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

<code sql> 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