We propose a new performance indicator to evaluate the productivity of research institutions by their disseminated scientific papers. The new quality measure includes two principle components: the normalized impact factor of the journal in which paper was published, and the number of citations received per year since it was published. In both components, the scientific impacts are weighted by the contribution of authors from the evaluated institution. As a whole, our new metric, namely, the institutional performance score takes into account both journal based impact and articles specific impacts. We apply this new scheme to evaluate research output performance of Turkish institutions specialized in astronomy and astrophysics in the period of 1998-2012. We discuss the implications of the new metric, and emphasize the benefits of it along with comparison to other proposed institutional performance indicators.