Avon Products Inc., the struggling cosmetics giant, will split off its North American business as part of a $605 million deal with private-equity firm Cerberus Capital Management.

Cerberus will acquire an 80 percent interest in the North American division for $170 million, according to a statement Thursday. That business also will assume about $230 million in long-term debt from the parent company, which will contribute $100 million in cash to the new entity.

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