Considered you climb with 2000 fpm before the engine fails, you will travel the required 500 ft while saying " Oh, look at that, an engine failed ". By the way: the biggest hairsplitters / beancounters I fly with will watch the "LVR CLB" message flash five to seven times before slowly and carefully bringind back the thrust levers, starting to accelerate at acc. alt. plus 500 to 800. The whole problem is more of a theorethical nature.