I am not sure if it is exposed in the SDK. Note that the miminum fee depends on a couple of different components, one of which is the size of the transaction itself. This means that if you compute the tx minimum fee and recreate the transaction with that new fee - the bytesize of the new transaction could as well be bigger than the previous one. This would mean something counterintuivite: adding more fee could require adding a bit more fee 
I think this is something @bruteforce.chain had faced already so I poke him.