When it comes to setting a value or determining the cost of something, there are plenty of synonyms for the phrase "puts a price on." You could say "values," "assesses," "appraises," "estimates," or "determines the worth of." All of these phrases convey the idea of assigning a monetary or other quantifiable value to an object or service. Other possible options include "quotes a price for," "fixes a value on," "labels with a price tag," or "prices." Each one has a slightly different connotation and may be appropriate depending on the context, but they all capture the essence of assigning a value to something.