Peruvian DGAC to FAA:
Based on my instructing expereince back in 2002-03 (probably has changed from those days by the way), the FAA will issue you with a PPL without any problems however your CPL and IRA will have to be converted which will most likely include a checkride.
This will require meeting the appropriate experience requirements as detailed in the FARs, Part 61 to be more specific, so buy the 2009 FAR/AIM!. But you won't need the total hours requirements for the license/rating since you have those already (250hrs for CPL and 40hrs for the IRA) presumably, but will require the PIC hours, night hours, complex hours, x-countries, 3 hrs in prep for checkride, etc, etc
I am also guessing they will ask you to take the written exams for both.
I suggest you make an appointment at your local FSDO, and go in with logbooks and licenses and get an official version on how to convert from an inspector!
Regards,
OW