But the documents provide a glimpse of values Mr. Trump assigned to some of his properties that are out of line with other available estimates.

[The testimony could create more legal issues for the president.]

On his 2012 balance sheet, Mr. Trump described an estate he owns in Westchester County, N.Y., as being worth $291 million. He bought the property, Seven Springs, in 1996 for $7.5 million. In 2018, Mr. Trump said in a federal ethics filing that the property was worth no more than $50 million.

Also in 2012 — just as the economy was beginning to recover from the financial crisis — Mr. Trump valued his skyscraper at 40 Wall Street in Lower Manhattan at $527 million. An article in The Wall Street Journal that year reported that property had a value of about $400 million, based on sales of comparable properties. It would be three more years until the building achieved Mr. Trump’s valuation, according to Trepp, which tracks commercial real estate lending.

The 2012 Journal article also estimated that Mr. Trump’s golf resorts and related real estate in the United States and Scotland were worth nearly $1.6 billion. The Bloomberg Billionaire’s Index as of this week valued those properties at $650 million.

In the 2013 financial statement, Mr. Trump said that $4 billion of his nearly $9 billion net worth was attributable to his “brand value.” He did not report such a hard-to-measure asset in 2011 and 2012.

The financial statements for 2011 and 2012 carry the heading “compilation reports,” which in accounting terms means that the accountants that prepared them merely compiled information from their client without auditing the underlying figures. The 2013 statement does not appear to have been prepared by an accountant, and includes language that is not part of generally accepted accounting principles.

[Mr. Cohen characterized the president as a con man, a cheat and a racist.]

Determining the value of huge pieces of real estate is an exercise in subjectivity. In Mr. Trump’s case, according to bankers who have worked with him, he tended to make assumptions that were more aggressive than others in the real estate business would. For example, they said, he often made unrealistic forecasts about how much revenue he expected a property to generate, a practice that would result in a greatly inflated value for that asset.