Richard Bove said that when you add it all up, Bear will eventually cost JPMorgan Chase $65 a share.

While some may think that JPMorgan is getting Bear Stearns at a bargain price, "I do not," Bove said in a note to clients. "Bear Stearns is a deeply troubled company which would have no value if the Federal Reserve had not stepped in to bail it out."

JPMorgan does not need Bear Stearns mortgage operation, has a "much stronger investment banking business," and the Bear Stearns New York headquarters is "just another piece of Manhattan real estate that it must rid itself of," Bove said.

While JPMorgan Chase may want Bear Stearns' prime brokerage business, it is likely that the unit's best customers have already left for Goldman Sachs, he said.

Bove currently has a "Market Perform" rating and $44 price target on JPMorgan Chase. The target implies he expects shares to drop about 6 percent over Monday's $46.55 close.

"What is most disturbing about this deal is that it uses a great deal of Morgan capital to buy a company that is losing market share, in a series of businesses that are declining in size, with a top management team that is best described as sclerotic," he said.