I also have an IXUS 86' IS, and it's actual focal length is 4,6-17,3 mm as stated on the front of the lens. Since the IXUS have a very small sensor (~36 times smaller than a full-frame 24*36 mm sensor) that zoom-range corresponds angle-wise to 28-1'5 mm on a full-frame camera, such as my Nikon D7''. That is the famous crop-factor. My D7'' has a 24-7' mm zoom, and since it is full-frame there is no crop-factor involved.
DOF (depth-of-field) depends on focal length, aperture and distance camera-to-subject. Another way of putting it is it depends on aperture and magnification scale.
If you and you subject stay in the same place, but you zoom to different focal lengths, and keep the same aperture, a longer focal length gives shorter DOF. But you also get completely different images: the more you zoom the less of the subject you capture.
If you keep your aperture the same, but move yourself and then zoom so that the subject is always equally large in the resulting image, the DOF is the same!
And then compact IXUS versus big DSLR: when you use your 1'5 mm zoom-position, it is actually only 17,3 mm. On my D7'', 1'5 mm is 1'5 mm. 17,3 mm gives huge DOF.
Two links for more info:
http://www.dofmaster.com/dofjs.html
www.tawbaware.com/maxlyons/calc.htm