However 20$ seems a little far fetched. Also the logic that market cap should equal transaction volume seems a lil flawed.
Nope, it is monetary theory. If a monetary asset serves the purpose, and only serves the purpose, of buying stuff with, then its value (in fact, the inverse: the price of the goods expressed in that monetary asset) can easily be found using P x Q = M x V.
It's simple bookkeeping:
"the amount of money over the counter" = "the total price of all the goods and services bought with it" (in a given period).
The amount of money over the counter = the amount of money existing, times the average number of times a same unit has been spend. That is M x V. M = the amount of money existing, V is the average number of times the same unit is spent (in the given period). It is also called the VELOCITY of the money. V = 1/T, where T is the average holding time (in number of periods).
If the considered period is 1 year, and a coin gets spend on average 12 times per year (once a month), then the velocity is 12. The holding time is 1/12 (of a year which is a month).
If there are 1000 coins, and they are on average spend 12 times a year, then 12 000 coins went over the counter to buy stuff with that year.
That must then be equal to the total price of goods that was bought, which is P x Q, where Q is a "reference good" and P is the price of the reference good. Say that the reference good is "a loaf of bread", then the total amount of goods (expressed in equivalent loafs of bread) exchanged in a year is Q, and P is then the price of a loaf of bread.
P x Q is nothing else but the total price of all the goods that was bought, so it must be 12 000 coins too.
Hence, M x V = P x Q
Example: if the total amount of goods bought with bitcoin is $20 billion a year, and a bitcoin is held on average 14 days, then V is about 25. M being 15 million (coins) we have that M x V = 375 million (coins traded a year).
If we take as "reference good" something that's worth $1.0 we have:
375 million = P x $20 billion.
P is the price (in bitcoin) of the reference good (worth $1). So 1/P is the price of a bitcoin.
We find: 1/P = 20 000 / 375 = $53.3
So if bitcoin is used to buy 20 billion worth per year, and coins are on average held 14 days between a trade, the price of a coin should be $53.
What we have is that a lot of coins were held a lot longer, but a lot less stuff was bought with it.
It was not really used as a currency.
This is all bogus considering Bitcoin's primary uses are currently
insurance against fiat implosion,
speculation, and lastly black market. Your primitive formula that doesn't address it's two main uses at all is obviously not valid in this discussion when it only partially addresses the black market and nothing else. If it was that simple, you would be a billionaire in the gold commodity market, but you already know it won't work.
Where's your variable for fear index of fiat markets amongst dozens of other missing variables? Your forumula is not useful for predicting really anything in this context.