Coty Inc. is bent on getting bigger through acquisition.

Reports that it won an auction for three parts of Procter & Gamble Co.’s beauty business sent Coty’s stock up 20.1 percent to a high of $31.29 on Tuesday morning. Shares later closed at $31.09, up 19.4 percent, on the New York Stock Exchange on Tuesday.

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The New York Post first reported that the $12 billion deal bundles together P&G’s CoverGirl and Max Factor brands, along with Wella and fragrances, which includes Hugo Boss, Gucci and Dolce & Gabbana. When asked if a deal was imminent, both Coty and P&G declined to comment.

Bank of America Merrill Lynch analyst Olivia Tong estimates the three parts of P&G beauty portfolio generate roughly $5 billion in sales, which means the addition of the P&G brands would more than double Coty’s $4.49 billion sales. It would catapult Coty to the spot of the fifth-largest global beauty company — behind the Estée Lauder Cos. Inc. — up from its current rank of number 12 on WWD’s annual ranking of the top 100 largest beauty firms.

“It clearly increases Coty’s stature in the marketplace, and it is a very well-run company,” said Bernstein analyst Ali Dibadj, who nodded to the operational expertise of Coty’s chairman and interim chief executive officer Bart Becht.

Reports suggest that Coty is likely to pursue a Reverse Morris Trust structure, which as Morgan Stanley analyst Dara Mohsenian stated, “would leave P&G shareholders with a majority stake in Coty, and would eliminate taxes on the transaction for P&G.”

The deal would dramatically change P&G’s beauty portfolio, leaving only Olay and Pantene and several other retail hair-care brands remaining. In some eyes, such a move would recast P&G’s beauty business as a personal-care operation.

At the WWD Beauty Summit on June 9, Alex Keith took issue with that assertion, declaring, “Is P&G getting out of beauty? The answer is a resounding ‘no.’” She said she returned to the division seven months ago to “get our beauty business back on track.”

Keith said, “Our journey is not the pursuit of becoming the biggest. It is simply the pursuit of becoming better until better becomes best.”

The deal would shift the balance of power to a much smaller player.

“Coty becomes bigger, and P&G becomes somewhat smaller,” said Dibadj. “P&G clearly loses scale in the beauty business, which is something it hadn’t leveraged anyway.”

Several sources speculated that a deal with P&G is likely contingent on taking Wella, which at least one potential suitor said was too wounded to consider buying.

“I guess the investment community thinks Coty’s management is far superior to that of P&G,” said industry consultant Allan Mottus. “The question is, are the brands too beaten up to be resuscitated?”

Despite the pop in Coty’s stock price, not everyone on Wall Street viewed a deal with Coty as a victory for P&G shareholders.

ConsumerEdge Research analyst Javier Escalante noted, “One lesser-known valuation angle is that P&G actively seeks the retention of post-merger synergies when structuring [Reverse Morris Trust deals] and Coty’s portfolio looks better in a comp sheet than it does operationally.” He continued, “In our view, Coty doesn’t have much synergy to offer. It lacks global go-to-market capabilities and its distribution partnerships in emerging markets are too new to be reliable. …Coty’s weak fundamentals underscore that structural changes of portfolio touching both the category and geographic axis are risky. Coty’s China TJoy is a good example and relevant to understand P&G’s problem with Wella. This $346 million acquisition [of TJoy] destroyed value.”  Escalante explained that the brand itself was discontinued and its distribution network disbanded.

He noted that should the deal take place, L’Oréal stands to gain the most, as Coty grapples with reviving P&G’s beauty brands.

Coty has struggled to grow sales since its initial public offering in June 2013. In its most recent quarter, Coty’s net revenue declined 7.4 percent to $933.8 million, from $1.01 billion in the year-ago quarter. Sales were flat in constant currency.

Coty has been active on the acquisitions front, and in 2012 it boldly pursued a $10.65 billion takeover bid for Avon Products Inc., which it dropped in May 2012. One year later, Coty successfully completed its IPO. Since then, Coty has been focused on wringing out costs and aims to funnel some of the savings into its 10 “power brands,” which include Adidas, Calvin Klein, Chloé, Davidoff, Marc Jacobs, OPI, Philosophy, Playboy, Rimmel and Sally Hansen.