You will need a better power supply. You can get the XFX 550W bronze for cheap, probably the minimum I power delivery I would recommend with any certainty. Plenty of amps. Considerably better than the CX series.
You are probably right, but you also have the get-more-than-you-need principle for PSUs. If money is an issue, then 550-600+ will probably be fine. 420 probably not.