Is it appropriate for parents to read our kids' text messages?

Reading text messages was a condition of getting the cell phone. My 13-year-old knew from the beginning that I would be reading all text messages and nothing gets deleted until I see all messages. Plus, all of her friends who text message her knows that I review all her messages and was told not to send or forward any inappropriate messages otherwise their parent was going to get a call from me. It might seem harsh for but, I want my daughter (and her friends) to understand that it’s a privilege to have a cell phone that texts and as part of that privilege, there are rules.