Andria Mullins, financial manager of Webster Electronics, has been asked by the firm's CEO, Fred Weygandt, to evaluate the company's inventory control techniques and to lead a discussion of the subject with the senior executives. Andria plans to use as an example one of Webster's "big ticket" items, a customized computer microchip that the firm uses in its laptop computers. Each chip costs Webster $200, and it must also pay its supplier a $1,000 setup fee on each order; the minimum order size is 250 units. Webster's annual usage forecast is 5,000 units, and the annual carrying cost of this item is estimated to be 20% of the average inventory value. Andria plans to begin her session with the senior executives by reviewing some basic inventory concepts, after which she will apply the EOQ model to Webster's microchip inventory. As her assistant, you have been asked to help her by answering the following questions:

a. Why is inventory management vital to the financial health of most firms?

b. What assumptions underlie the EOQ model?

c. Write out the formula for the total costs of carrying and ordering inventory, and then use the formula to derive the EOQ model.

d. What is the EOQ for custom microchips? What are total inventory costs if the EOQ is ordered?

e. What is Webster's added cost if it orders 400 units at a time rather than the EOQ quantity? What if it orders 600 units?

f. Suppose it takes 2 weeks for Webster's supplier to set up production, make and test the chips, and deliver them to Webster's plant. Assuming certainty in delivery times and usage, at what inventory level should Webster reorder? (Assume a 52-week year, and assume Webster orders the EOQ amount.)

g. Of course, there is uncertainty in Webster's usage rate as well as in delivery times, so the company must carry a safety stock to avoid running out of chips and having to halt production. If a 200-unit safety stock is carried, what effect would this have on total inventory costs? What is the new reorder point? What protection does the safety stock provide if usage increases or if delivery is delayed?

h. Now suppose Webster's supplier offers a discount of 1% on orders of 1,000 or more. Should Webster take the discount? Why or why not?

i. For many firms, inventory usage is not uniform throughout the year but instead follows some seasonal pattern. Can the EOQ model be used in this situation? If so, how?

j. How would these factors affect an EOQ analysis?

(1) The use of just-in-time procedures.

(2) The use of air freight for deliveries.

(3) The use of a computerized inventory control system, in which an electronic system automatically reduced the inventory account as units were removed from stock and, when the order point was hit, automatically sent an electronic message to the supplier placing an order. The electronic system would ensure that inventory records are accurate and that orders are placed promptly.

(4) The manufacturing plant is redesigned and automated. Computerized process equipment and state-of-the-art robotics are installed, making the plant highly flexible in the sense that the company can quickly switch from the production of one item to another at a minimum cost.

This makes short production runs more feasible than under the old plant setup.

k. Webster runs a $100,000 per month cash deficit, requiring periodic transfers from its portfolio of marketable securities. Broker fees are $32 per transaction, and Webster earns 7% on its investment portfolio. How can Andria use the EOQ model to determine how Webster should liquidate part of its portfolio to provide cash?