Write a shell program to check whether given username is valid or not

This shell program checks and returns the appropriate message about the logged in users in system also checks whether user name is valid or not.

list_users=`cat /etc/passwd | cut -d ":" -f 1 | grep $1`
list_logged_users=`who | cut -d " " -f 1 | head -1`
echo "**********************************"
if [ "$list_users" == "$1" ];
then
# if valid user
if [ "$list_logged_users" == "$1" ];
then
echo "The given user is logged in"
exit 1
else
echo "The user not logged in"
fi
else
echo "Not a valid user"
fi