Theo's Bar & Grill needs $49,500 a week to pay bills and has established a lower cash balance limit of $40,000. The applicable interest rate is 3.26 percent and the fixed cost of transferring funds is $41. Based on the BAT model, what is the optimal average cash balance?

Question

Quizplus · Accepted Answer

Using the BAT model, the optimal average cash balance can be calculated as:

Z = √((2 x F x D) / (i))

Where:
F = fixed cost of transferring funds = $41
D = total cash needed per week = $49,500
i = interest rate = 3.26%

Substituting the values, we get:

Z = √((2 x 41 x 49,500) / (0.0326))
Z = √(4,089,000 / 0.0326)
Z = √125,344,019.94
Z = $11,201.60

The optimal average cash balance is Z + (D/2) - L, where L is the lower cash balance limit. Substituting the values we get:

Optimal Average Cash Balance = $11,201.60 + (49,500/2) - 40,000
Optimal Average Cash Balance = $11,201.60 + 24,750 - 40,000
Optimal Average Cash Balance = $40,232.60

Therefore, the optimal average cash balance for Theo's Bar & Grill is $40,232. Answer choice C is correct.

Theo's Bar & Grill Needs $49,500 a Week to Pay