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 optimum initial cash balance?

Question

Quizplus · Accepted Answer

The BAT model formula is:
Optimum initial cash balance (Z) = [(3 x TC x E)/4 x i]^1/3 + [(4 x D x i)/3]^1/3
Where:
TC = the transaction cost per transfer
E = the variance of daily cash flows
i = the interest rate per period
D = the total disbursements per period

Plugging in the given values, we get:
TC = $25
E = (15,000)^2 = 225,000,000
i = 0.05/12
D = $440,000

Z = [(3 x 25 x 225,000,000)/(4 x (0.05/12))]^1/3 + [(4 x 440,000 x (0.05/12))/3]^1/3 = $72,663.96

Therefore, the optimum initial cash balance is $72,664 (rounded to the nearest dollar). The best choice is B.

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