(Reuters) - Apollo-backed Realogy Holdings Corp plans to sell 40 million shares in its initial public offering at between $23 and $27 each, valuing the real estate services company at up to $3.51 billion.

Large sponsor-backed IPOs have been absent from the U.S. market this year, as private equity companies held off on exiting their investments in the face of continuing market volatility.

With the stock market stabilizing in recent months, bankers expect an uptick in IPO activity towards the end of this quarter.

Realogy franchises brokerage brands like Century 21, Coldwell Banker, Era, Sotheby's International Realty and Better Homes.

Realogy, owned by Apollo Global Management LLC (APO.N) and Paulson & Co, filed with regulators in June to raise up to $1 billion in its IPO, as it looks to lighten its debt load.

As of June 30, the company had a total debt of $7.34 billion. Realogy intends to cut its debt by about $2.8 billion after the offering.

The company was taken private by Apollo for about $6.65 billion in December 2006. Apollo Funds currently own about 73 percent, while Paulson & Co has a 15 percent stake in the company.

After the offering, Apollo's stake would be diluted to slightly over 50 percent, Realogy said in an amended filing on Friday.

Another Apollo-backed company, Berry Plastics Group set IPO terms earlier this month, valuing the plastic container maker at up to $2 billion.

Realogy expects to list its shares on the New York Stock Exchange under the symbol "RLGY."

Goldman Sachs and JP Morgan are acting as representatives to the underwriters for the offering.