  Let $\Lambda$ be an artin algebra and let $\mathcal{P}^{<\infty}_\Lambda$ the
category of finitely generated right $\Lambda$-modules of finite projective
dimension. We show that $\mathcal{P}^{<\infty}_\Lambda$ is contravariantly
finite in $\rm mod\,\Lambda$ if and only if the direct sum $E$ of the
indecomposable Ext-injective modules in $\mathcal{P}^{<\infty}_\Lambda$ form a
tilting module in $\rm mod\,\Lambda$. Moreover, we show that in this case $E$
coincides with the direct sum of the minimal right
$\mathcal{P}^{<\infty}_\Lambda$-approximations of the indecomposable
$\Lambda$-injective modules and that the projective dimension of $E$ equal to
the finitistic dimension of $\Lambda$.
