87 percent of parents believe scholarships and grants will cover at least part of their children's undergraduate expenses

The study looked at the college saving habits and goals of parents with children under 18 and compared them with what college financial aid administrators have to say about college funding. Financial aid administrators said 92 percent of parents overestimate the amount of scholarship money their children will receive. Meanwhile, parents are not saving much on their own for their kids' educations, the study found.

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"Parents with children ages 14 to 17 plan to have an average of $12,000 saved when their child reaches college age," the study found.

That would just cover the cost of one year's schooling at a four-year public college or university, according to the most recent data from the College Board, a nonprofit association based in Washington, D.C. It would fall far short of the $29,026 College Board estimate for one year at a private institution.

Jennifer DeLong, director of college savings plans for AllianceBernstein, said that instead of saving, parents are taking on debt to fund their children's educations. And they're also expecting the children to take on debt, which can make it harder for the young people to get on their feet financially after graduation.

"Parents do seem to understand the high cost of college, but they're not doing anything about it," DeLong said. "They're not considering college saving as part of their overall financial plan, they're not talking to financial advisers."

They're also not looking at opening savings accounts that can help parents accumulate money for college, including Section 529 plans. Funds invested in these state-sponsored plans, which are named for a section of the IRS code, grow tax-deferred, and withdrawals are tax-free when used for education.