An Application to Capital Structure Problems: Optimal Financing of a Company

In this chapter we present an application to corporate finance: how to optimally structure financing of a company (a project), in the presence of moral hazard. In the model the agent can misreport the firm earnings and transfer money to his own savings account, but there is an optimal contract under which the agent will report truthfully, and will not save, but consume everything he is paid. The model leads to a relatively simple and realistic financing structure, consisting of equity (dividends), long-term debt and a credit line. These instruments are used for financing the initial capital needed, as well as for the agent’s salary and covering possible operating losses. The agent is paid by a fixed fraction of dividends, which he has control over. At the optimum, the dividends are paid locally, when the agent’s expected utility process hits a certain boundary point, or equivalently, after the credit line balance has been paid off. Because the agent receives enough in dividends, he has no incentives to misreport. When having a larger credit line is optimal, in order to be allowed such credit, it may happen that the debt is negative, meaning that the firm needs to maintain a margin account on which it receives less interest than it pays on the credit line, as also sometimes happens in the real world. The continuous-time framework and the associated mathematical tools enable one to compute many comparative statics, by solving appropriate differential equations, and/or by computing appropriate expected values.