26. Your firm\'s management of its cash position is based on the Miller-Orr mode

Question

26. Your firm's management of its cash position is based on the Miller-Orr model. The weekely standard deviation of the disbursements is $8.600. The applicable weekly interest rate is 0.054 percent and the fixed cost of transferring funds is S65. Suppose your firm's target cash balance, C 68.830. (i) What lower cash balance limit (L) is consistent with this information. (ii) Find U*, the firm's implied maximum cash balance limit. (ii) Find your firm's average cash balance held over time. (iv)Using your answer to part (ii), find the average dollar cost incurred by the firm from holding cash over a two-week period.

Explanation / Answer

Miller-Orr Model

Miller-Orr Model determines an upper limit and return point for cash balances. It provides for cost efficient transactional balances and assumes uncertain cash flows. This model assumes that cash balances randomly fluctuate between an upper bound and lower bound. When the cash balances hit the upper bound, the firm has too much cash and should buy marketable securities to bring the cash balances back to the optimal bound. When the cash balances hit zero, the financial manager must return them to the optimal bound by selling and converting securities into cash.

The basic assumptions of the model are:

There is no underlying trend in cash balance over time,The optimal values of h and z depend not only on opportunity costs, but also on the degree of likely fluctuations in cash balances.

The model specifies the following two control limits:

h = upper control limit, beyond this cash balance should not be carried

0 = lower control limit, the firm should maintain cash resources at least to this extent of lower limit

z= return point of cash balance.

The Miller- Orr Model works as follows:

When the cash balance touches the upper control limit h, securities are bought to the extent of amount of difference between h and z so that the new cash balance reaches point z.When the cash balance touches lower control limit (0), marketable securities to the extent of the amount of difference between z and 0 is sold off so that the new cash balance again returns to the point z.

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