America Online Inc. has enjoyed confounding its critics for years, but last week it stunned its supporters.

AOL shareholders went to sleep that Sunday thinking that they owned a high-growth, highly profitable Internet company, and awoke the next morning to find a slow-growing, debt-ladened media giant in its place. Many were not amused.

AOL stock tumbled from $75 a share to almost $60 at one point last week, closing Friday at $63.18 3/4.

Discussion boards on various World Wide Web sites were filled with screams of anguish by individuals over their lost savings and accusations of betrayal as they saw the stock price plummet. But the most pressing questions raised were variations on this: Should stock in the new AOL, after it acquires Time Warner Inc., be priced based on "Internet valuations" or traditional valuations?

Tom Kerr, a portfolio manager at Reed Conner & Birdwell, a Los Angeles-based investment adviser for institutional clients, said if the new company were like AOL, it would have a market capitalization of $1 trillion. Clearly that's ridiculous. If it were valued like Time Warner, the company's market cap would be significantly less, meaning AOL's stock would plunge even further.

Kerr takes the hybrid approach adopted by many analysts and portfolio managers in the wake of the deal--he expects to see valuations settle down to something in between. If the proposed merger works as planned, the companies are probably trading at a fair price right now, said Kerr. If AOL's stock settles around $60, the combined AOL Time Warner would have a market cap of about $276 billion, compared with $340 billion when it was announced, he said.

Henry Blodget, Merrill Lynch & Co.'s influential Internet analyst, said in a report last week that he thinks investors would value the new AOL Time Warner using the same "new economy" valuation logic they used to run up AOL's stock, at least for a while.

"The most important factor for determining whether the stock will rise over the long term is an assessment of whether the entity's future will continue to excite people ('the story')," Blodget wrote. "As the enthusiasm about the company grows, more people will want to own the stock and the multiple will expand."

But if the investing public doesn't get swept up by "the story," then the most important factor in determining the stock price would be future cash flow, he said.

Pat Dorsey, a senior stock analyst at Morningstar Inc., thinks the proposed AOL Time Warner should be valued as a media company. Despite having majority ownership, AOL would account for less than 20 percent of the revenue of the new company.

Thus, Time Warner's annual revenue growth of less than 10 percent is certain to pull down the annual 50 percent revenue growth of AOL. Dorsey conservatively expects the new company to produce revenue growth of slightly less than 20 percent a year. He expects that moderate savings would produce cash-flow growth of slightly more than 20 percent.

Dorsey thinks that the current stock levels price the deal "richly but not absurdly. There are a lot of risks with this merger."

In fact, part of AOL's problem is that the risks are easily quantifiable--slower growth and Time Warner's enormous debt load. It's the rewards that are harder to quantify. The new company could be a monster success, becoming the media and Internet powerhouse of the 21st century. It could well have the resources and infrastructure to finally make interactive television happen.

The new company also would have 100 million subscribers, by Dorsey's estimates, and the ability to track their buying habits. That could be a marketing gold mine, he said.

But mega-mergers are notorious for not delivering on their promises. Companies get distracted by power struggles and culture clashes.

As investors try to decipher this deal, there are some early warning signs they should watch.

Are a lot of changes going on? "Any merger of this size is going to require a lot of shaking up to make it work," said Dorsey. "If you don't see a lot of news about that in the next couple of weeks, it may mean that folks don't even know where to start. You probably want some executives to lose jobs, that will mean somebody is in charge. Of course, you don't want [AOL President Robert] Pittman or [AOL Chairman Steve] Case to lose jobs."

Can the merging companies tell "the story" in a coherent and compelling way? "So far, they haven't been able to," said one mutual fund manager. "The fact that so many people are running around the Street complaining they don't know if this is fish or fowl" shows that the two companies either don't know their story or have failed to communicate it to Wall Street.

AOL was a fairly straightforward company to comprehend. Its revenue came from subscriber fees, electronic commerce fees and advertising. Individual and institutional investors could all grasp the story.

The proposed AOL Time Warner would have money coming in from dozens of companies, with different ways of charging for goods and services and complicated ownership structures.

"I wouldn't be surprised if more than a few owners at large mutual funds just threw up their hands. They probably already had big gains in the stock if they had held it for any length of time," said Dorsey. Others probably invested in AOL because they wanted a high-growth Internet company for their portfolio, decided the new AOL would not be that, and then dumped the stock.

As "the story" gets told, revised and re-revised by the market, AOL's stock is expected to bounce up and down. Investors who hold onto it should expect a roller-coaster ride for the next several months, analysts say.

Where will it settle? That depends on whether investors ultimately decide the new AOL is fish or fowl.