Abstract Recent empirical research documents a tendency of multinational enterprise affiliates to bunch around zero reported profit. We set up a theoretical model of multinational firm behavior in which we allow for corner solutions in the choice of the optimal transfer price due to insufficient profits or losses of affiliates. Such constraints in the choice of the transfer price induce bunching and generate investment effects in the low-tax as well as the high-tax country. In equilibrium, affiliates might overinvest and the investment effects generate a tendency for too high profit taxes. The analysis provides a micro-foundation for the investment effects that result from transfer pricing. The finding stands in contrast to the existing literature where transfer pricing choices are unconstrained.