The board of Burger King has agreed for the Miami-based fast-food chain to be taken private for the second time in its history, after accepting a $4bn bid from 3G Capital, a little-known US investment group backed by Brazilian investors.

New York-based 3G Capital has won the Burger King board’s unanimous approval for its $24-per- share cash takeover bid, which values the burger chain at $4bn including about $750m of assumed debt.

Jorge Paulo Lemann, Marcel Telles and Carlos Sicupira – all Brazilian billionaires – are among the big investors in 3G Capital who will be providing the equity to finance the hedge fund’s bid. JPMorgan and Barclays Capital are providing debt for the deal.

Burger King has lagged behind fast-food rivals such as McDonald’s during the economic downturn, but 3G aims to expand by opening new stores in Latin America and Asia.

Burger King has a 40-day “go shop” period to solicit other offers. However, analysts said 3G’s bid valued the burger chain at 8-9 times its earnings before interest, tax, depreciation and amortisation, higher than most recent restaurant deals.

TPG, Goldman Sachs Capital Partners and Bain Capital bought Burger King for $1.5bn in 2002 from Diageo, the UK spirits group, and took it public in 2006.

The private equity groups, which still own about a third of Burger King, have already made healthy profits and are expected to make a total gain of at least four times their initial investment.

Mr Lemann is Brazil’s third-richest man and number 48 in the world, according to Forbes.

He helped build up Ambev, which merged with Interbrew to create InBev and later merged with Anheuser Busch to become one of the world’s largest drinks groups.

Alexandre Behring, 3G managing partner, plans to become co-chairman of Burger King, alongside John Chidsey, who will be replaced as chief executive.