It depends on the PSU, they are not all rated the same, there are some 400W units that can deliver 350W from their 12V rails, there are others that can barely deliver 200W from their 12V rail which powers you CPU and GPU. As long as its not a super crappy 400W unit it should be fine, the 950 needs about 150W, but the rest of the systems needs about another 100W.
If you can link to a page with the info on your PSU we can give you a very definitive answer, its likely yes but there are some odd balls out there that dont stand a chance.
If you know what the brand and model number of the PSU thats all we would need. If your unsure of what those are you may be able to tell by looking at the back of your PC, but if the information is not there, open up the side of your case and get it from the lable on the PSU.
Since Google only brought up 2 pages of results and none othe them included the specs of this PSU: AGI HP-W4307F3, I belive it would be safe to say that this is unfortunatly a bargain basment model and it would be very likely that it consists of lower quality parts and can not be trusted to delived the rated amount of power.
It would suggest if you can get a new PSU to do so just for the safety and to give your new parts a good reliable/clean power source.
You probably only need about 350w-450w PSU, use this tool Antec Power Supply Calculator and put in your PC specs to get a good estimate on how much power your PSU wil need, I gave a large estimate just to cover all the bases and to be safe, most PC that do not have high end graphics cards really use far less power than you would think and even ones with newest most powerfull GFX cards in Crossfire or SLI use below 700w.
I hope that helps you out, All the PSU's I listed should work for you perfectly and they are all top quality brands, you just need to see what is in your budget, consider if you are going to upgrade you GPU, and if you want to buy a 80+ certified for better power efficency.