Raising Capital from Heterogeneous Investors

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A firm raises capital from heterogeneous investors to fund a project. The project is implemented only if the total capital raised exceeds an initially unknown threshold, and the firm offers payments depending on project implementation. We study the firm’s optimal self-financing scheme that maximizes its payoff subject to all investors participating being the unique equilibrium outcome. The optimal scheme features full collateral: if the project is not implemented, each investor is refunded her capital. Under implementation, however, net returns differ across investors. If the distribution of the investment threshold is log-concave, the firm offers higher returns to larger investors. Moreover, higher dispersion in investor size raises the firm’s payoff.

Joint with Marina Halac and Eyal Winter.