The Logo Smith
This all might sound overly cynical, but I surely can't see any way to justify a Design Test, based on the assumption the designer has been approached and not the other way around.
I can't think of any good reason why any designer would put themselves at risk of doing a Design Test, other than a small chance of getting a job. You've got more chance of not being hired after a doing a Design Test, than you do if you oblige.
Just say No to Design Tests, please.
There's no reason you should be expected, let alone asked, to do a Design Test for someone you don't know, for a job you're not likely going to get.