How to approach supervisor about running a start-up along side PhD? I have had a good opportunity to begin a start-up that would be providing SaaS to Universities. The start up is not related to my PhD topic, other than it also relies on my programming skills. As it has reached an inflection point it has started taking about 5 hours a week to manage it, but I can easily put those hours in by working a different schedule (Late or at weekends). I have a co-founder which means if a busy time hit in the PhD they could take more burden temporarily.

Institutional factors

My university is very supportive of start-ups  with several different initiatives and programmes to ensure this happens. 

Early on in my PhD I asked my supervisor about how I should be spending my time during my PhD and they said I should keep side projects to my personal time and devote the working week to the PhD.

Context


1st Year PhD student in UK
Funded by UK Research Council
Had idea for project during undergraduate.


Other Questions related

Is it possible to work on extra activities (start-up project) during PhD? :
Very in favour of proceeding but advises caution if not in related field.

Responsibility/ethics of startups during graduate studies
Quite against the idea if it is not related field. Also asks about disclosure but does not answer regarding how to do this.

My dilemma

This idea has been pitched to people who are on a similar managerial level and could mention it to my supervisor.
They have thoroughly got behind the idea and want me and my co-founder to develop it.
I would rather tell my supervisor myself than them find out 2nd hand but am conflicted by the universities stance on supporting entrepreneurship versus my supervisor encouraging me to focus on the PhD for normal working time. 

I'm aware that somewhere down the line the start up could take off meaning I might have to go part time, if allowed. Should I mention this?

How should I go about bringing up the start-up to my supervisor?
First, make sure this is allowed at your institution.  Then develop a solid plan for how you will handle both projects before taking it to your supervisor.  To the first point, it seems that you already have, but make sure that you understand your institution's rules.  For instance, is it allowed to use school resources?  What does that mean in your institution?  It could mean something as obvious as using a school computer to run a simulation for the business, or something as subtle as taking a phone call in your school office.  You need to be 100% sure that you are not violating any institutional policies.  

Some institutions are hands-off when it comes to external projects as long as they aren't done on campus, others aren't.  For instance, where I did my masters, we were not permitted to make income outside of the school without losing an equivalent amount of funding.   Where I did my PhD this was not the case.

Next, make a clear plan for your advisor to understand.  As was pointed out in the comments, both projects are going to take a LOT of time to do well.  Your PhD should be the priority.  You need to make sure that your advisor understands precisely what working on the business and working on the PhD mean.  Be realistic.  It's very likely that you will check your business email while working at school, so don't pretend that you won't.

Your advisor has already stated that you should keep your side projects to your free time.  You need to be very clear what that means.  PhDs aren't necessarily like jobs.  You might not be able to get much research done one morning because the ideas aren't there, then work well into the night to make huge progress.  Does that unproductive morning count as free time? 

Have a strong plan for what you want from your advisor. "I want you in on this" is not helpful.  "I need a support person in the role of algorithm development.  Here are the specific responsibilities I was thinking.  What do you think?"  is much better.  

Finally, make it clear how much freedom the advisor has in this business.  Is he a co-founder, making equal decisions?  Is he an employee?  A contractor? A board member? Will you pay him?  What happens if he decides to hire a few co-op students and bring his long-time collaborator on board?  Who retains control of the business?  Who has ownership?  These aren't unique questions to student-advisor businesses, but they are important to get straight up front.  The worst thing that can happen is you both have different ideas for your responsibility and the business gets away from you.