Roark Capital is in the early stages of weighing an initial public offering of Inspire Brands, the owner of fast-food chains Dunkin’, Arby’s and Jimmy John’s, people with knowledge of the matter said.

The private equity firm has held preliminary discussions with potential advisers about a listing of Inspire in late 2024 or 2025, depending on market conditions, according to the people. Inspire could be valued at roughly $20 billion in any listing, they said, asking not to be identified discussing confidential information.

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