Can't edit office files on share folder

I am using Windows Server 2008 R2. I shared a network Drive with the following permission

Share permission        : Authenticated users     Read only

NTFS permission         : Authenticated users    default permission on parent folder

Inside that parent folder I have the many folders for each department

Each department folder I have gave default permission with write option to the each department manager and department also inherited permission is unchecked on the child folder. But when I try to edit MS office files inside those child folder and get the following error message “Access is denied: Contact your Administrator”