For example, if it is stock, there can be P/E ratio, or Price Sales ratio. For Bitcoin, are there some common ways people use to estimate the value of one Bitcoin?
Unlike stocks or precious metals, Bitcoin has no inherent value; it is only worth what people are willing to pay for it, and the only way to determine that is through trading activity on an exchange.
You can try to use the same technical analyses that are used on the stock and forex markets to predict the future price, but it's incorrect to call that its "proper value".
Like most other forms of money, bitcoins don't have any intrinsic value. Unlike commodities, they do not have material value and they cannot be used in manufacturing, and unlike stocks, bitcoins don't represent assets or shares of some entity. Bitcoins are a purely digital good that represents nothing but itself and therefore has only relative value. In fact, some argue that the absence of intrinsic value makes bitcoins an outstanding candidate for money. Given that, I'm not sure whether it makes sense to distinguish between price, value, and purchasing power of bitcoins.
The price of bitcoins is discovered on the market: the current price is that of the latest trade that a buyer and a seller agreed on. The price is updated whenever the highest bid and the lowest ask intersect.
I said proper value, because, imagine each person has 3 tokens, and is used among homeless people, and their net asset is $10, I think 1 token might be worth $1 or something? They care about $3 of liquid asset, and perhaps the 3 tokens represent the $3. Likewise, if the 3 tokens belong to people whose net asset is about $20 million, then it can be the liquid asset they can think of moving around is $1 or $2 million, so each token can be worth $300,000, and like you said, is a sports car
The price discovery is independent of the wealth of the market participants since the bitcoins do not represent their other assets in any way. Even high-net-worth individuals (HNWI) can only influence the price through the market. One could argue that people whose wealth is mostly made up of Bitcoin may be more likely to sell some to diversify or cover expenses, while the general wealth of HNWIs protects them from being forced to sell. Possibly, HNWIs may also be willing to pay more for bitcoins than other market participants. As such, HNWIs may contribute more to a rising price than other market participants, but I still don't see how the price of bitcoin would be a function of the general wealth of Bitcoin holders.
That being said, some bitcoiners speculate on the price by assuming which other uses of money or gold it may replace. An example is Vijay Boyapati's description of four valuation frameworks for Bitcoin. Various banks have published research modeling Bitcoin's future value. For example, a Citibank analyst made news in November with their price prediction.
For Bitcoin, are there some common ways people use to estimate the value of one Bitcoin?
Markets decide the value of bitcoin in terms of currencies like USD, EUR, INR etc. Markets are based on supply and demand for everything that exists on this planet.
Stocks or metals have a certain value because people are willing to pay that amount for it. All the fundamental and technical analysis followed by different systems exists in Bitcoin markets as well with different data. At the end of the day everything depends on supply and demand. If there are more buyers and less sellers price goes up, and down if vice versa.
If interested to look at different charts for research: