  We discuss the thermoelectric and optical properties of layered
K$_{x}$RhO$_{2}$ (\emph{x} = 1/2 and 7/8) in terms of the electronic structure
determined by first principles calculations as well as Boltzmann transport
theory. Our optimized lattice constants differ significantly from the
experiment, but result in optical and transport properties close to the
experiment. The main contribution to the optical spectra are due to intra and
inter-band transitions between the Rh 4\emph{d} and O 2\emph{p} states. We find
a similar power factor for pristine K$_{x}$RhO$_{2}$ at low and high cation
concentartions. Our transport results of hydrated K$_{x}$RhO$_{2}$ at room
temperature show highest value of the power factor among the hole-type
materials. Specially at 100 K, we obtain a value of 3$\times$10$^{-3}$ K$^{-1}$
for K$_{7/8}$RhO$_{2}$, which is larger than that of Na$_{0.88}$CoO$_{2}$ {[}M.
Lee \emph{et al}., Nat. Mater. 5, 537 (2006){]}. In general, the electronic and
optical properties of K$_{x}$RhO$_{2}$ are similar to Na$_{x}$CoO$_{2}$ with
enhanced transport properties in the hydrated phase.
