Simple data rearrangement - hard to code

I have to columns with data: one with a company name, the other with a date. I need to create a third column in which the relative previous date appears, which is quite simple. However, the number of observations per company is inconsistent; therefore I cannot simply copy and move the date range.

Therefore, I need a macro which can do this for the 20,000+ rows of data I have, but this is beyond my coding abilities. Please help!

The data looks like this, and I basically need to create the new column:

Existing data New column
Company Date Previous Date
A 05/2003
A 09/2003 05/2003
B 08/1996
B 10/1996 08/1996
B 09/1997 10/1996
B 09/1998 09/1997
B 09/1999 09/1998
C 08/2000
C 12/2000 08/2000
C 12/2001 12/2000
C 12/2002 12/2001
C 12/2003 12/2002
C 12/2004 12/2003
D 08/1998
D 05/2000 08/1998

There is an example attached as well.

Thank you so much for your help!!!

Leon

I have added a "Fill Down" formula that does what you want.
See your sheet, modified and uploaded

Before sorting anything, make the dates permanent by
Select them all: Copy: (dont move selection) : Paste Special - Value

This removes the formulas and replaces them with the result values.

Save the formula somewhere else to use again.

What an elegant solution - didn't see how I could fix that with just formulas, but you made it look easy!

Thanks a lot!