There is always lots of hype about software processes for quality/productivity etc but like a lot of people, I was often unconvinced about their value. At the end of the day I enjoy coding, not writing documents and so I would pay lip service to the process of design and specifications but only the minimum amount of work and then dive into code. I was attracted to the idea of things like eXtreme programming which promised quality without the overhead of design and specification but sadly this is a lot of gas imho, quality is not just related to the lines of code but about a whole lot more which is why the process is important. Now that I have less process and less design and specification to work to than my previous employer, I find myself uncomfortable and pine for documents to solidify the quality of my work. So why have a process including design, specification etc?
1) The earlier on the process, the easier/quicker/cheaper it is to fix things. For example, I had a spec review which revealed that a whole chunk of functionality was not required. A minute making a decision saved me potentially days of code (however good it was)
2) It requires that your customers (even internal ones) think about what they want. It is easy to spend 10 seconds saying, "We want a page to do x" with all the cost associated with it, whereas for them to spend a few hours defining it means they will think about whether it is really worth it and allows holes in their assumptions to come out.
3) It enables everyone to have buy-in and sign-off on functionality including everyone agreeing formulas/workflows etc and also allowing budget holders to question the value of the work compared to the proposed benefits.
4) It reduces the likelihood of rework at a later date where the original system implements assumed functionality and then the customer realises it is wrong and needs it to be changed. EVERY change is a risk and takes time/costs money. These risks are in productivity and reputation and why bother reworking? Sometimes it is unavoidable but reduction is better than nothing.
5) It allows systems to be seen in a larger context by people who care about more than one area of the system. With one spec next to another on the desk, a manager can ask questions related to the interaction or consistency of systems/sub-systems with each other. For instance, they might notice duplicated functionality and allow something to be removed in one sub-system since it will be present in another.
6) It permits a quality system to be implemented. If you notice problems in code that are actually related to design weaknesses, how can these be fed back into the quality cycle unless you have design and specification stages to modify?
7) You can have code of 100% reliability/quality from the programmers point of view but that lives in a function/class/system that is not actually of any business use. This is why quality and process CANNOT rely solely on a code view of quality such as eXtreme programming and other shortcut processes.

If you don't have a system, start one. The managers will often need convincing that the extra time is worthwhile but actually if implemented properly it will save time not increase it although there no doubt will be some short term overhead as you learn the way things work.