Discussion: Let us look at the first (noun) definition of the word “value” at oxforddictionaries.com: “the regard that something is held to deserve”. Does this definition not imply an action of evaluation by some party or other? In fact, for something to have a value in this sense, then someone would have had to apply this definition from the verb (from dictionary.com): “consider with respect to worth, excellence, usefulness, or importance”.
With this definition, we can explain almost all the other definitions, both noun and verb. What’s more, this consideration (evaluation) must have taken place for any of noun uses to apply. Without such an evaluation (even if such an evaluation is performed by a mechanism), the “value” is simply an abstract property of a thing. Something only has “value” when there is interaction between it and the rest of the world, i.e. when an evaluation occurs.
It is also interesting to note that value is generally considered a relative attribute, although often the magnitude is not specifically stated, whenupon it is taken as being positively relatively significant (i.e. more significant than other things of a similar nature).
Conclusion: The root definition of value is “to consider with respect to worth, excellence, usefulness, or importance”, from which all other definitions stem, because nothing can have a value without being evaluated (whether by a person or a mechanism).