The average tuition “discount rate” among private, nonprofit colleges hit a record high of 42.4 percent in 2010, meaning that the average student now pays about 58 cents on the dollar of published tuition.

For students and their families, it means there’s more reason than ever to disregard the soaring sticker prices at private colleges. Eighty-eight percent of freshmen receive institutional grants, according to a survey of 381 institutions by the National Association of College and University Business Officers. The average grant covers 49 percent of published tuition and fees.

Institutional grants are a blend of aid based on need and merit. Top, endowment-rich institutions favor need-based aid and generally dispense it according to a fixed formula — i.e., your expected family contribution will rise and fall on a sliding scale according to your affluence.

Hundreds of schools just below that top tier hand out some mixture of need and merit aid. Merit aid is an increasingly powerful tool for such schools to assemble a competitive freshman class, typically by offering the most money to students with the strongest credentials.

For colleges, a rising discount rate is a worrisome sign, at least when it translates to declining revenue. Happily, the NACUBO survey suggests that revenues are inching up. The survey found net tuition revenue (after accounting for grant aid) rose about 2 percent in 2009 and 3 percent in 2010. This follows two years of net losses.

“This is an indication of the stability of our higher education system,” said John Walda, NACUBO president, in a release.