) remains unchanged.

E.g. Company has $100 market cap with 10 outstanding shares at $10/share. Company does $10 buyback. Afterwards, company has $90 market cap with 9 outstanding shares at $10/share.

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Company shares are valued based on future earnings. If the company is undervalued, the value of remaining shares increases over time. As the future value of the shares taken off market is greater than the current share value. Lots of companies have gone this route; market cap increases over time and existing shares increase in value.

If the company is overvalued, the shareholders just get screwed as the company is buying back shares which are already worth less than the future value of the companies earnings.

Companies dont generally trade at their book value

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