# 9.8 Cash Optimal Order Quantities Model: Baumol’s Cash Optimization Model

Corporations must maintain cash in order to pay salaries, accounts payable, taxes, etc. They receive cash from sales and other activities; not all cash receipts are required for immediate, outgoing payments. Some cash will therefore be invested in low-risk, short-term securities in order to earn some return on the funds, rather than having the funds sit idly in a non-interest-bearing checking account. The question of how much to hold in ready cash reserves and how much to invest, is the job of the corporation’s cash manager. For corporations large enough to have a cash management department, millions of dollars are potentially being invested; naturally, the interest earned may be substantial.

The cash manager’s objective is to optimize cash level.  “Optimize” means not too much or too little.  If the corporation maintains too much cash on hand, it incurs an opportunity cost with regard to un-invested funds; it will not have earned any interest that it should have garnered. If it does not leave enough cash on hand, it may (unnecessarily) need to resort to costly borrowing in order to meet its payments. How much cash does the firm need to hold and, accordingly, how much in ST securities does it need to periodically liquidate (“order”) in order to meet its liquidity needs, e.g., for payroll, payables, etc.?

Below we shall construct a mathematical model aimed at resolving these issues; the model will be based on certain (initial) restrictive assumptions. Note that, under the assumptions (outlined below), there shall be a saw-tooth pattern resulting from periodically selling ST (money market) securities in order to replenish cash. The order quantity will be denoted by an undefined dollar point on the vertical axis with a diagonal line drawn to the horizontal from it. When cash reaches the horizontal axis minimum, the same quantity of cash is re-ordered and the pattern is repeated. At this point, we do not know the cash/dollar order amount on the vertical axis, nor the length of the intervals between re-order points on the horizontal.