Serious question:
What's the "fair price" of one bitcoin? and how do you arrive to that conclusion?
Depends on how many people use it and the average dollar value of their purchases.
that was the only approximately legit reply so far
If there was no speculation (including long-term hoarding), only use for e-payments, customers (buyers of stuff or services) would buy BTC just for payments, and give them to merchants (suppliers) or payment processors, who would then sell those BTC to other customers.
Let V be the total volume of such payments expressed in USD/day. Let T be the average time in days between the purchase of some BTC by one customer and its re-purchase by another customer, after going through a merchant or processor. Let N be the total number of coins available, and P the market price of one BTC. Then, the total volume of payments, in BTC/day, is N / T. Therfore, we musthave in we must have P *N / T = V, or P = V * T / N.
Today, N = 13.5 M BTC. BitPay currently processes ~1 million USD per day of payments; let's guess that V is ten times that, 10 M USD/day. Let's also guess T = 30 days. (Note, we are assuming that no one is hoarding, so that everybody passes the coins on as soon as pratical.) Then we get P = 10 * 30 / 13.6 = 22 USD.
You'd still have the issue of there being some hurdles to overcome before buying BTC to spend it on anything. On one hand, this is a disincentive to use BTC for transactions, on the other it is an incentive to 'hoard', as you put it, if you do prefer to use BTC for some purposes.
That aside, I think we can agree any tradeable asset will see some speculation. Looking at your formula, it occurs to me you might add two variables to account for this. One is the growth rate of the BTC price and another is the average speculator's patience - how long they're willing to wait for profits to reach their targets. Of course both are unknown and actually somewhat interlinked, so it's no wonder price discovery is a messy business.