If we had no speculation, only demand for e-payments, the price would follow the equation P = V * T / N, where P is the price ($/BTC), V is the volume of e-payments ($/day), T is the mean time between successive payments with the same coin (days), and N is the number of currency units in circulation (BTC).
Assuming N = 14 million, guessing T = 14 days, and V = 5 million $/day, gives P = 5.00 $/BTC only.
The guess T = 14 days assumes that most coins that someone receives in payment for something, or buys to spend, are sold or used to pay for things at various times within one month. (BitPay sells all the coins that they receive within a day or two, for example.)
The guess V = 5 million $/day is based on various bits of evidence that indicate that BitPay has been handling about 1 million $/day of payments over the last year. Since they are believed to be the largest bitcoin payment processor by volume, a factor of 5 seems to be a fair guess for the total volume of e-payments. This estimate includes other processors and raw bitcoin payments, but excludes illegal trade, since that is being curtailed and cannot be relied upon as a sustainer of the price. (Anyway, it seems unlikely to be more than 1 million $/day).
It is not correct to use for V the total USD transaction volume extracted from the blockchain, because most of the latter (probably more than 90%) is movement of coins between wallets that belong to the same person, or that is not payment for goods or services -- such as tumbling, hot/cold wallet flow, deposits and withdrawals at exchanges and similar sites, gambling, etc.
Clearly, the current price (~220 $/BT) is still largely sustained by speculation and speculative holding.
I like the Money Velocity Theory approach because I can understand it. But I think your estimates are misleading.
IMO:
N = number of coins that are being actively exchanged because they are the only ones that can be part of a velocity equation. At best I'd say N = 3 millions. The rest is hoarded or lost.
T = 14 days looks like reasonable to me, considering the average bitcoiner is likely to do a couple of purchases in a month.
V = use estimated onchain USD transaction volume from blockchain.info = above 40 million USD.
That would give a BTC valuation above 40 * 14 / 3 = 187 USD, which is in line with what I expect.
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