We estimate the mass of the intermediate-mass black hole at the heart of the dwarf elliptical galaxy NGC 404 using Atacama Large Millimeter/submillimeter Array ( ALMA ) observations of the molecular interstellar medium at an unprecedented linear resolution of \approx 0.5 pc , in combination with existing stellar kinematic information . These ALMA observations reveal a central disc/torus of molecular gas clearly rotating around the black hole . This disc is surrounded by a morphologically and kinematically complex flocculent distribution of molecular clouds , that we resolve in detail . Continuum emission is detected from the central parts of NGC 404 , likely arising from the Rayleigh–Jeans tail of emission from dust around the nucleus , and potentially from dusty massive star-forming clumps at discrete locations in the disc . Several dynamical measurements of the black hole mass in this system have been made in the past , but they do not agree . We show here that both the observed molecular gas and stellar kinematics independently require a \approx 5 \times 10 ^ { 5 } M _ { \odot } black hole once we include the contribution of the molecular gas to the potential . Our best estimate comes from the high-resolution molecular gas kinematics , suggesting the black hole mass of this system is 5.5 ^ { +4.1 } _ { -3.8 } \times 10 ^ { 5 } M _ { \odot } ( at the 99 % confidence level ) , in good agreement with our revised stellar kinematic measurement and broadly consistent with extrapolations from the black hole mass – velocity dispersion and black hole mass – bulge mass relations . This highlights the need to accurately determine the mass and distribution of each dynamically important component around intermediate-mass black holes when attempting to estimate their masses .