Exactly three weeks from today, shareholders of copper companies Asarco Inc. and Cyprus Amax Minerals Co. will vote to decide whether to accept a $5 upfront dividend and continue as shareholders of a merged Asarco Cyprus.

The outcome of the meeting will depend on how the shareholders respond in the meantime to rival bidder Phelps Dodge Corp.'s offer to exchange $2.6 billion worth of its own stock for the combined outstanding shares of the two companies.

The three-way bidding war offers an interesting insight in the calculations that shareholders must sometimes make as they ponder rival and complex bids. Should shareholders agree to a merger that will vault their companies into the No. 1 copper producer--or accept a deal that might bring them less now but make them part of an even larger company?

The saga started on July 15, when Asarco and Cyrpus announced a two-way merger, with each Cyprus share fetching 0.765 shares of Asarco, or about $14.50, which at the time offered investors a negligible premium.

Then, on Aug. 11, Phelps Dodge announced a counter bid for the two companies, offering 0.3756 Phelps shares for each share of Asarco ($22.04) and 0.2874 for every Cyprus share ($16.86). On Aug. 20, Phelps sweetened the swap ratio to 0.4098 ($24.05) for Asarco and 0.3135 ($18.39) for Cyprus.

In response, Asarco and Cyprus offered the $5 upfront dividend, bringing the value to $19.50 in a two-way merger, subject to shareholder approval of the deal.

Asarco and Cyprus believe their stocks have been undervalued by Phelps and that their shareholders will reject the offer. "We are confident that we will be successful," said Kevin Morano, president and chief operating officer of Asarco.

In an effort to emerge victorious, the two parties are wooing shareholders directly. In a recent advertisement, Asarco and Cyprus urged their shareholders to reject Phelps Dodge's offer.

Executives of the three companies will be hitting the road soon to personally meet with large institutional shareholders.

"Asarco and Cyprus create all the value [in the three-way merger with Phelps], yet they want to give a much smaller shareholding [ownership percentage] in the merged company," Morano said.

In the three-way merger proposed by Phelps, Asarco and Cyprus say, they bring 57 percent of the new company's production; 61 percent of the reserves; four of the five lowest cost mines; lower cash costs and 92 percent of the synergies. Being the value adder, the two companies want 50 percent of the combined company's ownership, and not 43 percent offered by Phelps Dodge.

To achieve half ownership, Phelps would have to offer 0.53 of Phelps stock for Asarco ($31.10) and 0.4055 for Cyprus ($23.79), bringing the total value of the deal to $3.38 billion.

But a Phelps spokesman said that any further sweetening of the deal was unlikely. "We consider the offer very firm," said the spokesman. Phelps chief executive Douglas C. Yearley has said that no counter-bid will be made if the two-way merger is approved.

One reason why Phelps is averse to raising the bid is that it will be dilutive to its future earnings. At the current price, the deal will boost the earnings of the copper giant.

Still, analysts believe, Phelps may increase the price, given the strategic importance of the deal. "A $3 increase in bid for both the shares is a reasonable valuation," said Vahid Fathi, mining and metals analyst at ABN Amro Holding NV.

The incentive for acquiring the two companies, even at a marginally higher premium, is strong. Apart from the fact that Phelps will lose its No. 1 position if Asarco and Cyprus merge, the copper industry is prone to wide fluctuations in demand and, hence, price. After a three-way merger, Phelps would be the only producer of copper in the United States, since BHP Copper Inc.--a copper producer on par with Asarco and Cyprus--closed shop this year.

By controlling the supply of copper into the market, Phelps would be able to make the demand and prices less volatile. "A consolidation will yield a softer boom and bust cycle," said Fathi. In other words, Phelps could become the "swing factor" in the copper industry.

That kind of a power would likely attract the Justice Department's scrutiny. Analysts believe that the three-way deal stands a good chance of passing an antitrust probe, since copper is a commodity and there are several other producers elsewhere in the world.

To begin with, however, Phelps shareholders must approve the all-stock acquisition when they meet on Oct. 13.

CAPTION: Phelps Dodge, Asarco and Cyprus Amax Minerals made their case to shareholders in these recent full-page newspaper ads.