This paper develops a stochastic framework for determining transactions and precautionary demand for money. Through application of the principles of inventory management, the analysis integrates and extends the work of Baumol, Tobin, and Miller and Orr. Optimal money holdings are shown to depend on the rate of interest, on the mean and the variance of net disbursements and on the cost of portfolio adjustment. The properties of the distribution of the payment period are analyzed. The optimal solution is obtained by minimizing net present value of cost. This solution is compared with the one obtained by the conventional method of minimizing the steady-state cost.