“Fixing regression bugs is analogous to digging a hole only to find the next day it has been filled in and having to dig it out again”
Ask any manager, developer or tester working on software without tests what the main pain points are. Nearly all the time the main one mentioned is dealing with regressions. This is bugs that were fixed a year ago which returned. Regression bugs cost the software industry billions of dollars a year. Worse still they are demoralising to everyone involved. Finding or fixing the same bug over and over causes you to start looking for new projects or new jobs.
A good regression test suite generally solves these problems. It may not prevent every bug from reoccurring but it will catch most of them. It also gives peace of mind that you have not reintroduced these bugs again once fixed. Lastly it saves time by checking if the bug is fixed for you.
“Software is never finished, only abandoned”
Another advantage to come out of having a good test suite are the improvements to the software itself. Not only is testable software generally better written then non-testable software, a collection of tests provides a nice safety next when you start to improve your product. Software as a general rule is constantly in flux with changes and improvements or left as is. If your software is never improved or built upon you may want to consider if you really need tests. That said there are other reasons to test software beyond what is mentioned above.
If none of the above points are selling testing to you consider this. As mentioned testable software is usually well designed modular software. This allows greater code reuse saving time and money. It also allows new developers to quickly understand what they are dealing with allowing them to become productive faster. If nothing else writing testable software will save you time and money in the long run by making things easier to understand.