Coty Inc. agreed to buy 40-plus Procter & Gamble Co. beauty brands for about $12.5 billion in a deal that would more than double its sales and transform it into one of the world’s largest cosmetics companies.

The transaction will be conducted as a Reverse Morris Trust, meaning P&G will spin or split off the business, which will then merge with a Coty subsidiary, the companies said in statements Thursday. The arrangement is meant to reduce taxes for the companies’ shareholders.

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