Now that Goldman, Sachs & Co. has decided to hold a public offering of shares, most market watchers expect the firm to join its Wall Street competitors and buy an asset management firm.

Such an acquisition would not come cheap. Takeover prices for asset management companies are high, and few wish to sell.

Merrill Lynch & Co. demonstrated last November just how dear a big acquisition in this arena can be when it agreed to pay $5.2 billion for Mercury Assets Management Group PLC of London. That price was a 31% premium over Mercury's market price and was the equivalent of 3% of its assets under management.

Goldman has acquired a few smaller asset management firms, but its operations are nowhere close to the size and scope of Merrill Lynch or its other chief Wall Street rival, Morgan Stanley Dean Witter & Co.

The principal reason is that Goldman, the last large traditional investment banking partnership on Wall Street, has lacked the resources to acquire such capacity.

By contrast, Morgan Stanley went public in March 1986.

However, investment bankers and analysts at rival firms say Goldman is armed with one key advantage if it pursues a costly asset management acquisition: Its own bankers are intimately familiar with the people in that business because they have advised them for years.

Goldman's investment bankers have long underwritten debt or equity offerings and provided advice to such prominent names in the business as T. Rowe Price Associates of Baltimore and Mellon Bank Corp. of Pittsburgh.

"They know who's out there and who's willing to sell," said one analyst.

Some investment bankers around Wall Street suggested that Goldman could explore some kind of merger with Mellon, which owns Dreyfus Corp. and has over $300 billion of assets under management.

Mellon, which has built a formidable asset management franchise under the zealous leadership of its chairman and chief executive, Frank V. Cahouet, has spurned all previous offers to sell.

It emphatically rejected an unfriendly bid from Bank of New York Co. this spring. At Mellon's side during that episode was its investment banker, Goldman Sachs.

Some observers said the climate for a possible sale of Mellon could change after Mr. Cahouet retires later this year.

But even if Mellon and Goldman are on friendly terms, most analysts consider a marriage between the two unlikely. Mellon's market value of $17 billion towers over the likely market value of Goldman's initial public offering.

Analysts say Goldman would probably have to conduct a follow-up offering-make public more of the firm's equity-to finance a merger with Mellon.

That in turn could dilute the value of the shares Goldman elects to make public. "Imagine Goldman Sachs diluting its own stock," said one rival investment banker.

But most analysts said Goldman could persuade its new shareholders to accept a big, dilutive acquisition-assuming it can find a company willing to sell.

After all, Merrill Lynch's stock has held up well since the costly Mercury deal, thanks to the continued bull market.

"In acquisitions like this, you tell investors not to focus on earnings, but look at the cash flow that will be generated," one analyst said. "And so far they have bought into that."

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