The Timberline ﬁrm expects a total need of €12,500 over the next 3 months.They have a beginning cash balance of €1,500, and cash is replenished when it hits zero.The ﬁxed cost of selling
Securities to replenish cash balances is €3.50.The interest rate on marketable securities is 8% per
Annum.There is a constant rate of cash disbursement and no cash receipts during the month.
If interest rates were to rise to 1.00% per month, what would the ﬁrm's total savings be if it switches
From its current practice to the optimum practice (as given by the Baumol model)?

Question

Quizplus · Accepted Answer

Using the Baumol model, we can calculate the optimal cash balance for Timberline as:

EOQ = √((2DS)/H)

where:
D = total cash need over the next 3 months = €12,500
S = fixed cost of selling securities = €3.50
H = interest rate on securities = 8%/12 = 0.67% per month

EOQ = √((2*12,500*3.50)/0.67%) ≈ €982.40

This means that Timberline should sell securities and replenish its cash balance whenever it falls to around €982.

If interest rates were to rise to 1.00% per month, the new optimal cash balance would be:

EOQ = √((2*12,500*3.50)/1.00%) ≈ €793.72

This means that Timberline would need to sell securities more frequently in order to maintain a lower cash balance. The total cost of selling securities would now be:

Total cost = (D/Q)*S + (Q/2)*H

where:
Q = optimal cash balance = €793.72

Total cost = (12,500/793.72)*3.50 + (793.72/2)*1.00% ≈ €85.91

Compared to the current practice of selling securities whenever the cash balance hits zero, the savings from switching to the optimum practice would be:

Savings = Fixed Cost - Total Cost
Savings = 3.50 - 85.91
Savings ≈ - €82.41

This means that Timberline would actually incur higher costs by switching to the optimum practice in this scenario, so it should stick to its current practice. The answer is therefore None of the above.

The Timberline ﬁRm Expects a Total Need of €12,500 Over