Ph.D. admission with funding from current employer My employer is considering contracting part of a research project to a university and I'm currently the project leader. I found that I might use this opportunity to pursue a Ph.D. degree and talked to the management of my company. They agreed for me to do a Ph.D. using this funding (I will still have to commit other affairs in my current company but that will only be part-time). We also found a professor willing to supervise me provided that the funding will be available from my employer

So my question is, would the admission committee consider this approach problematic? As I'm the representative of the industry funding provider of my Ph.D. research, if I'm admitted to the program. Also, just to be selfish, how do I gently let the department know that I will not (at least within my influence for this particular project) fund other student for this project?
Two things came to my mind:


Self-Finance and End Results: First thing first, broadcasting to a department that you have the money and you need a PhD position might not be a good idea. This is because just spending the money does not give you the PhD at the end. You need a good supervisor and research group to do the research. Throwing money at situation works in business, and might work in academia in other situations (e.g., buying equipment); however for your own PhD I would suggest to carefully pick and choose. You might spend the money and not getting the results at the end.  
Guidance from supervisor: Your target is to do a PhD (with a one supervisor or two) with your company's funding. There are some issues here, for example, who is actually doing your implementation work (e.g., your coding if you are in a computing field) if you have a team behind you? I would suggest to find an academic first, and talk to him/her about this situation. Also, this way you don't go under the university's pressure and some non academic management to throw money at the research, because this will be hopefully sorted and guided by your supervisor(s).