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The video tutorial provides examples of recapitalization, starting with the scenario of ABC Company having $100 million in debt at the end of 2018. In 2019, ABC raised $20 million in new debt to buy back stocks. Prior to the recap, the stock price was $10 and ABC had 70 million shares outstanding. The question is how many shares ABC has after the recap. By using the formula for repurchased shares (D new - D old / P prior), where D new is the new debt raised in 2019 ($20 million), D old is the old debt from 2018, and P prior is the stock price before recap, we can calculate the shares remaining after the recap.