VICTORIA, Tex.— Shareholders of FVNB Corp. have approved a proposal to go private, the company said in a statement late Monday.

More than 82% of shareholders voted for this option, in which the company will buy out those with less than 2,000 shares at $45 per share. The company will pay about $16.9 million for about 375,000 shares.

The vote, at FVNB’s annual shareholders’ meeting, effectively ended Prosperity Bancshares’ bid to buy FVNB for about $150 million. Prosperity, of Houston, has made several offers in recent months to buy the company, but all have been rejected.

David M. Gaddis, the president and chief executive officer of $750 million-asset FVNB, said he thought the shareholders “appreciated the fairness of our offer” and the bank’s commitment to the community. Though the final number of shareholders will be determined only after the transaction closes in the next few days, Mr. Gaddis said, it will be below 300, which will allow the bank to de-list itself.

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