  We consider a mixed stochastic control problem that arises in Mathematical
Finance literature with the study of interactions between dividend policy and
investment. This problem combines features of both optimal switching and
singular control. We prove that our mixed problem can be decoupled in two pure
optimal stopping and singular control problems. Furthermore, we describe the
form of the optimal strategy by means of viscosity solution techniques and
smooth-fit properties on the corresponding system of variational inequalities.
Our results are of a quasi-explicit nature. From a financial viewpoint, we
characterize situations where a firm manager decides optimally to postpone
dividend distribution in order to invest in a reversible growth opportunity
corresponding to a modern technology. In this paper a reversible opportunity
means that the firm may disinvest from the modern technology and return back to
its old technology by receiving some gain compensation. The results of our
analysis take qualitatively different forms depending on the parameters values.
