M32 is the prototype for the relatively rare class of galaxies referred to as compact ellipticals. It has been suggested that M32 may be a tidally disturbed r1/4 elliptical galaxy or the remnant bulge of a disk-stripped early-type spiral galaxy. This Letter reveals that the surface brightness profile, the velocity dispersion measurements, and the estimated supermassive black hole mass in M32 are inconsistent with the galaxy having, and probably ever having had, an r1/4 light profile. Instead, the radial surface brightness distribution of M32 resembles an almost perfect (bulge+exponential disk) profile; this is accompanied by a marked increase in the ellipticity profile and an associated change in the position angle profile where the ``disk'' starts to dominate. Compelling evidence that this bulge/disk interpretation is accurate comes from the best-fitting r1/n bulge model, which has a Sérsic index of n=1.5, in agreement with the recently discovered relation between a bulge's Sérsic index and the mass of a bulge's supermassive black hole. An index of n>=4 would also be inconsistent with the stellar velocity dispersion of M32. The bulge-to-disk size ratio re/h equals 0.20, and the logarithm of the bulge-to-disk luminosity ratio log(B/D) equals 0.22, typical of Sφ galaxies. The effective radius of the bulge is 27" (~100 pc), while the scale length of the disk is less well determined: owing to possible tidal stripping of the outer profile beyond 220"-250", the scale length may be as large as 1.3 kpc. M32 is a relatively face-on, nucleated dwarf galaxy with a low surface brightness disk and a high surface brightness bulge. This finding brings into question the very existence of the compact elliptical class of galaxies.