Burger King Holdings Inc , the No. 2 U.S. fast-food chain, agreed to sell itself to investment firm 3G Capital for about $3.26 billion (2.11 billion pounds) in a deal analysts said would give the restaurant breathing room to fix its business.

At $24 (15.58 pounds) per share, the deal represents a 46 percent premium to Burger King's price before news of the deal talks emerged on Wednesday.

Including the debt that New-York based 3G will assume, the deal is worth about $4 billion (2 billion pounds), the company said on Thursday. The transaction is expected to close in the last three months of 2010.

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.

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

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 issued a research note saying that a $23 (14.93 pounds)-per-share price would satisfy shareholders.

TPG Capital LP , Goldman Sachs Capital Partners and Bain Capital Investors collectively own about 31 percent of Burger King and will tender their shares into the offer, which is due to begin by September 17.

Under terms of the deal, Burger King can solicit higher bids from other third parties until October 12.

Burger King's private equity investors took the company public in May 2006 at an initial share price of $17 (11.04 pounds).

Before details of the deal became public on Wednesday, shares in Burger King were down more than 31 percent since the end of 2008. McDonald's shares were up nearly 18 percent.

On Thursday, shares of Burger King were up more than 24 percent at $23.44 (15.22 pounds) in morning trading and had gained nearly 15 percent on Wednesday. Larger rival McDonald's Corp rose 0.4 percent and Wendy's/Arby's gained nearly 7 percent.

CATCHING UP TO MCDONALD'S

Burger King has lagged McDonald's and other fast-food chains as its key customer base takes a deeper hit from persistently high unemployment rates.

Last week, the company forecast weak demand during its new fiscal year due to the U.S. economy's slow pace of recovery and government austerity programs in several European countries.

West said going private would free Burger King from the distraction of pleasing Wall Street and allow it to make major changes to its business.

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

It will also need to invest in other improvements to better compete, such as the kind of point-of-sale technology that McDonald's uses to spot trends immediately, rather than wait for monthly sales reports, West said.

Forte said he would like to see Burger King's new owners stick with the company's barbell strategy of selling low-priced and high-priced food, further improve relationships with franchisees and remodel stores.

Burger King Chief Executive John Chidsey will stay on during the transition period before taking the newly created position of co-chairman of the board.

3G Managing Partner Alex Behring will also be co-chairman once the deal closes.

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

(Editing by Michele Gershberg, Dave Zimmerman)