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America’s wealthiest private colleges and universities will soon start writing millions of dollars in checks to the federal government to pay a new tax on their massive endowments, after spending the past two years pleading unsuccessfully for relief.

Harvard University announced Thursday that its new tax payment for the fiscal year that ended in June is likely to reach $50 million, including $37.7 million on the earnings from its endowment. Harvard’s $41 billion endowment is the largest university investment fund in the world, and experts anticipate that it will also have the heaviest tax burden.

Harvard president Lawrence Bacow called the tax “damaging” in his annual letter about university finances.

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It has the “potential to hinder Harvard’s ability to grow investments in financial aid, teaching, and research across campus,” Bacow said.

Other universities are also calculating how much they will owe the federal government, with the first checks due to the Internal Revenue Service in mid-November.

Dartmouth College with its $6 billion endowment estimates it will pay $4.5 million in new taxes. Wellesley College, which has a $2.2 billion endowment, expects to owe the federal government about $1.5 million in taxes for its endowment, officials there said.

The tax on college endowments was one of several controversial elements in a tax overhaul approved by President Trump and the Republican-controlled Congress in late 2017.

The IRS expects the new 1.4 percent tax on university investment income will affect fewer than 40 institutions; it applies only to schools that enroll more than 500 students and have endowments worth at least $500,000 per student. But many of the country’s most well-known and well-funded campuses are expected to take a hit, including Yale University, Princeton University, MIT, and Amherst College.

Higher education institutions have deployed squads of lobbyists and sent their presidents to Washington, D.C., to fight the tax, arguing that it will siphon money away from campus necessities.

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Harvard officials have said the university’s withdrawals from the endowment help to pay for about 35 percent of the school’s $5.2 billion in annual operating expenses. The university also gave undergraduates in the past year $193 million in financial aid with money from its endowment.

But the new tax is likely here to stay, said Robert Kelchen, an associate professor of higher education at Seton Hall University. It’s helping fund tax cuts elsewhere that the federal government has already promised, he said.

And for many wealthy universities, the total amount owed isn’t necessarily what concerns them, Kelchen said. On the local level, many Massachusetts colleges and universities don’t pay significant property taxes because they are considered nonprofits. However, they often pay a smaller amount in lieu of property taxes.

The universities are more troubled about what the new tax will mean in the future.

“In the grand scheme of things, it’s a small tax,” Kelchen said. “But they are worried that it will go up.”

Kelchen noted that increasing the tax could have bipartisan support. For Republicans, an increase would be an opportunity to poke elite colleges in the eye. For Democrats, it could create an opportunity to distribute the new revenue to public or less well-financed universities, he said.

And many college officials fear that the endowment tax is just the opening salvo for the federal government to keep squeezing them for additional money, he said.

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Some universities already see their fears creeping into reality.

The IRS still must finalize the tax guidelines, even though the first payments based on the expected rules are due in November. The rules are likely to be set in the coming months, but the most recent draft includes an unexpected levy on investment income beyond the endowment, said Liz Clark, the vice president for policy and research at the National Association of College and University Business Officers, a trade group.

The IRS has also proposed taxing the interest colleges earn when they provide student loans and the revenue they generate from dorms and faculty and staff housing, Clark said.

It is unclear whether colleges have changed their practices to prepare for the tax.

A report last year by an economist at the Federal Reserve Bank of Cleveland suggested that some institutions may “behave strategically to avoid being subject to the tax.” For example, some may try to manage their enrollment or change how they report or count students. Some small institutions may intentionally keep enrollment below the 500-student threshold to avoid being eligible for the tax, according to the report.

“Colleges may also find other ways of circumventing the law,” Peter Hinrichs, the Federal Reserve economist, wrote in his analysis.

Clark said she is not aware of any colleges making changes to skirt the new tax law.

Most have been too preoccupied trying to understand the complicated rules and accurately calculate the impact, she said.

“It’s unpredictable,” Clark said of the tax.

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Deirdre Fernandes can be reached at deirdre.fernandes@globe.com. Follow her on Twitter @fernandesglobe.