DECLARE @date_t datetime
DECLARE @d datetime
SET @date_t = '20200820'
SET @d = DATEADD(m, 1, @date_t)
SET @d = DATEADD(d, - DAY(@d), @d)
SELECT @date_t, @d

CREATE OR ALTER FUNCTION dbo.XF_LAST_DAY(
    @ad_date datetime
) RETURN datetime AS
BEGIN
   DECLARE @d datetime
   SET @d = DATEADD(m, 1, @ad_date)
   RETURN DATEADD(d, - DAY(@d), @d)
END