So you're using the Project Tool to re-projecting a map into a new projection.
Before you can start the process, you have to choose from the many transformations. The attached file (World Projections.xls) lists where in the world each projection transformation should be used.
For example, if your map is in PSAD56, and you want to project it to WGS84, the Project Tool will ask you which transformation you want. Checking the lists for Bolivia, I find: PSAD_1956_To_WGS_1984_2
I reformatted the file in Excel because I found working with the Word file clunky. These is an official ESRI list, current for ArcGIS 9.2. The original file is here: http://downloads.esri.com/support/TechArticles/PEgt_namewhere92.zip
I found this in a very helpful PDF on projections and transformations, which has other excellent links: http://www.lib.unc.edu/reference/instruction/2007FallPLAN714/coosys_quick_ref_bib.doc
Nico goes over using the Project Tool in this tutorial: http://www.mapaspects.org/courses/gis-and-anthropology/weekly-class-exercises/week-3-acquisition-digital-data
For South America, Nico has this advice: http://www.mapaspects.org/articles/psad1956_transform
The second attached files has only the transformations relevant to Peru and Bolivia.
Happy GISing, Erik.