For example professional investor apply the Capital Asset Pricing Model (CAPM) to determine the intrinsic value of an equity. What would be the result of such a financial analysis?
This question might be a bit off-topic and likely to result in unproductive debate, but maybe it's worth providing a couple references anyway.
CAPM can't tell you the value of an equity. It tells you what rate of return investors will demand for a given amount of volatility; if you hold a risky asset, you can expect a higher rate of return over time, as compensation for risking a loss.
But CAPM assumes that investors have already incorporated all available information into the current market price. This is the "efficient market hypothesis." Therefore, according to CAPM the intrinsic value of ether is precisely its current market cap. If the market cap doubles or halves, that will still be the case.
A good book on this is A Random Walk Down Wall Street; for a skeptical view on CAPM and the efficient market hypothesis, see Mandelbrot's The Misbehavior of Markets.
If you assume that equities can be mispriced (as many investors and academics do), then figuring out their value is hard. However, one formula for the value of a currency is pretty simple: basically, take the total value of goods exchanged for the currency over the course of a year, and divide by the average number of times a currency unit changes hands over that year. This is the velocity of money; wikipedia has a good article: https://en.wikipedia.org/wiki/Velocity_of_money
Unfortunately, we don't really have the input data for that formula.
We could also use any financial calculator to figure a present value based on our expectations of future growth, but since our expectations could be wildly inaccurate, that wouldn't really tell us much.