Oct 1 (Reuters) - Coty Inc (COTY.N) said on Friday it would swap around 9% of its stake in professional beauty business Wella with KKR & Co Inc (KKR.N) for some of the cosmetic maker"s shares the U.S. buyout firm owns, valuing the deal at $426.5 million. The deal cuts Coty"s stake in Wella to around 30.6%, valued at about $1.38 billion. The CoverGirl cosmetics maker sold a 60% stake to KKR for about $2.5 billion in December last year, with its remaining 40% stake valued at $1.3 billion at the time. Coty said the value of Wella has increased since the closing of the majority stake sale, as reopening of salons across the globe has sparked a recovery in the business. The deal, which is expected to close in the second quarter of Coty"s fiscal 2022, will also help the Gucci fragrance maker simplify its capital structure and save $52 million annually, while also boosting its profits. KKR"s ownership in the Hugo Boss fragrance maker would reduce to the equivalent of about 45 million Coty Class A shares, representing a stake of about 5.2%.