TITLE: Example of non accessible model categories
QUESTION [14 upvotes]: By curiosity, I would like to see an example of a model category with the underlying category locally presentable which is not accessible in this sense (and just in case: even by using Vopěnka's principle).

REPLY [7 votes]: An example which does not depend on set theory is the equivariant model structure on the category of maps of spaces by Emmanuel Farjoun.