Shell Programming and Scripting

I posted this already in another thread, but was told that I should create a seperate thread for the following question:

How do I strip the extension when the delimiter might occur multiple times in the filename?

For example:
I have 2 files as input for my script.
test.extension
test.foo.extension

In my script I want to see "test" and "test.foo" as results.
But the following script-snippet gives "test" for both files.
I know this is caused by the -f1 that I use as setting for cut. But I want to know which command I should use so it starts looking for the delim-character from the right i.s.o the left (probably a different command than cut, but which?)

Code:

!/bin/sh

FILE_NAME=$1
if [ ! -r ${FILE_NAME} ]
then
  echo "Could not find file ${FILE_NAME}"
  exit 1
fi

FNAME=`echo "${FILE_NAME}"| cut -f1 -d'.'`

echo "FNAME = ${FNAME}"

TIA