Costs are tangible, making them objective, even if they have underlying subjectivities. The cost of milk is objective, even if your purchasing habits are subjective.

You are correct that "cost" has more than one definition, but, as already discussed, the one we are talking about equates to consequence, not an amount of money. Your milk analogy doesn't fit. Whether or not a so-called consequence is seen as a consequence is in the eye of the beholder.