Updated: 4:56 p.m. ET

Avon Products (AVP) is weakened and vulnerable -- and Coty pounced on the opportunity with an unsolicited $10 billion acquisition offer.

Avon immediately rejected the bid, but that didn't stop its shares from soaring Monday as investors sensed opportunity -- and negotiation. News of the offer pushed Avon's shares up $3.34 to $22.70. Volume topped 64 milion shares -- more than 10 times the daily average.

There are many problems with Coty's offer -- but that doesn't mean a merger of the cosmetics companies is a bad idea.

Coty, which is privately held, is much smaller than Avon, with revenue of about $5 billion -- less than half of Avon's 2011 revenue of $11.3 billion. JPMorgan (JPM) is arranging the debt financing, though questions remain about how Coty can afford such a massive acquisition.

Coty at first shopped itself to Avon as an acquisition, but Avon shot that idea down, CNBC reported. S&P had recently downgraded Avon's debt, and maybe Avon didn't think it could afford the purchase. Coty, for its part, has been on an acquisition spree, gobbling up a majority stake in Chinese skincare company TJoy Holdings in 2010, for example.

Merging the product lines of the two companies makes sense. The deal would be the biggest in the cosmetics and toiletries industry since Procter & Gamble (PG) acquired Gillette for $57.3 billion in 2005.

So what's wrong with Coty's offer? It was probably just too low. Coty's bid was a 20% premium over Friday's closing price for Avon, equaling a multiple of 1.1 times Avon's revenue last year, and 8.7 times 2011 EBITDA. That's not great, but not chopped liver either.

It's clear that Avon shareholders would do better under Coty's management. CEO Andrea Jung has allowed Avon to flounder for years. Last year, the company stunned investors when it announced that it faced two regulatory probes for allegedly violating both Regulation FD and the Foreign Corrupt Practices Act. And let's not forget the disastrous implementation of a computer system in Brazil and the company's repeated earnings disappointments.

Avon's board has decided to replace Jung, whom CNBC's Jim Cramer called "one of the worst managers I have seen in my career," as CEO. But for reasons that mystify most, they let her remain as executive chairman for at least two years. Two former Avon CEOs denounced the board's idiotic decision.

It wouldn't be surprising to learn that Jung blocked an alliance with Coty in a last-ditch effort to hang on to power. The company is not saying if this is the case, however.

The Avon board ought to figure out how to make the deal work or find another merger partner. Shareholders might get a better deal than the one that Coty has offered once it begins to seriously review its options. Maybe Coty will raise its offer, or one will emerge from a rival such as Estee Lauder (EL), whose 2011 revenue topped $8 billion.

Jonathan Berr thinks his skin tone is "autumn." He does not own shares of the companies listed here.

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