Citigroup Inc. said Wednesday that it has finalized an agreement with the federal government that clears the way for a highly diluted stock exchange to take place, boosting common equity levels and giving the federal government a one-third stake in the New York company.

Assuming full conversion rates, Citi would swap $58 billion of preferred stock and trust-preferred securities into common stock, boosting shares outstanding by 75% when the exchange is completed around July 30.

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