In this paper, we compare the performance of a homogeneous organization in which group members and the leader belong to the same group, with a heterogeneous organization in which the leader is an outsider. Using a modified public goods game in which leaders' performance in a real effort task determines the marginal return to the public good we focus on the effect of shared group membership on: i) the effort of the leader in the real effort task, ii) cooperation of group members and iii) group members' payoffs. When the leaders are selected randomly, we find that homogeneous groups tend to out-perform heterogeneous groups. This is due to lower performance of the out-group leader and not to differences in cooperation. This effect disappears when high-performance leaders are selected. High performance out-group leaders tend to over perform relative to in-group leaders, yet, there are no differences in cooperation once we control for the marginal incentives to invest in the public good. The results of our study have important implications for how organizations can deal with the arrival of out-group leaders.