Problem
I. The Gentry Garden Center sells 90,000 bags of lawn fertilizer annually. The optimal safety stock (which is on hand initially) is 1,000 bags. Each bag costs the firm $1.50, inventory carrying costs are 20%, and the cost of placing an order with its supplier is $15.
i. What is the Economic Ordering Quantity?
ii. What is the maximum inventory of fertilizer?
iii. What will be the firm's average inventory?
iv. How often must the company order?
II. Barenbaum Industries projects that cash outlays of $4.5 million will occur uniformly throughout the year. Barenbaum plans to meet its cash requirements by periodically selling marketable securities from its portfolio. The firm's marketable securities are invested to earn 12%, and the cost per transaction of converting securities to cash is $27.
i. Use the Baumol model to determine the optimal transaction size for transfers from marketable securities to cash.
ii. What will be Barenbaum's average cash balance?
iii. How many transfers per year will be required?
iv. What will be Barenbaum's total annual cost of maintaining cash balances? What would the total cost be if the company maintained an average cash balance of $50,000 or of $0 (it deposits funds daily to meet cash requirements)?