In a classical paper, Allen and Faulhaber (1989) provided a signaling explanation for underpricing in the IPO price. Their main insight is that good-type rms nd it optimal to signal their type by underpricing their initial issue of shares, and investors know that only the best can recoup the cost of this signal from subsequent issues. In this note, we argue that their proof of the main result is not complete because they only checked part of the incentive compatibility conditions without showing that their outcome is robust against all possible deviations. We show that a good rm always has an incentive to deviate to raise the IPO price slightly from its equilibrium price if the price is the only signaling device. This implies that there is no separating equilibrium, that is, signaling by underpricing does not occur in equilibrium in the case of one- dimensional signal. If the rm can choose the equity fraction to be sold as well as the price, however, a high-type (good-type) rm can signal its high protability by choosing a low fraction of equity. In this case, a high-type rm still engages in underpricing in the sense that it sets a lower IPO price than the real value of the rm, but underpricing cannot be a signal because both types choose the same price in equilibrium.