Persisting in a controversial Florida expansion, Michigan's First of America Bank Corp. on Wednesday agreed to pay $23.6 million, or 250% of book value, for a limping thrift in Sarasota.

Kalamazoo-based First of America, with $22 billion of assets, said it had arranged a stockswap acquisition of Presidential Holding Co., parent of a $224 million-asset thrift with seven branches.

Based on trading values at Tuesday's close, First of America would exchange about .93 of a newly issued share for each of presidential's 716, 188 shares.

'Minimal' Dilution Seen

The thrift subsidiary, Presidential Bank, earned $1.02 million in 1993, for a 0.42% return on assets, according to Sheshunoff Information Services Inc. The deal, expected to close by the first quarter of 1995, will bring only "minimal" dilution next year, First of America said. Combined with completed and pending thrift acquisitions, the Presidential deal will give First of America $1 billion of assets and 50 branches in Florida. First of America's stock recently fell to a 52-week low as Wall Street reacted to a contracting net interest margin and the prices of recent acquisitions in Florida and Illinois. I.n trading on Wednesday, the stock was unchanged at $35.75. Carole Berger, a Salomon Brothers Inc. analyst who last month downgraded First of America's stock, conceded that cost savings potential would rise as the banking company bulked up in Florida, reducing the potential for dilution. But she said First of America's officers may be underestimating the difficulty of converting thrifts into profitable commercial banks.

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