How do assets impact the likelihood of receiving need grants? Assets certainly do come into play, but this existence of savings is one of the biggest hang-ups people have.
There is much misinformation. Savings do not come into play as much as people might think. The family's income is a much bigger factor than assets. Also, the FAFSA counts asset types differently than the CSS profile. The CSS Profile will include assets such as retirement, home equity, 529 plans held by a grandparent, and dig into the financials of both custodial and non-custodial parents. You should know the type of financial review for your student's application list - see CSS Profile schools.
Simple FAFSA math - After-tax income (AGI) is roughly 20% - so if your after-tax income is 150k and you have no savings, your EFC would be $30k.
Simple FAFSA math - After-tax income (AGI) is roughly 20%, and assets are 5.64% - so if your after-tax income is the same as above, your countable savings ( excluding retirement) are $100k, your EFC would be $35,650.
There is no reason to be afraid to save. Saving is a good thing. If you are doing well financially and making a good income, you will most likely improve that situation when your student is a senior. Would you rather have $100,000 in the bank or save $5,650 a year in college and only IF your student was accepted to a school that meets 100% of your need?