Fragrance maker Coty has made public a $10 billion offer for Avon Products Inc. (NYSE: AVP), the struggling direct seller of beauty products, after private talks proved unfruitful.

The cash offer of $23.25 a share, a 27 percent premium to Avon's average share price over the past three months, values the New York company at about $10 billion.

Coty, which is also based in New York, disclosed that before making its offer public, it had tried to reach a deal with Avon privately. On March 7, it offered the beauty-products company $22.25 a share.

Privately held Coty made two additional disclosures about its acquisition attempt: It doesn't intend to launch a hostile takeover, and remains willing to consider a higher offer provided Avon can justify such a move.

Avon's board flatly rejected the latest offer, saying Coty was offering only 1.1 times Avon's net revenue and 8.7 times earnings before interest, taxes and amortization, based on 2011 figures, which is significantly below multiples [that] an iconic consumer company is worth in a change-of-control transaction.

Avon, which sells lipstick, hairspray and other beauty products through direct marketing, has been struggling in recent years.

It has reported declining net income for the past four years. Late in 2011, the company announced it was seeking a replacement for longtime CEO Andrea Jung.

Still, Coty is attracted to Avon's marketing infrastructure, specifically its 6.4 million sales representatives. The fragrance company believes this distribution channel, which has a strong presence in many emerging markets, could be used to sell Coty's own products.

Shares of Avon closed up 17.25 percent at $22.70.