If I buy another company do I have to take on all their employees as well?
TUPE legislation is very complex and IT IS STRONGLY RECOMMENDED THAT YOU SEEK ADVICE FROM AN EMPLOYMENT LAW SPECIALIST BEFORE DOING ANYTHING. On a simple level, yes, if you buy a business all the employees will automatically transfer across to your business on the same terms and conditions of employment that they had prior to the transfer.
Can I make redundancies after buying another company?
You can but IT IS STRONGLY RECOMMENDED THAT YOU SEEK ADVICE FROM AN EMPLOYMENT LAW SPECIALIST BEFORE DOING ANYTHING. You can usually make redundancies for Economic, Technical or Organisational reasons but you will need to make sure you have planned what your structure is now and what the structure needs to be at the end of the process. The redundancies could be from your existing employees or those who have transferred in if you have duplicate roles eg you have two Sales Directors but you only need one going forward. You must go through a consultation process with all the employees affected.

