Having so much of the endowment in a single asset “is against everything I stand for,” Mr. Michaelson said. He and other trustees said they considered selling it in 2006, when the college was facing mounting financial deficits, but concluded that would be impractical. Cooper Union receives annual lease payments of $9 million from the owner of the Chrysler Building, Tishman Speyer Properties, and $18.2 million in so-called tax equivalency payments that would otherwise go to New York City. The right to the tax revenue couldn’t be transferred to a buyer.

But assuming a 5 percent return, a $27.2 million annual revenue stream would be generated by selling the Chrysler Building land for $544 million, which doesn’t seem so far-fetched a price. Tishman Speyer sold 666 Fifth Avenue, which hardly compares to the landmark Chrysler Building, for $1.8 billion in 2006, and bought the MetLife building in 2005 for $1.72 billion. And the Chrysler site might have been highly appealing to a sovereign wealth fund or other major real estate investor looking for a trophy asset. (A Cooper Union spokesman said the trustees needed to generate annual revenue of $55 million, which the lease is expected to produce beginning in 2018. The amount necessary to generate that revenue at a 5 percent return would be $1.1 billion.)

Still, it doesn’t seem the trustees made any serious attempt to even determine its market price, and the college seems to have had a nostalgic attachment to it as a part of its heritage. In 2006, Cooper Union defended the decision not to sell the land by describing it as “a gift from the children of Peter Cooper,” that is “the heart of the Cooper Union.”

Instead, Cooper Union renegotiated the lease with Tishman Speyer, which was not due to expire until 2047. The college negotiated an increase to $32.5 million in 2018, which rises every 10 years thereafter. But it still had to make it to 2018, five years into the future.

At the same time that Cooper Union decided not to try to sell the site, it borrowed $175 million, using the Chrysler site as collateral, to build a new engineering and art building and “to meet future operating deficits,” as the school acknowledged in court papers seeking permission for the loan. The term of the loan was 30 years, at an interest rate of 5.875 percent, which amounts to more than $10 million in interest payments a year. By today’s standards, 5.875 percent is exorbitant, but the college said it couldn’t refinance the loan at a lower rate.

Hardly anyone disputes Cooper Union’s need for new engineering facilities. Whether it needed that particular building, at such high cost — about $166 million — remains a matter of dispute. Trustees told me that the college’s development consultants told them that a signature building with a marquee architect — in this case, Thom Mayne of Morphosis Architects — would attract a large donor eager to have his or her name on a trophy building.