  Utilizing ultraproducts, Schoutens constructed a big Cohen-Macaulay algebra
$\mathcal{B}(R)$ over a local domain $R$ essentially of finite type over
$\mathbb{C}$. We show that if $R$ is normal and $\Delta$ is an effective
$\mathbb{Q}$-Weil divisor on $\operatorname{Spec} R$ such that $K_R+\Delta$ is
$\mathbb{Q}$-Cartier, then the BCM test ideal
$\tau_{\hat{\mathcal{B}(R)}}(\hat{R},\hat{\Delta})$ of $(\hat{R},\hat{\Delta})$
with respect to $\hat{\mathcal{B}(R)}$ coincides with the multiplier ideal
$\mathcal{J}(\hat{R},\hat{\Delta})$ of $(\hat{R},\hat{\Delta})$, where
$\hat{R}$ and $\hat{\mathcal{B}(R)}$ are the $\mathfrak{m}$-adic completions of
$R$ and $\mathcal{B}(R)$, respectively, and $\hat{\Delta}$ is the flat pullback
of $\Delta$ by the canonical morphism $\operatorname{Spec} \hat{R}\to
\operatorname{Spec} R$. As an application, we obtain a result on the behavior
of multiplier ideals under pure ring extensions.
