Private equity giant Kohlberg Kravis Roberts & Co. plans to go public on the New York Stock Exchange later this year via a share swap with its publicly listed leveraged buyout fund, the buyout shop said in a statement Sunday.

KKR’s latest proposal to go public replaces an earlier plan to raise $1.3 billion in a conventional initial public offering — a difficult proposition in today’s market, which has punished shares of KKR’s listed rivals.