is the any studies done you can point out, or is it just personal anecdotal evidence?
"...automated test suite saved the client 117 days of manual effort per testing cycle."
Sure, it takes more time to construct any given feature with unit tests versus a completely untested solution. However, any time you need to change the code, add a feature, or change something it interacts with, you are saving an incredible amount of time both in testing and the prevention of bugs discovered in production.
I really don't understand how, in the long run, automated testing can't save you time. If you don't think so, you obviously haven't maintained any software.