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I agree with you, it’s solely a balance sheet transaction as it doesn’t affect a company’s revenue or profit.
When a company buys back stock, it first reduces its cash account on the asset side of the balance sheet by the amount of the buyback. Say a company repurchases 100,000 shares for $50 each. The company would subtract $5 million from its cash balance. In the equity section, the company increases the “treasury stock” account by $5 million. Treasury stock represents money paid out to reacquire stock; it is a “contra equity” account that offsets contributed capital, so increasing treasury stock $5 million has the effect of reducing net contributed capital $5 million. The balance sheet is back in balance.