BullsNBears, a purveyor of ﬁnancial databases, estimates it they disburses $440,000 monthly in order to pay bills. The ﬁrm's opportunity rate is 5%. The ﬁxed cost of transferring money is $25 per
Transfer. Based on historical data, the standard deviation of monthly cash ﬂows is $15,000 and the
Lower cash balance limit is $20,000. For Miller-Orr model questions, assume the interest rate is
0)5% per month.
Using the BAT model, what is the optimal average cash balance?

Question

Quizplus · Accepted Answer

To find the optimal average cash balance using the BAT model, we need to first calculate the target balance, which is given by the formula:

Target Balance = Lower Limit + (3 × Standard Deviation × Transfer Cost) / 4 × Opportunity Cost

Here, the lower cash balance limit is $20,000, the standard deviation of monthly cash flows is $15,000, and the fixed cost of transferring money is $25 per transfer. The opportunity cost is given as 5% per month.

Plugging these values into the formula, we get:

Target Balance = $20,000 + (3 × $15,000 × $25) / 4 × 0.05 
               = $36,250

The optimal average cash balance is given by the formula:

Optimal Average Cash Balance = (2 × Target Balance × Monthly Cost) / (3 × Monthly Cost + Transfer Cost)

Substituting the values given in the question, we get:

Optimal Average Cash Balance = (2 × $36,250 × $440,000) / (3 × $440,000 + $25) 
                             = $36,332.87 ≈ $36,332

Therefore, the best choice is B, with an optimal average cash balance of $36,332.

BullsNBears, a Purveyor of ﬁNancial Databases, Estimates It They Disburses