Time Warner said it rejected Murdoch's unsolicited offer, of which 60 percent would be Twenty-First Century Fox stock and 40 percent cash, a far-reaching proposal that would reshape the media landscape.

A number of Time Warner shareholders said Fox and Murdoch, its chairman and chief executive, may have to raise the bid to as much as $95 a share and boost its cash component to wrap up a merger. Murdoch offered about $85 a share when the bid was made in June.

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"Rupert has got to figure out a way to get more cash in the deal," said Mario Gabelli, Chairman and CEO of Gamco Investors.

Gamco's funds own about 3.6 million shares of Time Warner. Like many other shareholders, Gamco also owns stock in Murdoch's company — about 10.5 million shares — and Gabelli said some of his own investors are not eager to increase the number of those shares as part of a merger.

Another executive at one of Time Warner's large institutional shareholders also said he would look for Murdoch to offer a higher ratio of cash to firm up the value of the deal. Prospects for gains in Fox stock in the near term could be constrained by the difficulties of merging the two businesses, including wringing out cost savings, and the effect of the likely debt burden Fox assume after borrowing billions of dollars.

"Cash is cash, so you know exactly what the value is," this person said.

Even though this executive, who spoke on condition of anonymity because of company policy, said he thought the overall value of the proposed deal was fair, Murdoch can still raise his bid.

"It's a corporate poker game for sure, and Murdoch never plays his best card first. There's always another card left to be played," this person said.

RISK AND UNCERTAINTY

Time Warner shares rose 17 percent to $83.13 in trading on Wednesday after the company disclosed the offer and its rejection. Including the assumption of Time Warner debt, the deal would have been worth $94.3 billion, according to Thomson Reuters data. Twenty-First Century Fox shares fell 6 percent to $33.

Time Warner said the strength of its own strategy and "significant risk and uncertainty as to the valuation" of Fox's stock were reasons for rejecting the bid. It also noted the stock did not have voting rights, a type of share that typically trades at a discount.

A Time Warner spokesman declined further comment. A spokesman for Twenty-First Century Fox declined to comment.

Mitch Zacks, portfolio manager and principal of Zacks Investment Management of Chicago, said Time Warner's board may have rejected the offer as a bargaining tactic.

"My guess is that if the offer goes to about $95 per share, the board would have a hard time turning it down," he said.

Zacks declined to discuss exactly what price he would accept to sell his own shares. He said his firm has about 192,000 Time Warner shares and none of 21st Century Fox.

Zacks also noted low interest rates make it easy for companies to finance borrowing but that stock prices are at all-time highs, creating currency for deals and helping drive an M&A boom. A high stock price could be tempting Murdoch's company to prefer stock than cash as its currency.

Shawn Narancich, executive vice president at Ferguson Wellman Capital Management in Portland, Oregon, said with Wednesday's price run-up, Time Warner now trades in line with some competitors, about 20 times estimated 2014 earnings.

Time Warner's growth projections could justify its rejection of the original offer, Narancich said. As a shareholder he said he would likely sell Time Warner shares if Fox or another buyer offered $90 to $95 a share.

"At those levels, it becomes harder for Time Warner to argue the merits of continuing to remain independent," Narancich said.

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