Yes, that is fundamentally correct.
The calculations can be simplified: $13,839 of qualified expenses less $4000 used for the American Opportunity Credit (AOC) = $9839 can be covered to tax free scholarships and grants. $15,316 - 9839 =$5477 of the scholarship/grant is taxable.
The taxable amount can be reduced further by any book, computer and other course materials not already include in the $13,839 of qualified educational expenses.
How to enter in TurboTax (TT): $13,839 in box 1 at the 1098-T screen, $15,316 in box 5. When asked how much of the scholarship was used for Room & board, enter $5477. TT will automatically apply the $4000 difference to the AOC.
That question answered, brings up another question:
How is your son not your dependent? Scholarships and grants are not considered him supporting himself. Only loans in his own name (no parental co-signing) are considered self support. How old is he? Is he a full time student? Does he have earned income. There are restrictions on students, under 24, without earned income, getting the refundable portion of the AOC.
