We provide a new framework for valuing multidimensional real options where opportunities to exercise the option are generated by an exogenous Poisson process; this can be viewed as a liquidity constraint on decision times. This approach, which we call the Poisson optional stopping times (POST) method, finds the value function as a monotone sequence of lower bounds. In a case study, we demonstrate that the frequently used quasi-analytic method yields a suboptimal policy and an inaccurate value function. The proposed method is demonstrably correct, straightforward to implement, reliable in computation and broadly applicable in analyzing multidimensional option-valuation problems.