A framework for modelling cash flow lags

Traditional models of irreversible investment problems assume that the investment starts generating cash flows immediately, i.e., at the same time as the investment is undertaken. Real-world investment situations are characterized by time-to-build or investment lags, which means that there is a time difference between when the investment is made and when the investment starts generating cash flows. We combine two existing models of investment lags to obtain a flexible, yet simple, way of modelling and analyzing the effects of investment lags. Both traditional models, and models that incorporate the effects of time-to-build, typically assume that the expected future cash flows generated by an investment are represented by a single cash flow that reflects the size of the market value of an investment. To reflect real-world cases where investments generate cash flows in several time periods, we present a framework in which cash flows are explicitly allowed to be spread out in time. Our model can be used to incorporate cases where an investment is partially sold in different time periods. Using an irreversible optimal investment timing problem case study, we show how our framework makes it possible to easily compare the effect of different cash flow timings. In this case, the value and the timing of the investment depend on a constant that in a natural way can be decomposed into three parts, thereby showing the influence of the value and timing from the respective parts of the framework.