PjM section 4 page 45  answer is correct
I think everyone is overthinking this  the ARE handbook answer is correct.
You have a change order construction cost that is $108,810.
You apply a 10% profit on that cost (OHP, markup, whatever you want to call it) = $10,881.
You add those together and get $119,690 (or you could multiply by 1.1) total change order
This is $19,690 over what is left in the Construction Budget. The Construction Budget always includes OHP.

Profits are calculated by dividing by the inverse target profit percentage (0.90 in this case). Profits and markups are not the same thing.
I do not have the handbook in front of me (or the total that others have said should be correct), but based on the numbers you provided, the total (including profit) should be $120,900.
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