The mystery of the favicon file or the .ico extention has been solved. No need for the favicon .ico extention for photoshop. All you simply  need to do is set the the final image size to 16px x 16px at 72dpi and set the color mode to indexed color. To set the color mode go to the main menu>image>mode>indexed color. Then Save as .bmp but save the file as favicon.ico. Done.