Optimal dividend policy and growth option

We analyse the interaction between dividend policy and investment decision in a growth opportunity of a liquidity constrained firm. This leads us to study a mixed singular control/optimal stopping problem for a diffusion that we solve quasi-explicitly establishing connections with two auxiliary optimal stopping problems. We characterize situations where it is optimal to postpone dividend distribution in order to invest at a subsequent date in the growth opportunity. We show that uncertainty and liquidity shocks have ambiguous effect on the investment decision.