Billionaire investor Nelson Peltz's Trian Group is bidding $55 to $60 per share for Family Dollar Stores Inc , sending shares of the discounter up 31 percent in extended trading.

Trian's bid represents at least a 25 percent premium to Family Dollar's closing price of $43.96 on the New York Stock Exchange on Tuesday. Family Dollar had 126.4 million shares outstanding as of December 27, 2010, which would imply a deal of $7.6 billion at $60 per share.

Peltz's Trian Group owns about 8 percent of Family Dollar's outstanding shares, according to a regulatory filing on Tuesday.

Shares in the company jumped 31 percent to $57.78 in extended trading.

(Reporting by Lisa Baertlein)