By Chelsey Dulaney 

Family Dollar Stores Inc., less than a week after gaining shareholder approval to sell itself to Dollar Tree Inc., said Monday its December sales improved as the discount retailer benefited from fewer markdowns.

For the month ended Jan. 3, Family Dollar said its sales increased 3.6% to $1.21 billion from a year earlier. Same-store sales, which exclude newly opened stores, increased 1.2%, compared with a 3% decline last December.

Family Dollar became the target of a prolonged takeover battle last year after agreeing in July to be bought by Dollar Tree Inc. in a deal now worth $8.7 billion. Dollar General Corp., which has long eyed buying up its main competitor, swooped in weeks later with a higher $9.1 billion all-cash offer. Dollar General ultimately wasn't able to satisfy Family Dollar's concerns that combining the two biggest dollar-store chains would face significant antitrust hurdles.

After securing the blessing of proxy advisers Glass, Lewis & Co. and Institutional Shareholder Services Inc., Family Dollar shareholders overwhelmingly approved the deal with Dollar Tree on Thursday.

The deal comes as Family Dollar has struggled in recent quarters as its profit and margins have slipped, underscoring the importance of a deal for the company. A plan to lower prices disappointed customers, and its latest quarter's results were worse than expected, in part because of distractions from the pending merger.

Family Dollar said its December margins widened by 59 basis points to 34.91% as the retailer benefited from fewer markdowns, increased purchase markups and a smaller freight expense.

Write to Chelsey Dulaney at Chelsey.Dulaney@wsj.com

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