How and why to properly write copyright statements in your code

One question I've had about copyright is, suppose you start with a large source file that is MIT or BSD licensed, and then changed it quite substantially - say translate it from Fortran to C++, refactor large functions into smaller ones, delete code you don't need, rename variables and function names from 6- character obscure names to reasonable ones, reorder functions to eliminate forward declarations, add dynamic memory management functions, etc. - are you still forever obligated to keep the original attribution? Perhaps no single line remains the same, but the algorithm is still the same as the original. Does the code have "memory" of its origins? At some point has it changed so much as to be an original work?

Personally I'd be happy to keep crediting the original authors. But from a business legal perspective, anything with external authors or copyright markings causes concern and trouble, so I'm just curious what the bounds are. Any thoughts?