The fivefold increase in JPMorgan Chase & Co.’s takeover bid for Bear Stearns all but assures that Bear shareholders will approve the deal when they cast a final vote on it in mid-May.

JPMorgan yesterday raised its offer for Bear to $10 a share, up from an initial fire-sale price of $2 a share, and agreed to buy nearly 40% of the company. With Bear’s current directors now pledging to vote in favor of the new deal, JPMorgan can expect to gain nearly 45% of the overall vote in the months ahead, effectively guaranteeing approval of the takeover. At this point, “there’s just no way this deal won’t get done,” the co-founder of the investment bank Lane, Berry & Co., Frederick Lane, said.

Following news of the increased price, Bear’s shares rose 89%, to $11.25, in New York Stock Exchange trading, while JPMorgan stock gained 57 cents to reach $46.54 late yesterday.

The fact Bear’s shares topped the $10 bid price indicates the market may be hoping that JPMorgan will increase its offering price for a third time, experts say. But JPMorgan is hoping that this second offer is sufficient to please Bear shareholders who were furious over JPMorgan’s initial offer of $2 a share. That offer had immediately provoked threats of shareholder lawsuits and efforts to solicit higher bids from competitors.

As part of the deal announced yesterday, JPMorgan also pledged to buy 95 million newly issued shares of the investment bank, giving JPMorgan a 39.5% stake in Bear. The stake is enough to provide the bidder with an almost certain majority in upcoming shareholder votes, but not quite enough to trigger a shareholder vote, which is required when the stake hits 40%.

“Our board of directors believes that the amended terms provide both significantly greater value to our shareholders, many of whom are Bear Stearns employees, and enhanced coverage and certainty for our customers, counterparties, and lenders,” the chief executive of Bear Stearns, Alan Schwartz, said in a statement yesterday.

Under the agreement, the Federal Reserve Bank will provide financing for $29 billion of Bear’s most illiquid assets, with JPMorgan backing the first $1 billion of potential losses. Initially, the central bank had agreed to assume all $30 billion of the investment bank’s potential losses.

The Fed said its involvement was intended to “bolster market liquidity and promote orderly market functioning.”

A resident scholar at the American Enterprise Institute and a former Fed official, Vincent Reinhart, said he was unconvinced by the Fed’s rationale. “You could have made the argument that this was about market liquidity a week ago when Bear Stearns was only getting $2 a share,” he said. “But by continuing to provide a backstop, the government essentially is helping sweeten the deal for a failing bank and exposing taxpayer dollars to a credit risk.”