NEW YORK (MainStreet) — While more parents than ever are seeing the value of college, they are also seeing the value in majoring in something that will one day pay off those college loans.

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While 87% of parents say college is "very important" to their children's futures — up from 81% in 2012 — 42% of parents now say earning potential after graduation is more important to their child's education than his or her major compared to 38% last year, according to a new survey commissioned by Discover Student Loans.

"Families are becoming more sensitive to college affordability and the return on investment," said Mark Kantrowitz, publisher of the Edvisors Network of websites about planning and paying for college. "Parents are taking a more nuanced approach. They want their children to be able to earn a living, especially if they are borrowing to pay for college. But they also want their children to be happy."

Despite the concern of rising student debt and falling potential income, the poll found 87% of parents say college is "very important" to their children's futures — an increase of 6% from last year. The survey also found parents who say a college education is only "somewhat important" dropped from 14% to 11% over last year.

"We're encouraged that parents continue to see the life-long benefits of a college education," said PK Parekh, vice president for Discover Student Loans.

While some parents are steering their kids toward more lucrative majors, Kantrowitz said others are steering them toward lower-cost colleges where the student can graduate with less debt. He said the key is to keep the student's debt in sync with their income after graduation.

He added that can be achieved either by pursuing a more lucrative field of study or by enrolling in a less expensive college. For example, if the student wants to major in basket weaving — which presumably doesn't pay very well — parents should not send him to the most expensive college in the field.

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The survey also revealed 81% of parents plan to help pay for their children's college education, an increase from 74% a year ago. But a willingness to pay doesn't correspond to an ability to pay. 70% of families are very or somewhat worried about having enough money to contribute, compared to 75% last year.

"They are comparing college costs based on net price. If the net price is close, they are choosing the college with the better perceived quality," Kantrowitz said. "If the net price differs by more than $5,000, they are choosing the less expensive college. In between, they are agonizing over the decision. They are also increasingly sensitive to the amount of debt, in part due to increased media coverage and in part due to debt increasing while family income remains flat."

The survey also reveals parents are still likely to help their children pay back some college loans they may need, with 58% saying they are very or somewhat likely to help pay — up 3% from last. Some 40% of parents also think their children fully understand the amount of debt they will have after graduation, while 32% think they only somewhat understand and 15% don't think they understand at all.

"Families also should consider the entire cost of a college education, beyond just the first year of school, so they fully understand the financial responsibilities they are taking on," Parekh said. "Being aware of all the costs involved will help families better prepare and anticipate monthly payments."

--Written by Chris Metinko for MainStreet