Shell Scripting to check file exist and whether file is writable or not

Write a shell script to check to see if the file "/etc/shadow" exists. If it does exist, display "Shadow passwords are enabled." Next, check to see if you can write to the file. If you can, display "You have permissions to edit /etc/shadow." If you cannot, display "You do NOT have permissions to edit /etc/shadow." 



#! /bin/bash

if [ -e "/etc/shadow" ]
then
echo "Shadow Passwords are enabled"
if [ -w "/etc/shadow" ]
then
echo "You have permission to edit shadow password"
else
echo "You do not have permission to edit shadow passwords"
fi
else
echo "Shadow Passwords are not enabled"

fi