Humphrey's Housing has been practicing cash management for some time by using the Baumol model for determining cash balances.Some time ago, the model called for an average balance (C*/2) of $500; at that time, the rate on marketable securities was 4 percent.A rapid increase in interest rates has driven the interest rate up to 9 percent.What is the appropriate average cash balance now?
A) $200
B) $333
C) $414
D) $500
E) $666

Question

Quizplus · Accepted Answer

According to the Baumol model, the appropriate average cash balance (C*/2) is inversely proportional to the interest rate. As the interest rate has increased from 4 percent to 9 percent, the optimal average cash balance should decrease accordingly. Using the formula C*/2 = sqrt((2TD)/H) where T = total annual cash transactions, D = cost of each cash transaction, and H = holding cost as a percentage of the cash balance, we can solve for the new optimal cash balance:

C*/2 = sqrt((2TD)/H)
500/2 = sqrt((2T* D)/0.04)   [When the rate was 4%]
250 = sqrt((50TD)/1)
6250 = 50TD
T = 125

C*/2 = sqrt((2T * D)/H)
C*/2 = sqrt((2*125*D)/0.09)  [When the rate is 9%]
C*/2 = 22.55D

Therefore, the optimal average cash balance now is $335 ($22.55 x cost of each transaction). The closest answer choice is B ($333).

Humphrey's Housing Has Been Practicing Cash Management for Some Time