paypal claim to have done $44 billion of trade in Q3 2013(1). so lets assume paypal do $4x44 billion of trade for the year.
there will only ever be 21 million BTC in existence* , there are much less than that right now (12 million ish).
4x44,000,000,000/21,000,000 = $8380/BTC
this assumes of course, that Bitcoin totally replaces paypal and nothing else (which is already not true).
* - this ignores the fact that there are already thousands, if not millions of BTC that have been lost due to lost wallets, forgotten coins, invalid transactions, etc.
i.e. if it becomes the new Paypal, how much would one bitcoin need to be worth?