Considering the market evolution, mining difficulty and the trade volume the real price of BTC is somewhere above 15 000 dollars.
Is it?
So what will be the real value of bitcoin after the mining difficulty increases?
The real value of bitcoin is its current value and eve it differs from exchange to exchange that is what the decentralized curreny look like.
Real price and real value differs from each other.
To answer your question, no one can give that answer what will be the real value when mining difficulty increases. But I'm pretty sure that it will be higher than it is today.
No one can say what will happen in future so just take the current value as real and don't expect anything higher even if the chances to go high are there.