Selective universities regularly employ policies that favor children of alumni (known as "legacies") in undergraduate admissions. Since alumni from selective colleges and universities historically have been disproportionately white, admissions policies that favor legacies have disproportionately benefited white students. For this reason, legacy policies lead to additional costs in terms of reductions in racial diversity. As larger numbers of minority students graduate from colleges and universities and have children, however, the potential pool of legacy applicants will change markedly in racial composition. This analysis begins with a review of the history and objectives of the preference for children of alumni in undergraduate admissions. We then consider the specific case of the University of Virginia and employ demographic techniques to predict the racial composition of the pool of potential legacy applicants to the university. Significant changes in the racial composition of classes that graduated from the University of Virginia from the late 1960s through the 1970s foreshadow similar changes in the characteristics of alumni children maturing through the next two decades.