Disclaimer - Yes, I'm aware it's possible for Bitcoin to go to $250k - $1million a coin under ideal circumstances and all that, but I'm trying solely to estimate when and how it will be virtually guaranteed to pass Paypal in a normal, logical market:
Bitcoin supposedly needs 20 meg blocks to do paypal # of transactions per day. If Bitcoin market cap was equal to paypal, it would be around $3100 a coin at the moment. Since bitcoin is currently 1/20th of paypal TPS (transactions per second), but market cap is 1/10th of paypal, it appears there's currently a 2x markup in cap for the decentralized aspect of Bitcoin. You will find very few people willing to store their life savings on Paypal, yet many people actually do with Bitcoin (Roger Ver is one I think), so this 2x markup in value makes sense due to the always open, basically zero downtime, permisionless utility it provides, and is likely to increase much higher.
Having said that, If you're to assume sole value of the network is determined by transaction processing capability relative to it's competitors with only a 2x markup for decentralization, then with 10 meg blocks, Paypal market cap and $3100 coins are in reach by normal market forces. It seems the free market has decided this 2x markup for decentralization as a current fair price, but as Bitcoin gains in acceptance and network effect, I believe that markup variable will grow larger due to acting as a store of value amongst other things.
Due to the Chinese network infrastructure, they seem to be trying to veto any blocks larger than 4 megs currently. I think the Hong Kong block scaling meeting will end up with something like 4-5 meg blocks fork as a current compromise, then with a baked in change to 8-10 meg blocks 2-4 years out without a fork. I believe by the time the halving occurs in 8 months, we'll have 4 meg blocks or higher, and following this reasoning, making Bitcoin capable of hitting $1600 without a bubble since 78% will have already been mined with 4% inflation.
If a 4 meg fork is acquired, and 8 meg or higher blocks are further baked into a future date without an additional fork, it might be able to surpass that before the date comes, hitting something like $3000 during the 12.5 block reward period. The current 2x markup for decentralization may also increase higher at any time, but it's definitely not going lower as trust in banks degrades more. People like Mircea Popescu seem to depend entirely on this markup raising for Bitcoin price appreciation, but I think it's far more effective to leverage both attributes as long as it's not detrimental (as in fatal) for the system.
TLDR = Normal market forces without a bubble can easily take Bitcoin to 5x current market cap ($1600 per coin) with a 4 meg block size during the 12.5 block reward period, and just as easily 10x current market cap ($3100 a coin) if 8-10 meg blocks are incorpated to activate at a future date without an additional fork. These are prices factoring in Bitcoin mostly as a money transmitter and not a store of value. Other factors such as store of value and speculation can drive it much higher like seen with gold as mentioned in this thread:
https://bitcointalksearch.org/topic/incoming-163000000000-market-cap-and-7700-coins-1235466