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For young couples, tax-prep season becomes even more complicated once you add a child to the mix. When Mrs. Tepper and I welcomed our son into the world two years ago, little did we appreciate how the new deductions and credits would impact our bottom line.

Last year we dove blindly into our returns and hoped to come out ahead on the other side. This year I wanted a little advice, so I turned to Naomi Ganoe, a CPA and director at the accounting firm CBIZ MHM. She spelled out three of the basic tax breaks that new parents need to understand.

1. Dependent Exemption

You are already entitled to an exemption, which works very much like a deduction—that is, it reduces your taxable income, in this case by $4,000 for 2015 ($4,050 for 2016 )—and you get an extra one for each child you care for. If you're in the 25% bracket, one personal exemption cuts your taxes by $1,000. For the Teppers, our three exemptions lower our taxable income by $12,000.

Keep in mind that high earners don't get the full benefit. Personal exemptions start to phase out for 2015 at $309,900 for married couples filing jointly and completely disappear at $432,400.

2. Child Tax Credit

Some parents can also receive this $1,000 tax credit for each child. Credits are more valuable than deductions and exemptions, because credits deliver a dollar-for dollar reduction in your tax bill; a deduction simply lowers your taxable income.

There's an income phaseout on the child tax credit, however: For married couples filing jointly, it begins at $110,000 in adjusted gross income. "There is a $50 reduction for every $1,000 earned above that level," says Genoe. "It doesn't take very long before you earn too much to see the credit." So a family making $115,000 will cut its taxes by only $750. Also, you can't avail yourself of the credit in the year your kid turns 17.

3. Child and Dependent Care Credit

Parents also get some relief from the tax code for child care costs, which can be exorbitant. (Sending your infant to a daycare center in Illinois, for instance, costs slightly more than sending your 19-year-old to a public university, according to Child Care Aware of America.)

With children under 13, you have two possible ways to catch a break. You may be able to sign up for a dependent-care flexible spending account at work. That lets you use pre-tax dollars to pay for up to $5,000 of care, yielding a savings of $1,250 for someone in the 25% tax bracket.

With or without an FSA, you can take the child care tax credit—worth 20% to 35%, depending on your income, of up to $3,000 you spend on care for one kid, $6,000 for two or more. A married couple filing jointly with an adjusted gross income over $43,000 in 2015 can reduce their tax hit by 20% of child care bills up to these amounts, says Ganoe—a maximum of $1,200 for families with two or more kids.

If you pay for child care expenses with your FSA, however, you can claim a credit only for those costs that aren't covered by your FSA.

There are other important tax breaks that parents should understand. Families that adopt a child can take advantage of a sizable tax credit. And as your children get older, you're entitled to a $2,000 deduction for tuition, although this also is subject to income restrictions (married couples filing jointly can't take advantage if their modified adjusted gross income is above $160,000).

Fortunately, the Tepper family's taxes are relatively simple this year—and our tax software program ought to prompt us to take any of the tax breaks we qualify for. A more complicated tax future will begin to kick in as we add more children and property, but there's a bright side: More complex taxes tend to accompany more income and more assets.