You're implicitly assuming that everyone holds all of their BTC for one year before spending them.
To illustrate, let's assume that BTC are used for all transactions, but no one holds them. Everyone holds dollars, or euros, or gold, or whatever. When they need to make a transaction they hop on an exchange, buy some BTC, and buy their cup of coffee with the BTC. Then the coffee-seller unloads his new BTC immediately and holds gold or silver or tulip bulbs as his store of value.
Given a reasonably automated system, each transaction might take 1 minute. This means that you need 79 trillion _dollar-minutes_ per year, or about $150 million at any given moment. Dividing this by 21 million BTC gives a price of about $7.15 per BTC.
Even if people do hold all of their liquid value in BTC, they aren't going to hold it all for a year before spending it. A more realistic estimate might be 79 trillion $ * 3 days -- most people and businesses are operating pretty hand-to-mouth. 237 trillion dollar-days per year comes out to $648 billion at any given moment. This does give a fairly appealing target price for BTC-optimists, about $31k per BTC, and puts the upper bound on the value of a satoshi at $0.0003.
Why make a "realistic estimate" without reference to actual figures?
US GDP ~$15 trillion
USD (notes and coins) >$1 trillion;
USD (M1 aggregate) >$2 trillion
i.e. a dollar gets "spent" on activities that contribute to GDP between 7 and 15 times a year, depending on what aggregate you count as a dollar
(of course the actual picture is complicated by a lot more non-productive transfers not counted in GDP)
Velocity of circulation (the ratio of national income to money supply) in real world economies is a surprisingly low number, and whilst Bitcoins are a little more efficient to transact with than electronic bank interchanges, they're also not designed to be inflationary to encourage turnover.
You make a good point in noting that I didn't address the issue of short term holding and possible frequent circulation. It would certainly seem to make the valuation of a bitcoin smaller.
That said, I can't think of a back-of-the-envelope type calculation that I'm happy with, though I'll grant that my crude calculation is likely too high.
Does anybody have any idea what the rate of bitcoins being 'stranded' is?
To illustrate, let's assume that BTC are used for all transactions, but no one holds them. Everyone holds dollars, or euros, or gold, or whatever. When they need to make a transaction they hop on an exchange, buy some BTC, and buy their cup of coffee with the BTC. Then the coffee-seller unloads his new BTC immediately and holds gold or silver or tulip bulbs as his store of value.
Given a reasonably automated system, each transaction might take 1 minute. This means that you need 79 trillion _dollar-minutes_ per year, or about $150 million at any given moment. Dividing this by 21 million BTC gives a price of about $7.15 per BTC.
Even if people do hold all of their liquid value in BTC, they aren't going to hold it all for a year before spending it. A more realistic estimate might be 79 trillion $ * 3 days -- most people and businesses are operating pretty hand-to-mouth. 237 trillion dollar-days per year comes out to $648 billion at any given moment. This does give a fairly appealing target price for BTC-optimists, about $31k per BTC, and puts the upper bound on the value of a satoshi at $0.0003.