A Short Note on My Value Notion

Good start of an exploration, this focuses on the instantaneous (current) exchange value of a currency.  Unmentioned, but critical to this, is the consumption value of the goods/services - what's 50 cups of coffee worth to you?  This is often called "utility".  Some additional dimensions to add to your model as you get deeper:

• Time-dependent value (both changing prices for coffee/dollar AND changing utility to you)
• Multi-step exchange (you could buy the coffee with dollars, or buy dollars with gold and then coffee with those dollars, or buy coffee with barter for some other good, which you acquired though some chain of trades).
• Investments (business and future cash flows) and speculation (useless-to-you assets you hope will appreciate).  Understanding liquidity and risk factors is just a scratch of kthis topic.
• Interaction and relative values of different media of exchange (dollars, euro, various crypto, etc.).  These change relative to each other.  Your theory is incomplete until you explain why.
• Labor valuation is it's own entire field.  It's very rare that there's a stable, linear payment for hours worked, and the (dis)utility / unpleasantness of work is very hard to quantify.
• Human irrationality - not only do different people have different values for a cup of coffee, but people are BAD at predicting how much they'll want coffee next week, and downright awful at predicting how much they'll want to keep unspent just in case they need a car repair (or want to retire).

I suspect the last one ends up confounding the models of the prior topics, in terms of prediction.  Fundamentally, there IS NO answer to "what is the value of ...", if you think it needs to be objective and constant (or a function of time).   Your starting place is the ending place: it's worth what someone will trade for it.

If I can’t put this $100 into any usage, it is worthless. For instance, if the coffee shop, or the restaurant, or the hotel or any business in general refuses to accept fiat money, the value of that $100 will be zero.

This is technically true, but I think that would only be the case if you're destroying the money. Otherwise, money you don't spend today can be used in the future. Consider budgeting as a really common example. I might have $100 I want to use today, but instead I'm going to buy $100 worth of future groceries with it. You can also use money today to buy even more money in the future (and thus future goods and services) through savings or investing.

Even if you don't know exactly what you want to do with it, not spending money lets you have the choice of spending in the future. This is useful if you think prices will be lower, or if there will be new options, or if you might have just missed something.

Intuitively, the value of a fiat money can be represented by the units of consumables one can purchase using that money. On the other hand, the exact answer to the question of “what IS the value of $100 fiat money” is not yet obvious (at least to me). One can argue that when 10 meals can be purchased using $100, the value of that 10 meals can be hugely different for different people in the different parts of the world. But this argument feels like trying to argue the value of 10 meals rather than the value of $100. [...] Value of a business. Let’s say I am considering buying an Amazon online retail business. First I ask myself: How much am I willing to pay for this business? The answer to this question can be the value of that business. If I am willing to pay $10 million for the store, the value of that business is $10 million to me. If no one is willing to pay anything, the value of the business is essentially zero.

I think one thing that would help here would be to read about prices and where they come from, since I think you're occasionally mixing up your value for things the the price. I think this article explains it pretty well: https://www.econlib.org/library/Columns/y2007/Robertsprices.html

I can't tell, but I suspect this part of what's making this hard for you to answer. If the question is just "What determines the price of a cryptocurrency?" then the answer is basically "supply and demand". If the question is "How do individual people decide how they value a cryptocurrency?" then the answer is way more complicated (probably some combination of the price they think other people will pay for it, feel-good value of owning it / being part of a new thing, lowering the price to compensate for how annoying they are to use, raising the price because of how much easier it is to commit crimes with them, etc.).

I'm not sure if this really answers your question but hopefully it points in a useful direction.

My current understanding is that, in general, the value of something can be represented/quantifiable by the units of some other things that can be directly obtained by putting that thing into usage. If it stays idle without doing anything, the value is essentially zero.

I think this is a bit more complicated because one can keep cash balances in hand, in anticipation of future expenses. At all times, all money is actually idle in someone's account.

I can value a business to be worth $10M. But someone else might value it more/less than $10M. Does that mean there is no universal representation of the value of something?

Economic value is subjective, or at least subjective for all practical purposes. Willingness to pay is probably the best way we have to measure how much we value something. Although complications arise when we try to compare how much different people value something based on their willingness to pay, because different people have different budget constraints to begin with, and also diminishing marginal utility of money.

I think that it would be hard to come up with a universal value for anything, given the variance in circumstances we are all subject to. The question "Is it worth it?" is a personal one to each individual, and in fact can be deeply personal and private in some circumstances, depending on the worth/value of the object being evaluated. Thus, the question of modelling value would lead down the path of modelling people and their preferences/desires.

With regards to the value of cryptocurrency, I view the primarily value of it to me as a hedge. I trade centralized regulation for price volatility. Cryptocurrency is also the only type of currency that I know where knowledge of the private key is necessary and sufficient to transact on the network (to a first-order approximation, at least).