  For every metric space $X$ we introduce two cardinal characteristics
$\mathrm{cov}^\flat(X)$ and $\mathrm{cov}^\sharp(X)$ describing the capacity of
balls in $X$. We prove that these cardinal characteristics are invariant under
coarse equivalence and prove that two ultrametric spaces $X,Y$ are coarsely
equivalent if
$\mathrm{cov}^\flat(X)=\mathrm{cov}^\sharp(X)=\mathrm{cov}^\flat(Y)=\mathrm{cov}^\sharp(Y)$.
This result implies that an ultrametric space $X$ is coarsely equivalent to an
isometrically homogeneous ultrametric space if and only if
$\mathrm{cov}^\flat(X)=\mathrm{cov}^\sharp(X)$. Moreover, two isometrically
homogeneous ultrametric spaces $X,Y$ are coarsely equivalent if and only if
$\mathrm{cov}^\sharp(X)=\mathrm{cov}^\sharp(Y)$ if and only if each of these
spaces coarsely embeds into the other space. This means that the coarse
structure of an isometrically homogeneous ultrametric space $X$ is completely
determined by the value of the cardinal
$\mathrm{cov}^\sharp(X)=\mathrm{cov}^\flat(X)$.
