NEW YORK, United States — 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.

The move follows reports earlier this month that Avon was close to selling the North American business — a deal that drew concern from some investors. A shareholder group led by Barington Capital Group urged Avon to pursue a restructuring plan instead, rather than unloading its North American division at a “fire sale” price. But when the terms of the transaction were revealed on Thursday, investors applauded the deal, sending the shares up as much as 37 percent in early trading.

As part of the Cerberus agreement, the investment firm will make a $435 million investment in the parent company. It will take the form of convertible preferred stock with a conversion price of $5 a share. That price is a 46 percent premium to to 30-day volume-weighted stock and would equate to a stake of 16.6 percent, according to the statement.

Dividend Suspended

The company also suspended its quarterly dividend, saying it would reinvest that money in the business. Avon is on track for its fourth straight year of sales declines, hurt in part for a consumer shift in North America. Fewer customers there are buying products from door-to-door sales people — Avon’s hallmark. Shedding the domestic business will make it easier for the company to grow profitably overseas, Avon Chief Executive Officer Sheri McCoy said in the statement.

“The separation of Avon North America is the best way to ensure that both businesses have an unencumbered path to profitability and growth,” she said. “This was a key principle as we considered alternatives.”

By Nick Turner.