This is natural to think that in order to get the perfection one needs to pay for it. This is really hard to argue. However, what comes to quality, things may look not like they seem at the first glance. Quality may cost you additional time spent on operation that you would not do still producing a good product. But we all are humans and are not perfect in sense of quality of our work. In other words, we do make mistakes. So, we need all these additional measurements within the production cycle that allow us to see if the product complies to standards and requirements.
But when we talk about time and efforts spent on following procedures which only purpose is not letting us making the errors we should not forget about savings that we get using them. We have introduced all those practices not just in case but in response to problems we had in the past, in response to defects introduced or missed in the previous production cycles. Having deprived of them is going to save our time and resources!
The formula of quality cost includes not only explicit expenses on following quality processes but also implicit savings we get from following them. If you do not have savings then why bothering to do unnecessary actions? Even if process changes are introduced "just in case", we still do it to decrease the risk of having some problems in the future (lost user data -> frustrated clients -> bad reputation -> drop in sales).
In any case, if we make changes to the process we believe that we are going to have some saving, be it lower number of defects found at system testing, or fewer calls to customer support. So, we can infer that quality does not cost us money. Instead, it saves us money!
If you are still not convinced that introducing quality practices does not cost you a coin, just look at two automobile vendors: Alfa Romeo and Toyota. Both cars can be in same prices niche, both provide similar functionality and cost almost the same, but the difference in quality is huge. It's remarkable that Toyota does not spend more money for producing its cars than Alfa Romeo because they have a good quality system installed. So, they spend more at the early stages of development to save time at the later stages.
In order to create such a system in your company just look at the history of previous projects. Analyze defects that escaped development and testing phases. Try to estimate cost of one fix at different phases, and introduce practices that will eliminate most popular mistakes. You can easily calculate savings you will get from introducing those practices. Then simply compare it to the additional cost related to following those practices. I am sure the benefit will totally overweight the overhead expenses. If it doesn't just write me back. I am interested in that sort of anomalies ;)