Optimal Control Of Dividend Policy Under Tax Rate Differences

Dividend policy is a financial problem known as "the dividend puzzle". Various disputes of this area not only extend its research vision, but also propose theoretical basis for corporation finance and government's decision. We have noted that there is more and more research on the application of the optimal control theory to financial, investment and dividend policy, and many achievements have been made. The paper uses the optimal control theory to study the effect of the tax rate differences on the dividend policy. The mathematical tool used is optimal control theory. The paper first studies a firm without debt, and formulates a simple optimal control model. Then capital structure as a control variable is introduced into the model. Research shows that the dividend strategy at different stages should be different: (1) Dividend should not be paid and development should be the first task at the starting stage. (2) Although the marginal profit is less than the discount rate in the final stage, the firm should not issue dividend. This is because the loss is counterbalanced by the tax advantage of capital gain over dividend income. (3) If the interest rate is always higher than the discount rate, dividend should not be paid when the firm has debt. Whereas if the former is always lower than the latter, dividend should be paid during the equity ratio is maximum. Moreover, this paper studies dividend and financing strategy when parameters are changeable. Research shows that tax rate differences has important impact on dividend policy. The less the difference between tax rates on dividend and capital gain is, the longer the stage of dividend distribution is, and the firm should not blindly pursue scale effect and expand the capital. Whereas, too much differences motivates firms not to pay dividend. When there is no difference between the tax rates on dividend and capital gain, some classical results are contained by the model in this paper. Results from the model are helpful for the firm to make dividend policy and financing decision, and they are also useful for the government when it wants to change the situation that the most list companies generally do not pay dividend in China.