Capital change and stability when dividends convey signals

As shown in the previous literature, a change in the dividend-payout ratio can signal a change in the expected net-revenue. It can also affect capital expansion via its effect on retention. Optimal control theory is used to compute equity maximizing capital-expansion rules when dividends signal revenues. The conditions under which the signaling function can both (1) convey correct signals as to future revenue, and (2) lead to a stable equilibrium, are derived. As in Miller and Rock (1985), this stable equilibrium, which is more properly derived here in continuous time, violates the classical equality of internal rate of return with the cost of capital, and the difference is shown to be calculable. Practical time paths for dividends and capital are suggested for various signaling regimes. In addition, strong implications for the direction of empirical signaling research are suggested.