Different pricing for same coaching service given to an individual or a business

Hi, I am starting to make more offers to women in my current workplace to help them get unstuck in their current working life so that they can define and create their truest lives without asking anyone for permission. I have colleagues who ask me for coaching privately and now I have the same colleague who asked me to coach one of her team members (but via the company we both work for).

I am thinking about the offer I would make them and the price for a coaching session. In my mind it makes sense to ask for more money if it is a coaching request via the company than if it is for an individual. I am realising that I would provide the same service and value in both cases. Am I correct in my business approach of pricing or is it rather a model work? 🙂 Thank you for your help.