CHICAGO - Northern Trust Corp. on Monday agreed to buy a $200 million-asset banking company in Florida in a stock-swap deal valued at $56.15 million.

The target, Beach One financial Services Inc., is a one-bank holding company controlling roughly $200 million of banking assets and $400 million of trust assets.

The purchase price equals 2.5 times Beach One's book value, but Northern estimated the deal will dilute its 1994 earnings by less than 1%.

The transaction is expected to close in the second quarter of 1994, and it will boost Northern Trust's Florida franchise to roughly $1.5 billion of banking assets, $10.5 billion of trust assets, and 17 offices.

Northern will continue to scout for acquisitions that will complement its current operations in southern Florida, said David Fox, the company's chairman, president, and chief executive.

The bank subsidiary of Beach One operates in Vero Beach, a community in Indian River County. Mr. Fox said the unit's charter would be preserved, leaving Northern with a two-bank Florida holding company.

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