Equity Group Investments LLC has offered to buy the shares of Rewards Network Inc. that it does not already own in a deal that values the company at about $120 million.

Under the nonbinding offer, Equity Group said Wednesday, it will offer $13.50 a share, a 36% premium to Tuesday's closing price. Sam Zell, an influential real estate investment mogul, controls a more than 26% stake in Rewards Network, which operates dining rewards programs and other loyalty credit card programs. His offer is worth about $90 million.

In a letter to the board, filed with the Securities and Exchange Commission, Equity Group said it was prepared to "promptly negotiate" terms of the deal and would allow Rewards Network a 40-day "go shop" period to search for better deals.

Rewards Network issued a press release Wednesday confirming it had received "nonbinding indications of interest" and saying that it was evaluating the interest and other options.

The letter, signed by William Pate, an executive with Equity Group, said the firm was engaged in financing discussions and planned to take on $60 million in debt to close the deal. At Tuesday's close Rewards Network had a market capitalization of about $95.7 million.

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