  The merger of two supermassive black holes is expected to produce a
gravitational-wave signal detectable by the satellite LISA. The rate of
supermassive-black-hole mergers is intimately connected to the halo merger
rate, and the extended Press-Schechter formalism is often employed when
calculating the rate at which these events will be observed by LISA. This
merger theory is flawed and provides two rates for the merging of the same pair
of haloes. We show that the two predictions for the LISA
supermassive-black-hole-merger event rate from extended Press-Schechter merger
theory are nearly equal because mergers between haloes of similar masses
dominate the event rate. An alternative merger rate may be obtained by
inverting the Smoluchowski coagulation equation to find the merger rate that
preserves the Press-Schechter halo abundance, but these rates are only
available for power-law power spectra. We compare the LISA event rates derived
from the extended Press-Schechter merger formalism to those derived from the
merger rates obtained from the coagulation equation and find that the extended
Press-Schechter LISA event rates are thirty percent higher for a power spectrum
spectral index that approximates the full Lambda-CDM result of the extended
Press-Schechter theory.
