First Viginia Bank Inc. of Falls Church announced yesterday that shareholders have approved acquisition of the holding company's 21st bank -- Bank of Frederick County, based in Stephens City.

Purchase of the $11.8 million Stephens City Bank and its branch in Stonewall will give First Virginia 168 offices and assets of more than $1.47 billion.

First Virginia will acquire the bank by an exchange of stock. Each share of Bank of Frederick County will be traded for 1.5 shares of a new issue of First Virginia preferred stock that pays an 8 percent a year dividend.

First Virginia will issue about 210,000 shares of the new stock.

Officials of the bank would not put a cash value on the transaction. They said auditors value the new preferred stock at $8.50 a share, a total of $1.78 million. Stock in the Stephens City bank rarely changes hands, they noted; the last sale, more than a year ago, was at $15 a share.

Merger of the two banks still requires the approval of the Virginia State Corporation Commission and the Federal Reserve Board. The approval is expected soon.

First Virginia officials said they plan to operate Bank of Frederick County under the name First Virginia Bank of Frederick County. Like most banks acquired by the holding company, the Stephens City bank will be largely autonomous and will be run by its present management.

The acquisition extends First Virginia's service area into the northwest corner of the state and the area around Winchester. The Falls Church holding company's nearest office to the new bank is First Virginia Bank-Shenendoah Valley in Straussburg.