I run an individual business in Switzerland in the field of photography services. I would like to expand the business to a country in the European Union. Should I then set up a business in that country, or will this not be necessary and I can invoice using my current business and then pay income tax in Switzerland?
If need to establish a business abroad what will be my tax residency as natural person in that case?
If you do not go physically to EU, you do not need to set up a business there. You can do everything from here. However, from a certain sales threshhold in a country (the threshhold is different for each country), you need to levy and pay VAT in the said country. This is done through an EORI number if my memory serves me well.
If you have to go physically into a country, it gets more complicated. I know that if technicians had to come from EU to Switzerland (for commissioning equipment in a plant for example), we needed to declare them. I can imagine it is the same the other way round. (I am not talking about business meetings which are fine).
Also, if you bring a lot of equipment over the boarder, you might need to fill out an ATA everytime you cross (not super efficient).
As long as you stay in Switzerland and have your life center here, you should be taxabale in Switzerland. Your business is an other story (BTW, you might not be able to open a sole propriorship or even a GmbH type of business if you are not residing in the said country. To be checked).
That sounds a bit odd to me.
E.g. if you are a photographer and shoot internationally - you’d need to register and pay VATs across 10 countries?
I’d imagine (or hope rather 
) the invoicing (from CH only) would be simpler than that.
Btw VAT-eligibility probably depends on total income accrued (100k/year?).
As I said, as soon as you reach a certain threshhold in sales (not income in general), you are eligible to pay VAT in the said country. The threshhold is individual to each country.
I’d rather say liable or obliged to. 