  Aims: We predict the exoplanet yield of a space-based mid-infrared nulling
interferometer using Monte Carlo simulations. We quantify the number and
properties of detectable exoplanets and identify those target stars that have
the highest or most complete detection rate. We investigate how changes in the
underlying technical assumptions and uncertainties in the underlying planet
population impact the scientific return. Methods: We simulated $2'000$
exoplanetary systems, based on planet occurrence statistics from Kepler with
randomly orientated orbits and uniformly distributed albedos around each of
$326$ nearby ($d < 20~\text{pc}$) stars. Assuming thermal equilibrium and
blackbody emission, together with the limiting spatial resolution and
sensitivity of our simulated instrument in the three specific bands $5.6$,
$10.0$, and $15.0~\mu\text{m}$, we quantified the number of detectable
exoplanets as a function of their radii and equilibrium temperatures. Results:
Approximately $\sim315_{-77}^{+113}$ exoplanets, with radii $0.5~R_\text{Earth}
\leq R_\text{p} \leq 6~R_\text{Earth}$, were detected in at least one band and
half were detected in all three bands during $\sim0.52$ years of mission time
assuming throughputs $3.5$ times worse than those for the James Webb Space
Telescope and $\sim40\%$ overheads. Accounting for stellar leakage and
(unknown) exozodiacal light, the discovery phase of the mission very likely
requires $2$ - $3$ years in total. Roughly $85$ planets could be habitable
($0.5~R_\text{Earth} \leq R_\text{p} \leq 1.75~R_\text{Earth}$ and
$200~\text{K} \leq T_\text{eq} \leq 450~\text{K}$) and are prime targets for
spectroscopic observations in a second mission phase.
