Thank you both for your response.
Unfortunately, I didn't fully understand Smokemachine's script was doing.
BrowserUK, When I ran the above code, I continue to get the following error (for both lines): Use of uninitialized value in concatenation (.) or string at testscr.pl
As I am calling this within another perl script, I added backticks to the beginning and the end of the statement. But everything else remains the same (given that I am using the actual filenames within this line of code).
I've also tried the following code which seems to compile without any errors but the appended file is blank. Can someone help me see what I'm doing wrong here?

#accts_to_load.txt contains the filenames of al the files I want to ap
+pend together
$acctstoload = "/apps/tmp/invs/accts_to_load.txt";
open(ACCTLOAD, $acctstoload) || die("cannot open $acctstoload");

#Here, I want to give a specific name to the file all the split files 
+are being merged into
$batchfile = "mergedfile.txt";

while(<ACCTLOAD>)  {
`cat $_ >> $batchfile`;
}
[download]

I'm not sure what i'm doing wrong. Any suggestions would be appreciated. Thanks.