This is per design. You have created a model from database, which indicates that your code should never create a database.
The error message you get, occurs because it doesn't find the database and hence tries to create it.
To solve this you need to check your connectionstring to make sure it can find the database you want to connect to. If you really want to create the database you should go for code first. This means either to remove the "throw new exception" line and keep using the model (this means you can't update model from database anymore, as it then would reinsert the exception line), or you can reverse engineer a database to code-first model.
see http://msdn.microsoft.com/en-us/data/jj593170.aspx for reverse engineering tips.