Private nonprofit organizations are exempt from federal income taxes - i.e., they get a federal tax subsidy. Donations to qualified private nonprofit organizations are deductible from federal taxable income - i.e. such donations get a federal tax subsidy. These general principles apply to private nonprofit colleges.
But for some people, private nonprofit colleges are "nonprofit" only in a technical sense; for some people, nonprofit private colleges are quite profitable. See
Executive Compensation at Private Colleges, 2011 Chronicle of Higher Education (December 15, 2013). For example, for the year 2011 Robert J. Zimmer of the University of Chicago received compensation of $3,358,723 (from his university) and Lee C. Bollinger of Columbia University, $2,327,344 (from his university).
Capitalism run amok?
Note: The clerical presidents of most private Catholic colleges receive nominal or zero ($0) compensation from their universities. Go
here (for example, see Boston College) and
here and
here.
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