T-Sql change month and day

I need to convert a datetime field to the 1st day of the next month.  My sql below
works to change the day or month but I want the month and day changed in one statement.     Thanks.



declare @newdate  datetime,
            @olddate  datetime
            
            
            set @olddate = '2015-05-10'    -- want this to  be '2015-06-01' as @newdate
            
      
            set @newdate = DATEADD(m,1,@olddate)             ---adds 1 to month
            set @newdate = dateadd(dd, -DAY(@olddate) + 1, @olddate)                      --sets day to 1
            
            select @olddate,
                        @newdate