SunTrust Banks Inc., hoping to quell once and for all Wall Street’s speculation that it would eventually raise its bid for Wachovia Corp., insisted on Monday in its most forceful terms to date that no such increase in its hostile offer would be forthcoming.

And then it spelled out just how there might be a couple more dollars in the deal for Wachovia shareholders, assuming events play out to the Atlanta bank’s advantage in coming days.

The statements by SunTrust, which is in the midst of a two-month battle for Wachovia with Charlotte, N.C.-based First Union Corp., show the delicate balance the company must maintain as it courts Wachovia shareholders while simultaneously seeking to reassure its own that it won’t overpay.

Concerns that SunTrust might increase its bid are thought to be part of the reason that investors have been shying away from the company. At the same time, a rise in First Union’s share price has all but erased the premium SunTrust’s offer once promised over First Union’s friendly bid.

SunTrust is trying to persuade Wachovia shareholders to reject their company’s Easter Sunday merger agreement with First Union in advance of Wachovia’s Aug. 3 annual meeting. In a press release Monday, SunTrust said it wants to eliminate market perceptions that it might raise the bid it announced May 14.

“Although we have said from Day One that we would not raise our bid … speculation diverted attention from the merits of our proposal,” chairman and chief executive L. Phillip Humann said in a conference call Monday afternoon. “Our offer of 1.081 shares [for each Wachovia share] is our best and final offer. Best and final means just that, best and final offer.”

First Union has offered two shares for each Wachovia share, but SunTrust’s offer remains slightly more valuable in dollar terms.

Mr. Humann said speculation about whether SunTrust would raise its bid may have kept institutional investors from buying his company’s shares, and he used Monday’s announcement to make a pitch for them to resume buying.

Nancy Bush, an analyst at Ryan, Beck & Co., said, “They have been saying all along they wouldn’t raise the bid, and nobody was listening to them.”

Michael Mayo of Prudential Securities said he was surprised at the forceful tone of the announcement. Because institutional investors say that SunTrust’s offer must be at least 8% better than First Union’s to be attractive, he still thinks SunTrust will need to sweeten the bid. But Monday’s announcement makes that more difficult, he said.

“There’s a great risk now that if they were to increase their bid and lost, they could put their own independence at risk,” he said.

Wall Street appeared to respond to the appeal, as investors sent SunTrust’s shares up 2.4%. At least for the moment, that lifted the value of SunTrust’s bid to 5% better than First Union’s.

Mr. Humann also said the company would not offer any of the deal sweeteners that some analysts have speculated it could, such as paying cash in addition to the stock or selling part of its vast holdings of Atlanta-based Coca-Cola Co. so that it could pass along gains to Wachovia shareholders.

Nonetheless, SunTrust also said for the first time in a press release on Monday that if it wins its North Carolina court challenge to costly break-up provisions in the First Union-Wachovia deal, it would pass along some of the savings as a cash payment to Wachovia shareholders. The offer hinges on whether a North Carolina business court judge rules in SunTrust’s favor, something that is uncertain at best and which some analysts consider highly unlikely.

SunTrust sued both First Union and Wachovia seeking to invalidate a complicated set of provisions in their merger agreement that were designed to make it difficult, if not impossible, for another bank to merge with Wachovia. The anti-break-up provisions, similar to those found in other major corporate mergers, would allow First Union to buy up to 19.9% of Wachovia stock at $59.48 based on stock prices at the time of the deal. First Union could turn around and sell that stock, reaping a maximum of $780 million in profits, under the agreement.

SunTrust alleges that $780 million amounts to an “egregious” break-up fee, and has argued that $440 million would be more appropriate, based on other deals. If SunTrust were to win the court case, it says it would make cash payments totaling $440 million, or $2.16 a share, directly to Wachovia shareholders.

Executives have discussed the potential cash offer previously with analysts and institutional shareholders, but Monday was the first time the company mentioned the idea in a press release. Based on Monday’s closing stock prices, that would make SunTrust’s offer worth $74.62 per Wachovia share, or 8% more than First Union’s bid.

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