Kenneth Cole Productions Inc. shares topped the $15 price the company’s founder offered to take the shoe and clothing maker private, hinting investors may be anticipating other bids. Kenneth Cole, who holds 47 percent of outstanding shares, offered to buy the remaining stake in a deal that valued the business at $280 million. Cole, who is also chief creative officer, started the company in New York in 1982 with a focus on shoes. He currently holds 89 percent of the voting power. Cole said he intends to keep current management in place. “Recent market challenges have created a sharply competitive landscape, and I believe it is now more important than ever to embrace a more entrepreneurial perspective,’’ he said.