By Jessica Wohl

CHICAGO (Reuters) - Family Dollar Stores Inc <FDO.N> rejected Trian Group's bid to buy the company for at least $7 billion, saying it "substantially undervalues" the retailer.

The company's board said on Thursday that selling the company would not be in the best interest of shareholders.

Family Dollar, whose chairman and chief executive is the son of its founder, plans to open more stores and renovate older ones as it tries to capture more of shoppers' spending on basic goods such as food.

Last month, billionaire investor Nelson Peltz's Trian Group offered to buy Family Dollar for $55 to $60 per share in cash.

Family Dollar also said on Thursday that the board had adopted a shareholder rights plan that floods the market with shares if any one investor acquires a 10 percent stake. Such plans, often known as "poison pills," increase the cost of taking over a company.

(Reuters Insider: Family Dollar defense a bid for time - Lee http://link.reutera.com/pew38r.)

JP Morgan analyst Charles Grom said he had a hard time envisioning Chief Executive Howard Levine walking away from Family Dollar, which he has led since 1998. He downgraded the shares a day before Family Dollar rebuffed Trian's offer.

Trian's offer, announced in a regulatory filing on February 15, represented at least a 25 percent premium to Family Dollar's previous closing price of $43.96 on the New York Stock Exchange.

Family Dollar has been trading at a premium to rivals Dollar Tree Inc <DLTR.O> and Dollar General Corp <DG.N>, which Grom said seemed "a bit unwarranted."

Family Dollar shares fell 1.4 percent $49.70 Thursday morning, while Dollar Tree jumped 1.6 percent and Dollar General rose 0.4 percent.

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 customers hunting for bargains as the economic downturn persisted.

Family Dollar had 126.4 million shares outstanding as of December 27, 2010, implying that Trian's offer was worth $6.95 billion at $55 per share and $7.6 billion at $60 per share.

A spokeswoman for Trian was not immediately available for comment. Peltz has two other partners in the firm, Peter May and Ed Garden.

Leon Levine founded Family Dollar in 1959 in Charlotte, North Carolina. He retired in 2003. The company has more than 6,800 stores in 44 states.

In the past, Peltz has pushed for change at consumer companies ranging from ketchup maker H.J. Heinz Co <HNZ.N> to fast-food chain Wendy's <WEN.N> and luxury jewelry retailer Tiffany & Co <TIF.N>.

Morgan Stanley is advising Family Dollar and Cleary Gottlieb Steen & Hamilton LLP is its legal counsel.

(Reporting by Jessica Wohl; Editing by Lisa Von Ahn, Derek Caney and John Wallace)