The beauty business can get ugly fast when makeovers give way to takeovers. Just ask Ronald Perelman what it took to buy Revlon.

Now Avon Products (NYSE: AVP) looks like takeover bait, since Coty went public with a buyout offer the company had rejected -- its second offer, according to some reports. This naturally raises the antennae of the more speculative-minded Fools out there, but beware, Avon could be the date that looks ugly without her makeup the next morning.

A bidding war could inflate the stock price of a company that hasn't done much lately to justify a rich valuation. It's not quite putting lipstick on a pig -- Avon does have potential, but whether it can live up to it is an open question.

Coty initially said it wasn't interested in a hostile bid, and with good reason. As Fools have pointed out before, Avon has issues -- financial, operational and legal -- so getting into a bidding war is not a good idea. But now reports have surfaced that it's still lining up financing and hinting it could raise its bid.

And that follows reports that a former CEO of Mary Kay Cosmetics is circling the company with his investment firm. Richmont Holdings, a former Avon shareholder led by John Rochon, was reported by Fortune to be looking at Avon. That is, looking at Avon again, because Rochon was already turned down by Avon in the 1980s when he was vice chairman of Mary Kay and proposed merging the two companies.

Avon's management has said it's determined to go it alone, but the company has stumbled just when it should be making hay, as the economy begins to turn around and consumers find a little extra money to spend on face creams and eye shadow. And its main headline in overseas markets is a federal investigation accusing its Chinese employees of bribery.

Even as direct sales move online in the U.S., Avon's model is working in emerging markets, where it could reap big-time sales increases. Tupperware (NYSE: TUP) -- which not coincidentally is headed by a former Avon CEO -- is riding the direct-sales model to strong sales overseas and showing that a door-to-door business can be overhauled for the 21st century. But as Fool Brian Stoffel pointed out, Avon wasn't executing internationally under former CEO Andrea Jung. New CEO Sherilyn McCoy hasn't been in the job long enough to show whether she's up to the challenge, so investors will be guessing whether she can turn the ship around.

And the disruption from a merger doesn't help a company that's suffering from operational issues, as Morningstar's Lauren DeSanto pointed out in panning the potential Coty deal. It doesn't make sense for Avon to merge with Coty, which sells mainly through department stores; besides, Avon's customers are not clamoring for Lady Gaga perfume and Coty's other brands.

So it's possible Avon isn't merely playing hard to get and looking for a better offer. But is there a better offer to be had? Avon's management sniffed at the 20% premium Coty offered at $23.25 per share, and the stock ran up and ate that premium as soon as the offer went public. Morningstar has a $25 fair-value estimate on the stock, so one more spike fueled by a credible offer could put the stock over the top.

The CAPS community likes Avon, but it already trades at a rich valuation compared to similar cosmetics companies such as Revlon, as Fool Rich Duprey pointed out here. With a P/E around 19, it's hard to see how much more of a lift it can get before it begins to look overpriced.

Estee Lauder (NYSE: EL) trades much higher, with a P/E of 29, but it has a stable of brands known the world over and retail relationships worldwide, so it's well-positioned for the economic recovery. Revlon (NYSE: REV), which is more in Avon's league, trades at a P/E around 17.

Even if you feel you want to speculate on an Avon bidding war, it would be as a short-term trade, not a buy-and-hold investment. Long-term investors who buy into this company now could end up with an overpriced stock that may or may not deliver on its premium.

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