Trian Group offered to buy Family Dollar Stores Inc for $55 to $60 per share in cash as billionaire investor Nelson Peltz bet that low-income Americans will watch their pennies for some time yet.

Trian's bid, disclosed in a regulatory filing late on Tuesday, sent the discount retailer's shares up 26 percent in after-hours trading.

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

It's a bet on the low-end consumer not going anywhere anytime soon, said Wall Street Strategies analyst Brian Sozzi, who added that the company has also been gaining market share from discount giant Wal-Mart Stores Inc .

Family Dollar, which sells most of its items for $10 or less, caters to consumers with household incomes of $40,000 and below. Its shares soared nearly 80 percent last year, as it brought in new shoppers during the recession.

Sozzi predicted the offer to be a done deal given the premium and the fact that Peltz invited Family Dollar Chairman and Chief Executive Howard Levine -- son of the company founder -- to join as a bidder.

So in the case that it does IPO five or 10 years down the line, he has considerable wealth, Sozzi said.

Family Dollar said it would review the offer in due course.

Peltz did not immediately return calls seeking comment.

Trian said it owned about 8 percent of Family Dollar's shares, eclipsing Levine's 7.5 percent and making Peltz the company's biggest shareholder. In July, Peltz disclosed a 6.6 percent stake in the company and suggested that its shares were undervalued.

In addition to offering Levine the chance to participate in a buyout, Peltz said he urged Levine to have the board form a committee of independent directors to consider the bid.

Peltz has in the past pushed for change at consumer companies ranging from ketchup maker H.J. Heinz Co to fast-food chain Wendy's and luxury jewelry retailer Tiffany & Co .

SALES OPPORTUNITIES?

JMP Securities analyst Peter Keith said the offer looked a little expensive, at about 10 times his estimate for calendar 2011 earnings before interest, tax, depreciation and amortization.

My sense is that Peltz recognizes the long-term opportunity to drive increases in sales per square foot, said Keith, adding that Family Dollar's sales per square foot are around $160, while rival Dollar General generates about $195 per square foot.

Family Dollar and other low-priced retailers were big beneficiaries of consumers trading down to save money in the downturn. But as the economy recovers and stock markets climb, stores that cater to wealthier consumers -- such as Whole Foods Market Inc -- have experienced an uptick in sales.

Last month, Family Dollar reported first-quarter earnings and gave a second-quarter outlook that missed Wall Street estimates. The stock was down 12 percent year-to-date when the market closed on Tuesday.

Leon Levine founded Family Dollar in 1959 in Charlotte, North Carolina. He retired in 2003 from the company, which currently has about 6,800 stores in 44 states.

News of Trian's offer pushed up shares in other dollar stores, with Dollar General up 7.6 percent, 99 Cents Only Stores up 4.7 percent and Dollar Tree Inc up 5.3 percent.

Shares in Family Dollar were up 26 percent to $55.36 in after-hours trading.

(Additional reporting by Jonathan Stempel and Emily Chasan in New York; Editing by Bernard Orr, Tim Dobbyn, Phil Berlowitz)