  We show that any toric K\"ahler cone with smooth compact cross-section admits
a family of Calabi-Yau cone metrics with conical singularities along its toric
divisors. The family is parametrized by the Reeb cone and the angles are given
explicitly in terms of the Reeb vector field. The result is optimal, in the
sense that any toric Calabi-Yau cone metric with conical singularities along
the toric divisor (and smooth elsewhere) belongs to this family. We also
provide examples and interpret our results in terms of Sasaki-Einstein metrics.
