The below is my current understanding of it, based on the data collected while determining that there was a problem, and which areas of the game are (potentially) affected
I have not, at this time, had a chance to verify this in the code, nor confirmed the intended functionality. For my own sanity, I am going to assume that the Actual Total Cost is accurate (or at least closer to accurate than what the confirmation dialog suggests)
I have not determined whether there is an actual minimum cost.
Actual Total Cost =SUM_allprovinces (Development* (1+[local]Hostile Core Creation)) * 8 * (1- Administrative Efficiency) * (1 + Diplomatic Annexation Cost)
(rounded down to nearest integer)
(note that beneficial Diplomatic Annexation Cost modifiers are scripted/displayed negative, Administrative Efficiency, positive)
The Confirmation Dialog displays this as
"Due to their Development of FLOOR[Development*(1+HCC)] "
and
"the annexation will cost a total of FLOOR[development*(1+HCC)] * FLOOR[8*(1-AEff)*(1+DAC)] "
(floor being the rounding down to nearest integer)