No ... the program only computes an estimated underpayment penalty on the return ... the late filing and late paying penalties are only computed by the feds or state and billed later. 

My grandson never filed income tax for 2018 tax year. He has a refund coming.

Turbotax computer his federal refund as $101 and his Michigan refund as #20.  He will be filing in March 2020.  Can he ask for a direct deposit refund from both federal and state?  Will they deduct any penalty and late filing fees from his refund or will they bell him separately.  I was hoping for some help from the Turbotax app but  came up short.

How and when will he pay the late fining fee? Any idea how much it will be?

If you are getting a refund there is no late filing fee or penalty.  He has to mail both returns.  He can not use the Online version.  Online is only for 2019 now.  How did he prepare them?

I prepared both the 2018 and 2019 returns for him using Turbotax2018 Premier and Turbotax2019 Premier (I have been using Turbotax for years and have both copies onstalled on my PC.  I have created a pdf file for tax filing for each year using the two versions of Turbotax and there is no mention of penalites or fees.  He did file for 2017 tax year and got a refund.  According to each year's version of Turbotax he should be getting a refund for both 2018 and 2019 tax years.  Should he file both returns together in one mailing or should he file each year separately?    He will get the 2019 return in before the April15 due date but the 2018 will be late.  He never filed for an extension on his 2018 taxes.

@bobsimmons  Never mail two years of tax returns in the same envelope---if you do that one can easily be overlooked.  Mail each one in its own envelope.  Use a mailing service that will track it so you know it was received.  Prior year tax returns do not show up on the Where's my refund site--so the receipt from tracking is the only way you will know the IRS has the returns.

If you are getting a refund, there is not a penalty for filing past the deadline.  If you owe taxes, the interest/penalties will be calculated by the IRS based on how much you owe and when they receive your return and payment. The IRS will bill you for this; it will not be calculated by TurboTax.

Thank you all