It is recommended that you upgrade your PSU (Power Supply Unit) when installing a GPU (Graphics Processing Unit).
With that said there is a new budget GPU out which should work with your system without upgrading your PSU although I still highly recommend upgrading regardless to protect your investment.
The GPU I'm referring to is the GTX 750 Ti SC which doesn't require a 6-Pinn Power connecter. It draws the power it needs from the PCIe slot in which you will be installing it into. The TDP for this card is 65watt an the PCIe slot is capable of 75watt. Therefore you could use it without upgrading the PSU until you have the extra money to upgrade the PSU (which I'd upgrade ASAP)
The card can be found on www.newegg.com & www.amazon.com between $150.00-190.00
Hope this helps, and yes it will be able to play BF4 an all the latest games. Some with higher settings than others but you should be pleased with it since you do seem to be on a budget this will give you the best performance for your dollar. Feel free to look for other cards if you wish.
Also, I would suggest the EVGA version of this card. As it offers future G-synce tech an is the smallest model of these cards. Plus it looks stylish.
AMD + ASUS = Good Machine