Audits are a means to verify a system is defined, implemented and is effective. The system is unquestionably the means to achieve rewards:
1) Fewer workplace injuries and health issues, resulting in (one leads to the next)
a) less lost work time,
b) better employee retention,
c) enhanced readiness-to-work, from skilled and caring people staying on the job versus needing replacements
d) increased customer satisfaction.
2) Improved reputation as an employer
3) Enhanced standing in the community
4) Money saved on fines and legal redress from workplace accidents.
While a good system can arguably do this without an internal and external audit function, the auditor brings certain benefits:
1) Not being part of the group that owns the process, the auditor may observe issues or patterns of issues that internal people do not.
2) Being outside of the group that owns the process means improvements can be driven expediently, via the non-conformance process.
3) Customers and the community tend to respect a system more if they know it's being scrutinized by entities that do #1 and #2.
I can appreciate your question. In today's hard driving management environment I am constantly having to justify my value. But I can point to many violations of the law that I, the internal auditor have forced to be corrected: violations that would have brought fines if some bad thing eventually happened and we were to go under government or legal scrutiny. That amounts to real money but prevention is always harder to prove than a bad event's occurrence and consequences. For that you can point to organizations that did not have an objective, attentive and devoted audit program, and the ghastly consequences of getting it systematically wrong and no one making the corrections.
But suppose something does go wrong in spite of the audits.
OSHA has a policy of giving an organization credit for having a functioning program - doing so indicates the organization is intent upon doing the right thing. I don't know what kind of equivalent exists in your area, but I can vouch that this also works in legal circles, by ruling out negligence.
Lastly, if the auditor is skilled and educated in matters of workplace safety, you could actually do the math and point to that person's help in an ROI study of, for example getting a chemical labeling system cleaned up so employees don't drink acid when they believe they will be sipping water.
I hope this helps!