Synonyms for "under value" include "underrate," which means to underestimate or diminish the worth or significance of something. "Underestimate" is another word that can be used in place of "under value," implying that something is not being given its true worth or import. "Underappreciate" is another good synonym, which suggests that the value of something is not fully recognized or understood. Finally, "depreciate" is a synonym that can be used to describe something that is undervalued, or has lost value over time due to various factors. These words can be used interchangeably depending on the context and degree to which something is being undervalued.