I don't think "intrinsic value" is a term in economics. It's a term in investing.
Economics is far from clear about predicting how Bitcoin will end up. The professional economics world has yet to seriously weigh in about Bitcoin. I just searched the top 10 journals on this list: http://faculty.maxwell.syr.edu/whorrace/journals.htm and none of them appear to have anything published about Bitcoin.
That said, Bitcoin does have "intrinsic value" as a payment processor. Think about PayPal. There's two kinds of value in PayPal. First, they have their deposits, which are denominated in various different currencies, and which are backed by various governments and insured. Then there are the people, the servers, the contracts, the buildings, all the other stuff that's necessary for those deposits to actually move around the globe. Ebay didn't buy PayPal's deposits, which aren't really PayPal's, they belong to their customers, eBay bought PayPal's assets.
Think of Bitcoin like that stuff... a distributed payment processing company. It just as reliable as PayPal, except no one can ever freeze your account, and you can only transfer Bitcoins. PayPal was worth $1.5 billion to eBay, so that's a reference for your "intrinsic valuation" that you're working on.
You might be thinking "well PayPal wouldn't be useful if it could only transfer Bitcoins and the value of Bitcoin is $0 so there's a chicken and egg problem!" Except I don't see a scenario where Bitcoin goes to $0. Let's imagine Bitcoin crashes all the way down to $0.01. Bitcoin is still useful if you're trying to get money to your grandma in Cuba, or to pay your Latvian web development contractor. Maybe it's extremely volatile, but that's OK because you otherwise have no way to get your money where it needs to go, and you're only going to keep it in Bitcoins for a few days. You buy some Bitcoins, send where they're going, and the other side cashes them out.
Now why is this relevant? Well, if during those 4 days, there was $1,000,000 worth of money that people were trying to send this way, then there need to be at least $1m worth of Bitcoins to "float" those transactions. Essentially those people all show up on Monday being like "we don't care how much it costs because we're selling them again in three days, we just need $1m worth of Bitcoins to send to our grandma/contractor/etc". Therefore the "value" of Bitcoin goes up to at least $0.05 ($1m/21m).
This is just one of Bitcoin's many "intrinsic" values. It is the "payment processor of last resort" for everyone who falls through the cracks of Western Union/Paypal/etc. This creates a floor below which Bitcoin is unlikely to fall.