  We show that there exists a separable, nuclear C*-algebra with real rank zero
and trivial K-theory such that its multiplier and corona algebra have real rank
one. This disproves two conjectures of Brown and Pedersen. We also compute the
real rank of the stable multiplier algebra and the stable corona algebra of
countably decomposable type $\mathrm{I}_\infty$ and type $\mathrm{II}_\infty$
factors. Together with results of Zhang this completes the computation of the
real rank for stable multiplier and corona algebras of countably decomposable
factors.
