Hello there, markvis14!
It depends, the manufacturer recommends a 450w power supply for the entire system... if your PC doesn't have a lot of drives (physical and optical), a lot of cooling fans, LED lights, and you're not OC'ing your system, I don't think it's completely necessary to upgrade your PSU.
Other thoughts: i don't know what brand is your PSU, hence, i don't know if it's 80 plus certified, generic, don't know its amperage rating on the +12V Rail. There are a lot of factors.
400w i'd say it's a little tight. If you bought a ~110$ GPU, the least you could do, it's to chip in another ~60$ for a decent PSU.
Here: Newegg.com - Antec BP550 Plus 550W Continuous Power ATX12V V2.2 80 PLUS Certified Modular Active PFC Power Supply
Here: Newegg.com - Antec EarthWatts EA-650 GREEN 650W ATX12V v2.3 SLI Ready CrossFire Certified 80 PLUS BRONZE Certified Active PFC Power Supply
I'd recommend the EA-650. 60$ and 650W of pure 80 plus bronze power