Small nick on power cord from an electric alarm clock, and copper wiring exposed but intact
That cable, as is, will tend to "bite people". It also has damage that could increase resistance there causing that spot in the cable to get hot.  Continued flexing will worsen the wire damage and the heating.  

An electrical-tape repair will work temporarily, but I would not resell it like that.  

The right way is take your time and find a gray power cord of very similar style, open up the clock and replace the cable.