With the following steps I have managed to add the BG service again.
Regards...
PS C:\CAPPM\apache-tomcat-8.0.20\bin> service status all
[-] CA PPM Beacon [beacon] is stopped
[-] CA PPM App Server [app] is stopped
[-] CA PPM System Admin Server [nsa] is stopped
PS C:\CAPPM\apache-tomcat-8.0.20\bin> service add bg
Adding service(s)...
All services are already registered.
PS C:\CAPPM\apache-tomcat-8.0.20\bin> service status all
[-] CA PPM Beacon [beacon] is stopped
[-] CA PPM App Server [app] is stopped
[-] CA PPM System Admin Server [nsa] is stopped
PS C:\CAPPM\apache-tomcat-8.0.20\bin> service remove bg
Removing service(s)...
Done.
PS C:\CAPPM\apache-tomcat-8.0.20\bin> service add bg
Adding service(s)...
Done.
PS C:\CAPPM\apache-tomcat-8.0.20\bin> service status all
[-] CA PPM Beacon [beacon] is stopped
[-] CA PPM App Server [app] is stopped
[-] CA PPM System Admin Server [nsa] is stopped
[O] New service: bg. Use 'service deploy bg' command to create executables.
PS C:\CAPPM\apache-tomcat-8.0.20\bin> service deploy bg
Deploying service(s)...
Done.
PS C:\CAPPM\apache-tomcat-8.0.20\bin> service status all
[-] CA PPM Beacon [beacon] is stopped
[-] CA PPM App Server [app] is stopped
[-] CA PPM System Admin Server [nsa] is stopped
[-] CA PPM Background Server [bg] is stopped
PS C:\CAPPM\apache-tomcat-8.0.20\bin> service start all