A Modified ‘Square Root’ Process for Determining the Value of the Option to (Dis)invest

We determine optimal investment criteria for a capital project whose cash flows evolve in terms of a ‘modified square root’ process. The modified square root process has properties similar to the Cox, Ingersoll and Ross (1985)‘square root’ process but in addition, encompasses the possibility of negative cash flows. Although closed form solutions for the valuation equations implied by the modified square root process are the exception rather than the rule we are able to show that analytic solutions, in the form of infinite power series expansions, will always exist. Furthermore, we also show that when a prescribed set of regularity conditions is satisfied, these power series expansions converge to closed form valuation functions. The optimality criteria for capital investment decisions are then simplified considerably.