Jay Cashman, who runs a marine construction and dredging business in Boston, bought Kilkea Castle outside of Dublin in 2013. He said he had spent about 20 million euros (about $23.7 million) renovating the 12th-century castle and reviving the golf course that surrounds it. The annual payroll is €4 million ($4.7 million).

But Mr. Cashman, who rarely plays golf and doesn’t keep score when he does, said he did not expect to profit from the course. “It doesn’t make money but it sells the rooms,” he said. “It’s like a casino in the old days when they gave away the rooms and the entertainment. The golf course is a loss leader. But we make money in some other parts.”