This 105 characters seem to be working, but not putting any money on it
=TEXT(B2+(LEFT(A2,6)&RIGHT(A2,4)+2000),"mm/dd/")&TEXT(YEAR(B2+(LEFT(A2,6)&RIGHT(A2,4)+2000))-2000,"0000")
To Narayan's point,
=TEXT(B2+(LEFT(A2,6)&RIGHT(A2,4)+2000),"mm/dd/")&TEXT(RIGHT(A2,4)+SUM(YEAR((LEFT(A2,6)&RIGHT(A2,4)+2000)+N(INDIRECT("R"&ROW(A2)&"C"&{2,50},FALSE)))*{1,-1}),"0000") 'also' seems to be working