Burger King Holdings Inc agreed to sell itself to investment firm 3G Capital for $3.26 billion (2.11 billion pounds), giving the No. 2 U.S. fast-food chain breathing room to fix its business and close the gap with leader McDonald's Corp .

At $24 per share, the offer represents a 46 percent premium to Burger King's price before news of the negotiations emerged on Wednesday.

It was a call out of the blue, Burger King Chairman and Chief Executive John Chidsey told Reuters in an interview when asked about how the talks started. He declined to give additional details.

Chidsey will keep his roles during a transition period and then become co-chairman with 3G Managing Director Alex Behring.

The sale, worth about $4 billion including debt, is expected to close in the last three months of 2010. Burger King has until October 12 to solicit a richer offer from other buyers.

It looks like a good price for Burger King shareholders. I don't anticipate that someone is going to come in higher, said Telsey Advisory Group analyst Tom Forte.

The valuation is based on good fundamentals, which Burger King doesn't have and probably won't have for another year, said Stifel Nicolaus restaurant analyst Steve West. On Wednesday, he had issued a research note saying that a $23-per-share price would satisfy shareholders.

Analysts said the deal's valuation -- at almost nine times cash flow over the last year -- is higher than previous restaurant deals and could pave the way for more.

TPG Capital LP , Goldman Sachs Group Inc's Goldman Sachs Capital Partners and Bain Capital Investors collectively own about 31 percent of Burger King and will tender their shares into 3G's offer, due to begin by September 17.

Burger King's private equity investors took the company public just four years ago at an initial share price of $17.

At the market close on Tuesday, shares in Burger King were down more than 31 percent since the end of 2008. McDonald's shares were up nearly 18 percent.

Burger King's stock jumped 25 percent to close at $23.59, on Thursday, adding to Wednesday's 15 percent gain. Shares in bigger rival McDonald's rose 0.6 percent and Wendy's/Arby's Group Inc added 6.8 percent.

CATCHING UP TO MCDONALD'S

3G, a little-known investment firm, was last in the spotlight in 2008, when it waged a proxy battle alongside The Children's Investment Fund against U.S. railroad CSX Corp . That led to Behring joining the railroad's board.

3G's backers include Brazil's Jorge Paulo Lemann, who sits on the board at Anheuser-Busch InBev NV . Forbes magazine estimates his fortune at $11 billion.

This looks to be something of a new line of business for 3G, which has historically held a concentrated portfolio of high-quality publicly traded businesses, rather than buying companies outright, Bernstein analyst Sara Senatore said.

The deal is the biggest in a string of recent restaurant buyouts. This summer, Carl's Jr parent CKE Restaurants and Brinker International Inc's On the Border Mexican Grill & Cantina were sold to private equity shops.

Wendy's/Arbys in June said an unnamed party had expressed interest in a potential deal involving the fast-food company, while California Pizza Kitchen Inc and Benihana Inc are looking for buyers.

Burger King, which has been hurt by high unemployment rates among its core audience of young men, expects weak demand during its new fiscal year due to the U.S. economy's slow pace of recovery and government austerity programs in Europe.

Analysts said going private would free Burger King to make major changes without the distraction of pleasing Wall Street.

In particular, West said Burger King needs to remodel its restaurants, which he said are older and less appealing than those operating under McDonald's Golden Arches.

Burger King, known as the Home of the Whopper, also needs to upgrade its technology to allow it to track sales trends in real time, analysts said.

McDonald's has muscled a bigger share of the market by expanding its menu with salads and apple dippers -- which appeal to moms and kids -- and high-profit beverages like lattes, fruit smoothies and frappes.

Telsey's Forte would like to see Burger King's new owners stick with the company's barbell strategy of selling low-priced and high-priced food.

Value-priced menu items, like its previously offered $1 double cheeseburgers, boosted sales but squeezed franchisees.

On the flip side, it has introduced a new broiler system that allows the chain to quickly prepare larger, premium Steakhouse XT burgers that sell for around $4 and bone-in ribs, which quickly sold out despite their price of about $7 for an eight-piece order. Such items appeal to its young, hungry male clientele, but sales could be constrained by the weak economy.

Burger King is rolling out an expanded breakfast menu this autumn and Chidsey said 3G has strong connections internationally, where the chain has opportunities to expand.

Lazard Ltd, JPMorgan Securities LLC and Barclays Capital acted as advisers to 3G Capital. Morgan Stanley and Goldman, Sachs & Co advised Burger King.

JPMorgan and Barclays are providing financing. About $2.8 billion of the $4 billion purchase price is debt, with the remainder equity, a source familiar with the situation said.

(Additional reporting by Phil Wahba, Paritosh Bansal and Megan Davies in New York, with Guillermo Parra-Bernal in Sao Paulo; Editing by Michele Gershberg, Gerald E. McCormick and Richard Chang)

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