  Novae are some of the most commonly detected optical transients and have the
potential to provide valuable information about binary evolution. Binary
population synthesis codes have emerged as the most effective tool for
modelling populations of binary systems, but such codes have traditionally
employed greatly simplified nova physics, precluding detailed study. In this
work, we implement a model treating H and He novae as individual events into
the binary population synthesis code \binaryc. This treatment of novae
represents a significant improvement on the `averaging' treatment currently
employed in modern population synthesis codes. We discuss the evolutionary
pathways leading to these phenomena and present nova event rates and
distributions of several important physical parameters. Most novae are produced
on massive white dwarfs, with approximately 70 and 55 per cent of nova events
occurring on O/Ne white dwarfs for H and He novae respectively. Only 15 per
cent of H-nova systems undergo a common-envelope phase, but these systems are
responsible for the majority of H nova events. All He-accreting He-nova systems
are considered post-common-envelope systems, and almost all will merge with
their donor star in a gravitational-wave driven inspiral. We estimate the
current annual rate of novae in M31 (Andromeda) to be approximately $41 \pm 4$
for H novae, underpredicting the current observational estimate of
$65^{+15}_{-16}$, and $0.14\pm0.015$ for He novae. When varying common-envelope
parameters, the H nova rate varies between 20 and 80 events per year.
