Necessity is the mother of invention.
Step 1: What You Will Need
Wooden pants hanger
Dremel type tool with cut off wheel
2 wood screws (not too big, not to small)
Ruler / Tape measure
Eye protection Glasses / Goggles (not shown above)
Step 2: Prepare Your Hanger
Measure and mark off two holes on the hanger for mounting your hanger under a shelf. (see 1st diagram) The hole size should be the same diameter as your screws. Drill away.
With your cut off tool remove the top of your hanger and the inside metal rod. Be careful with what you cut off. You must leave the the metal holding the wooden rod and the hook at the opposite end! (see 2nd diagram) Put on eye protection. Cut away.
Step 3: Mount Your New Paper Towel Holder
Measure and drill two corresponding holes under your shelf or cabinet. Don't drill too deep, and the drill bit size must be smaller then the screw diameter so the screws have something to hold on to. (make sure your screws aren't so long that they go all the way through your shelf or cabinet) Align and screw your new paper towel holder into your shelf or cabinet. Mount away.
Step 4: You're Finished!
As long as you're happy with what you have done, don't mind if your friends laugh at you a little bit. Just don't tell them, and ask them to grab you a paper towel and see if they notice. Thanks for reading this and God speed!