Riverdale Country School, where tuition costs $45,600, wants the city to subsidize its construction of a new swimming facility, student center and its renovation of its existing gymnasium. View Full Caption Facebook/Riverdale Country

FIELDSTON — Riverdale Country School, the fourth-most expensive private school in the nation last year, wants the city to subsidize a new pool, gymnasium and theater for its privileged pupils, records show.

The tony Bronx academy, where tuition costs a whopping $45,600, has asked a quasi-city agency called Build NYC Resource Corporation to approve the issuance of $52 million in tax-free bonds.

The kindergarten to 12th-grade school wants the bonds to raise funds from investors for the construction of a new 13,087-square-foot “natatorium” that will house a six-lane swimming pool for competitive use.

In its bond application to Build NYC, Riverdale Country describes its current swimming facility as “beyond its useful life.”

The school also says in its application that it wants to build a 23,000-square-foot multi-purpose building that would include a theater, a student center with cafeterias and classrooms.

The school, located in the leafy enclave of Fieldston, describes the design of the new building as a “lens through which students can experience and study the surrounding environment.”

Riverdale Country also plans on renovating its existing gymnasium, adding new flooring, seating and lighting to support athletic and public assembly needs. The existing swimming facility in the gymnasium would be converted into a junior varsity training area, according to the school's application.

About $22 million of the tax-free bonds would also help the school refinance other debts.

Build NYC will hold a public hearing on Riverdale Country’s application on Thursday. The agency's board, which is controlled by Mayor Bill de Blasio's appointees, is expected to vote on the application next Tuesday.

Build NYC oversees a program that helps facilitate tax-free bonds for nonprofits planning major capital projects. The agency’s website says it gives greater consideration to projects that create jobs, augment services to a needy population or provide a service that will reduce the cost of the city providing that service. However, the agency also considers nonprofits' projects that don't meet those criteria.

Riverdale Country, which is a nonprofit, declined to say whether its project will serve a needy population or will meet other criteria Build NYC prefers.

"We feel we have made an appropriate application to Build NYC to finance these projects," Riverdale Country headmaster Dominic Randolph said in a statement. "Build NYC will determine whether our project fits their criteria."

The New York City Economic Development Corporation, which administers Build NYC, wouldn't say whether the school met any of its preferred criteria. But the agency said that Riverdale Country was entitled to apply for the subsidy "so long as it's compliant with local regulations and best practices."

The NYCEDC said that if the deal is approved, the city will lose an estimated $817,423 in taxable income from bond interest payments to investors — but money will be made on the back end. The agency claims the city will directly and indirectly collect about $29 million in tax revenue connected to the project's construction.

The NYCEDC said construction would probably not happen without the subsidy.

"It's highly improbable that Riverdale would move forward with capital improvements on this scale if not for the tax-exemption," the agency said in a statement.

But tax filings show the school isn't hurting for cash.

Riverdale Country’s most-recent filing shows that the school raked in $69 million in revenue and held net assets of $104 million in 2012. That year, it had an endowment worth $18.5 million.

Business Insider also listed Riverdale Country as the fourth-most-expensive private last year, charging $44,600 in tuition.

Randolph, who made $564,000 in salary and compensation in 2012, said many nonprofits similar to Riverdale Country have previously requested and received the tax-exempt bonds from Build NYC.

"It is common practice for nonprofit organizations such as schools, museums and cultural groups to seek financing from Build NYC for capital projects," he said. "We are following the same type of process to fund capital works as any other nonprofit entity does in New York City."

The NYCEDC called the Build NYC program crucial to helping nonprofits flourish and encouraging them to create jobs.

"Riverdale provides high-quality jobs to hundreds of New Yorkers, as well as educational opportunities to students of all backgrounds," the agency said.