By comparison, the cost of instruction grew 5 percent in that time period. The Bain report estimates that a third of colleges and universities are financially weaker than they were a few years ago.

“Much of the liquidity crisis facing higher education comes from having succumbed to the ‘Law of More,’ ” the Bain report said. “Many institutions have operated on the assumption that the more they build, spend, diversify and expand, the more they will persist and prosper. But instead, the opposite has happened: institutions have become overleveraged.”

Not all borrowing, even an eye-popping amount, is necessarily bad if you are an administrator at the University of Cincinnati, a state university with $1.1 billion in debt.

“The institution has profited mightily from the changes that we have made,” said Mitchel D. Livingston, vice president for student affairs. He noted that enrollment had increased and that the quality of the student body had improved, as had the “quality of life experience on campus.”

“We have gone from a second-choice institution to a first-choice,” he said.

Daniel M. Fogel, who resigned last year as president of the University of Vermont, said that given the lack of state support, many public colleges and universities had to borrow money just to remain adequate. He said that when he arrived at the university in 2002, some of the laboratories were inferior to those at many high schools.

“How do you bring people to teaching facilities that are really subpar?” he said. “It’s not a matter of gilding the lily, in many cases.”

Other schools also stood by their borrowing. John Beckman, an N.Y.U. spokesman, said nearly $900 million of the university’s debt was for its hospital and therefore had no impact on students. He said that N.Y.U.’s revenue increased 100 percent in the last decade, so that while debt also increased, the proportion of interest and principal paid against the overall budget has remained relatively steady.