The recent United States tour of the Broadway musical “Priscilla Queen of the Desert” had Korean money from the producer Seol and Company, which may soon mount the musical here. And the 2007 Broadway musical “Legally Blonde” had a million-dollar investment from Song Seung-whan, a theater impresario who thought the show could be a hit in Seoul with a Korean pop star in the bubbly lead role of Elle Woods, the law student played by Reese Witherspoon in the movie (which was popular here). The Korean production did make money, especially on nights when Jessica, a member of the red-hot K-pop band Girls’ Generation, was performing as Elle.

“I’ve been looking for another Broadway investment like ‘Legally Blonde’ that would attract our younger audiences and be perfect for a K-pop star, but I’m being picky,” said Mr. Song, whose main focus is his long-running play “Nanta” (or “Cookin’ ”), a comedy set in a restaurant kitchen that ran off Broadway and has been mounted in China, Japan, Vietnam and many other countries over the past decade.

Broadway and British producers see a potentially lucrative market in China, but they are proceeding with caution, they say, given that doing business there raises a hefty range of issues — royalty agreements, licensing contract terms, copyright protections, piracy concerns — that have yet to be negotiated or resolved with Chinese theater owners, producers and government officials. The Broadway hits “The Lion King,” “The Phantom of the Opera” and other musicals have had relatively brief runs in China, but the business arrangements for those productions have mostly been worked out show by show. For the Chinese market to develop, as it has in Seoul and Tokyo, standard producing agreements have to become the norm.

For now, the Korean investing strategy mostly benefits Broadway producers, who need financing for shows, and theater artists like the composer Frank Wildhorn, who has had several flops on Broadway but has become one of the most celebrated in his field in Korea. His musical “Jekyll & Hyde,” which lost money in New York, just celebrated its 10th anniversary in Seoul and is considered one of the most financially successful American musicals here. (By comparison, the composer Stephen Sondheim is barely known, and his musicals “Assassins” and “Company” sold poorly here.)

“You get another life over in Seoul,” Mr. Wildhorn said.

As Mr. Kim of CJ explained his goals, he could have been mistaken for an executive from another of the company’s many divisions, with talking points prepared in a memo and two large bulletin boards by his desk that listed monthly box office projections and performance schedules for CJ shows. His comfort with making deals certainly came as a boon for “Kinky Boots” — covering a significant share of its Broadway budget — and for its lead producers, who had grown accustomed to long negotiations with American investors over checks in the $50,000 and $100,000 range.

The musical had just begun its tryout production in Chicago in 2012 when one of those producers, Hal Luftig, received an email from a CJ executive asking to hear the Lauper score and read the script. Soon after, Mr. Luftig was in negotiations for the money; the only sticking point, he said, was that CJ wanted the right of first refusal to produce “Kinky Boots” in Australia as well as in Korea. The Australian territory had already been claimed by another producer.

Mr. Luftig promised that CJ would be next in line for Australia, which sufficed. Not long after, he had the money in hand.

“I wish more deals were done this quickly, easily, gentlemanly and without gamesmanship,” said Mr. Luftig, who also provided CJ executives with tickets to opening night on Broadway. “But the real benefit, I hope, is the relationship. Until now, I had no partners who knew how to exploit the markets in Korea, China and the rest. It’s not like I’m going to hop over to Seoul and say, ‘Let me figure out this market myself.’ ”