Dollar General Corp. offered $9.7 billion for Family Dollar Stores Inc., setting off a bidding war for a company that had agreed to an $8.5 billion takeover by Dollar Tree Inc. last month.

Dollar General plans to pay $78.50 a share in cash, compared with Dollar Tree’s bid of $74.50 a share in cash and stock, according to a statement today. The deal will generate $550 million to $600 million in cost savings annually three years after its completion, Dollar General said.

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