My Mac power cord was frayed and the wiring was exposed at the wall wort. I reinforced the cord by cutting it, fitting some shrink tubing over the worn area, and soldering the cord back together.
-soldering gun & solder
-shrink tubing and heat source (lighter)
Step 1: Cut the Cord
Obviously, unplug the power cord first. I cut my cord about a foot from the wall wort and then stripped the cord to expose the wiring.