A model to compare a defined benefit pension fund with a defined contribution provident fund

During 1994 universities and certain other institutions in South Africa were given the option of setting up private retirement funds as an alternative to the AIPF (Associated Institutions Pension Fund). Because of the underfundedness of the AIPF only a substantially reduced Actuarial Reserve Value could be transfered to the new fund on behalf of each member. Employees at these institutions had to make the difficult decision of whether to remain a member of the AIPF or to join a new fund. Several institutions created defined contribution funds as an alternative to the AIPF. In such funds the member carries the investment risk and most institutions felt the need to provide some form of top-up of the Transfer Value. A simple mathematical model is formulated to aid in the comparison of expected retirement benefits under the AIPF and a private fund and to investigate the management problem of distributing additional top-up funds in a fair manner amongst the various age groups within the fund.