My shell script stops after exec

I'm writing a shell script that looks like this:

 for i in $ACTIONS_DIR/*
    do
            if [ -x $i ]; then
                    exec $i nap
            fi
    done

Now, what I'm trying to achieve is to list every file in $ACTIONS_DIR to be able to execute it. Each file under $ACTIONS_DIR is another shell script.

Now, the problem here is that after using exec the script stops and doesn't go to the next file in line. Any ideas why might this be?