“I want to thank my family because they put up with me,” Trump told the crowd. “They say, ‘He’s crazy, he’s got to be crazy.’ But we knew we could get it done.”

One important footnote was missing, though: Trump didn’t build the course. He doesn’t own it, either. His company manages it for the city, whose taxpayers spent $127 million to sculpt it atop an old Bronx garbage dump.

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That hasn’t stopped Trump from prospering in a different way. With the course nearly finished, Trump secured a generous 20-year deal with the city allowing him to keep almost every dollar that flows in. Taxpayers for the first four years get nothing, except for the sprawling course’s utility bills.

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Trump has aggressively pushed to reduce the tax bills at his portfolio of sumptuous golf courses, dispatching lawyers to win lower tax valuations for the same clubs he tells election regulators are high-value gems.

But even at a golf course where Trump has no ownership and doesn’t pay property taxes, the Republican presidential candidate has found ways of profiting from public funds. In the Bronx course’s first year of play, city records show Trump’s company made $8 million in revenue while taxpayers covered $1 million in water and sewage bills.

Trump has often pointed to the lush New York links to support his claims of being a golf visionary and master businessman. In election filings this year, he listed the club with his other “assets” and said it was worth up to $25 million.

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The course also played a key role in a video tribute to Trump at the Republican National Convention last month, when actor Jon Voight said Trump “transformed a landfill into a championship public golf course and saved the city millions.”

But it was public money that turned the site, a 192-acre Bronx landfill closed in the ‘60s, into a rolling 18-hole course backdropped by the Manhattan skyline. Designed by legendary golfer Jack Nicklaus, it sits at the foot of the Whitestone Bridge connecting the Bronx and Trump’s native borough of Queens.

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Approved in the late ‘90s, the project slogged through years of legal delays, cost overruns and management fiascoes that led the New York Daily News to label it the “boondoggle in the Bronx.” The city axed its agreement with the course’s original developer in 2006, shortly before an auditor said the city had squandered millions in public funds.

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The city took over construction and began looking for companies that could operate the course once it was complete. To entice bidders to the risky proposition of managing a once-blighted dump, the city sweetened the offer, easing deadlines and allowing for a lucrative revenue-sharing deal.

In late 2011, the administration of then-Mayor Mike Bloomberg announced it had chosen Trump over two other candidates and offered him the 20-year contract. Trump had a well-regarded history as a city contractor, operating two skating rinks and a carousel in Central Park.

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Trump company officials said Bloomberg asked for Trump to bid on the Ferry Point contract, and city leaders admitted then that they were desperate to get the project back on track. “At this point, I don’t care if it’s Donald Trump, I don’t care if it’s Donald Duck,” City Councilman James Vacca said in 2012. “This golf course has waited far too long.”

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Adrian Benepe, who served as New York’s parks commissioner from 2002 to 2012, said the city had struggled for years to find a company willing and able to handle the job. Other operators, he said, would have received similarly favorable terms due to the inherent difficulties of running the site.

“People don’t like the terms, but those were the best terms we could negotiate at the time given the circumstances,” Benepe said.

Not everyone, however, was happy with the city’s negotiating. A representative for John C. Liu, the city comptroller who had first audited the troubled venture, voted in 2012 against the Trump deal, saying the office “was not comfortable with the compensation of the project.”

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Even now that the course is open, Liu said Thursday, “my sentiments have not changed one bit. … I just don’t think its worth about $200 million of public taxpayer money.”

In the years since the agreement began, Trump has declared himself an invaluable leader who rescued the course from disaster. In a statement to The Post, a Trump spokesman said it was “a prime example of government waste, fraud and abuse until Mr. Trump got involved.”

Ivanka Trump wrote in a blog post last year that her father whipped workers into shape by saying, “You guys have made a lot of money pushing sand around for the last 20 years, but that stops with me.” City officials, however, say Trump was merely a “concessionaire” let in after the bulk of the city’s design and heavy construction work was finished.

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As part of his deal, Trump agreed to build a $10 million clubhouse within the first five years, run the course and pay for the continued upkeep of greens, fairways and roughs. In return, the city agreed to cover water and sewer costs and let Trump keep all of the course’s earnings. Trump’s company only has to pay the city a growing share, starting at 7 percent, of the course’s yearly revenue starting in 2019.

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In the first year of the deal, Trump’s company tallied $8 million from greens fees, golf-cart rentals, banquets and other sales, city filings show. If the revenue-sharing deal had started immediately, the course would have owed New York $500,000 in the first year.

Trump’s victories, financial and otherwise, are now immortalized on the public greens. At the 12th hole, crews installed a plaque to commemorate its first hole-in-one — an 8-iron shot by Donald J. Trump.

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The city didn’t pay for that, parks spokesman Sam Biederman said: “Mr. Trump can afford to commemorate his golf triumphs himself.”

Shortly before landing the deal, Trump hired Ron Lieberman, a director of concessions for the city’s parks department who resigned in 2007. Lieberman is now a Trump Organization executive vice president of management and development, and he helps run Trump’s golf courses. The company declined to answer questions about Lieberman’s involvement in the New York deal or make him available for an interview.

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The Trump family and its foundations has found another way of raising money from the public course. The Eric Trump Foundation, founded by Trump’s son, will host a Golf Invitational & Auction Dinner at the course next month, with “bronze golf foursome” sponsorship opportunities starting at $10,000.

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When announcing the deal, the city said building the clubhouse would “create 100 new construction jobs,” and that the course would “generate economic activity in the Bronx.”

But Ferry Point has also become one of the most discomforting symbols of New York’s yawning class divide. The city’s most expensive public course operates in the city’s poorest borough, where one in three residents lives below the poverty line. Its GPS-equipped golf carts and high-end prices stand out of reach for many New Yorkers: An 18-hole weekend round of golf starts at $145, three times the price of the city’s other public courses.

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Construction has not yet begun at Trump’s promised clubhouse, and city officials say it’s too early to quantify the course’s economic impact. They point to Ferry Point’s 200 employees, about 100 of whom are Bronx residents, as a sign of its success.

But Geoffrey Croft, the founder of local watchdog group NYC Park Advocates, says he doubts the course’s low-income neighbors will see much “economic activity” — or that city taxpayers will ever make their money back.