We develop a theory of unit IPOs in which the firm going public issues a package of equity with warrants. We model an equity market where insiders have private information about the riskiness as well as the expected value of their firm's future cash flows. We demonstrate that, in equilibrium, high risk firms issue underpriced “units” of equity and warrants; lower risk firms, on the other hand, issue underpriced equity alone. In contrast to the existing literature, underpricing arises as a signal in our model in the context of a one-shot equity offering. Though developed in the context of IPOs, our model can also explain the issuance of seasoned equity offerings packaged with warrants. Further, the intuition behind the model generalizes readily to provide a new rationale for packaging call-option-like claims with risky securities other than equity, including convertible debt and debt with warrants.