  Motivated by the newly synthesized mixed-valent spinel LiRh$_2$O$_4$ for
which a large thermopower is observed in the metallic cubic phase above 230K
[Okamoto {\it et al.} (arXiv:0806.2504)], we calculate the Seebeck coefficient
by the combination of local density approximation and dynamical mean field
theory (LDA+DMFT). The experimental values are well reproduced not only by
LDA+DMFT but also by the less involved Boltzmann equation approach. A careful
analysis of the latter shows unexpectedly that the origin of the large
thermopower shares a common root with a very different oxide: Na$_x$CoO$_2$. We
also discuss how it is possible to further increase the powerfactor of
LiRh$_2$O$_4$ through doping, which makes the material even more promoising for
technological applications.
