Buster's needs $168,000 a week to pay bills and has established a lower cash balance limit of $75,000. The applicable interest rate is 3.17 percent and the fixed cost of transferring funds is $34. Based on the BAT model, what is the optimal initial cash balance?

Question

Quizplus · Accepted Answer

To find the optimal initial cash balance, we need to use the BAT model formula:
Z = [(2 × C × T) / i]^(1/2)

Where Z = optimal cash balance
C = fixed cost of transferring funds = $34
T = total cash needed per week = $168,000
i = interest rate = 3.17%

Plugging in the values, we get:
Z = [(2 × $34 × $168,000) / (0.0317)]^(1/2)
Z = $136,892.92

Since we have established a lower cash balance limit of $75,000, the optimal initial cash balance would be:
Optimal initial cash balance = Z + L
= $136,892.92 + $75,000
= $211,892.92

However, since the question asks for the best answer choice, we need to round this down to the nearest option. The closest option is D) $136,893, which is only $0.08 away from the actual answer. Therefore, the best choice is D).

Buster's Needs $168,000 a Week to Pay Bills and Has