A seemingly common point of failure for Apple MagSafe chargers is at either end of the charging cable from the power brick. Given that a new genuine Apple 85w retina charger retails for around $80, attempting to repair the charger seems to be a more economical option than replacing it.
The offending charger has had its insulation worn off for quite a while, exposing the ground shielding underneath. Over time, a significant portion of the (roughly 10 inches or so) wore off, and the ground shielding began to fray. So after putting it off for far too long, I grabbed my soldering iron and some heat shrink to fix this problem.
I cut through the charger cable about 4-5 inches from the end. I slipped a small piece of clear heat shrink down the length of the cable to the end. I’ve had charging cables break at this point, and since I’ve got the cable cut in two, I might as well reinforce this bit.
The white wire inside of the ground shielding is around 22-24AWG. Before stripping the insulation and soldering it back together, make sure that you’ve placed all of your heat shrink along the length of the charger cable.
Strip back some insulation from both wires and solder them together. Again, make sure that your heat shrink is on the wire before soldering it together. Make sure the inner wire heat shrink sufficiently covers the solder connection. Solder the ground shielding together as well.
Slide your heat shrink up the charger cable to sufficiently insulate your cable. Use a heat gun or hot air station to shrink the tubing. Again, since I had a rather large section exposed, and smaller lengths of tubing available, I had to overlap multiple pieces.
And that’s it. A quick 20-30 minute repair with a soldering iron and some heat shrink tubing to save $75!