The Miller-Orr model of cash management is developed for businesses with uncertain cash inflows and outflows. This approach allows lower and upper limits of cash balance to be set and determine the return point (target cash balance). This is different from the Baumol-Tobin model, which is based on the assumption that the cash spending rate is constant.
The Miller-Orr model of cash management can be used if the following assumptions are met:
The return point for the cash balance under the Miller-Orr model can be calculated as follows:
Return Point = Lower Limit + 1/3 × Spread
The lower limit is set by management. It depends on the acceptable risk of cash flows gap, creditworthiness of a business, and expected needs in cash. However, the lower limit can be set as zero if a business has sufficient investments in marketable securities or perfect creditworthiness and can raise additional short-term debt at any time.
The equation to compute the spread is as follows:
where F is the transaction cost, K is the opportunity cost of holding cash, and σ2 is a variance of a daily cash balance.
To find the upper limit of the cash balance, the following formula should be used:
Upper Limit = Lower Limit + Spread
When the Miller-Orr model of cash management is applied, we should take into account the following limitations:
As mentioned above, the lower limit or safety cash balance is set by a company’s management, but both the upper limit and return point depend on the spread. The return point under the Miller-Orr model is a cash balance that has to be restored if the actual cash balance reaches a lower or upper limit.
See the graph below to illustrate such situations.
The management of Stilmill Inc. has set a safety cash balance of $50,000. The standard deviation (σ) of the daily cash balance during the last year was $37,500, and the transaction cost was $75. The company also has the opportunity to invest idle cash in marketable securities at an annual interest rate of 8%.
|Daily interest rate =||8%||= 0.022%|
|Return point = $50,000 +||1||× $213,325 = $121,108|
Upper limit = $50,000 + $213,325 = $263,325