Shares of Avon Products Inc. (NYSE: AVP), the world's largest door-to-door retailer, plunged Tuesday after perfume maker Coty Inc. withdrew its $10.7 billion offer to buy the New York-based company, expressing frustration with a perceived lack of response and poor communication.

Your total lack of engagement with us leads us to believe that you remain reluctant to explore a friendly, negotiated combination on a reasonable timetable. Two months is enough. Consequently, as our deadline to begin discussions expired today, our proposal is withdrawn, Coty Chairman Bart Becht said on Monday, in a letter to Avon's directors.

Coty, which makes perfumes for Beyoncé, Celine Dion and Heidi Klum, reached out to fellow New York-based Avon about the merger at the beginning of March, but Avon did not make an effort to come to the table for discussions, according to Coty. Moreover, Coty approached Avon on May 10 with a 6 percent increase in the value of the offer, which brought it to $10.7 billion, and the backing of Warren Buffett's Berkshire Hathaway Inc. (NYSE: BRK-A).

The latest offer from Coty was $24.75 per share, a 15 percent premium over Avon's share price of $21.60 the day before the offer was made.

Wall Street analysts said the deal was appealing.

We agree that Avon is 'fixable,' however, we believe Avon's board and shareholders missed a good opportunity to be acquired by Coty, UBS analyst Nik Modi said on Tuesday in a client note. While Sheri McCoy and Kimberly Ross seem like capable executives, we believe the issues at Avon will take time and lots of money to fix: In fact, given our view on Avon's issues, we believe it may take two to three years to sustainably fix.

Avon shares dropped $2.15, or 10.37 percent, to $18.58 in afternoon trading.