When is "Major Rewrite" the answer for a codebase?

A horrible project was passed down to me which uses old Java, and Struts 1.0, tables with inconsistent relationships, or no relationships at all and even tables without primary keys or fields meant to be primary keys but aren't unique at all.

A few things like duplicate copy & paste components are turning me off. Looks like developers who built it never heard of code optimisation.

TL;DR When is a major rewrite of codebase the answer and what arguments can you use to support it in front of management?