If they couldn't jump it they would climb over it or dig under. I run a strand of barbed-wire near the ground at the bottom of my field fences and the rascals still dig under! Makes a great place to set a snare tho... A fence with a hot wire or barbed-wire on top does help keep them from climbing over.
They can jump 8' tall fences and easily bound distances of 12'+, and they're great climbers. Routinely I've watched them jump up on top of 6' tall fences like it was just jumping on top of a fallen log.
Coyote-proof fencing is very expensive. Cheaper, but not at all cheap and def not coyote-proof, is installing an overhang slanted outward at least 18-24" on top of a 6'+ tall fence with a skirt along the bottom, or a skirted bottom on the same fence with at least 3 strands of hot wire 6" apart. Still very expensive if there's any amount of fencing to upgrade.
Around here the 4 ft. fence works well because it keep our pack of dogs on one side and coyotes on the other. I'm not sure if, at night, they vault the fence.
As I understand it, coyotes an easily climb a 4-5 ft fences. I have heard of "coyote rollers" which appear to be effective at preventing canines from climbing a fence; you can Google their website. I think you could make easily make a coyote roller with some fencing wire and the piping of your choice.