Billionaire Paul Singer just made a big bet on further cost-cutting in health care.

Singer’s Elliott Management on Thursday disclosed an 8.3-percent stake in Advisory Board — a Washington, DC-based hospital-consulting firm — and the company’s shares jumped 16 percent to $42 on the news.

Just last week, the company announced layoffs and office closures, but Elliott sees more room for streamlining.

Advisory Board’s business includes a subscription service that provides industry research to health care organizations as well as technology and management consulting.

Elliott said in a securities filing it believes Advisory Board’s shares are “significantly undervalued” and that it aims for a “constructive dialogue” with its board.

Advisory Board responded that it is “always open to discussing constructive ideas for enhancing long-term shareholder value.”

Advisory Board’s stock had been cut nearly in half from its high of $69 in October 2013.

Despite the recently announced restructuring, Advisory Board is likely to be hampered by regulatory uncertainty in the health care space, people close to the matter told The Post.