I think you're going to need something stronger than 400W.
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You sure? On PCPartPicker I put together a build with GTX 960 in it when I was bored and according to it, less than 350 watts were used by the build.
Edit-
http://pcpartpicker.com/p/QM3nCJ Here, this uses 286w and has GTX 960 in it. Keep in mind I'm not installing anything else if possible, all I need is a GPU since my CPU and RAM are fine as is for now.