Chapter 28
Advance Issues in Cash Management
and Inventory Control
ANSWERS TO END-OF-CHAPTER QUESTIONS


28-1 a. The Baumol model is a model for establishing the firm's target cash balance that closely resembles the EOQ model used for inventory. The model assumes (1) that the firm uses cash at a steady, predictable rate, (2) that the firm's cash inflows from operations also occur at a steady, predictable rate, and (3) that its net cash outflows therefore also occur at a steady rate. The model balances the opportunity cost of holding cash against the transactions costs associated with replenishing the cash account.

b. Carrying costs are the costs of carrying inventory. Ordering costs are the costs of ordering inventory. Total inventory costs are the sum of ordering and carrying costs.

c. The Economic Ordering Quantity (EOQ) is the order quantity that minimizes the costs of ordering and carrying inventories. The EOQ model is the equation used to find the EOQ. The range around the optimal ordering quantity that may be ordered without significantly affecting total inventory costs is the EOQ range.

d. The reorder point is the inventory level at which a new order is placed. Safety stock is inventory held to guard against larger-than-normal sales and/or shipping delays.

e. The red line method is a technique for inventory control, as is the two-bin method. Computerized inventory control systems are just what the name implies. In the red line method, a line is drawn around the inside of a bin at the level of the reorder point, and the inventory clerk places an order when the red line shows. The two-bin method is similar--when the first bin is exhausted, items are ordered. With a computerized inventory control system, the computer starts with an inventory count in memory. As withdrawals are made, they are recorded by the computer, and the inventory balance is revised. When the reorder point is reached, the computer automatically places an order, and when the order is received, the recorded balance is increased.

f. Just-in-time systems refer to receiving inventories just as they are needed. Firms that employ such systems are attempting to minimize inventory carrying costs.
Out-sourcing is the practice of purchasing components rather than making them in-house.











28-2 a. Our suppliers switch from delivering -
by train to air freight. (a below)

b. We change from producing just in time to
meet seasonal sales to steady, year-round +
production.
c. Competition in the markets in which 0
we sell increases. (c below)

d. The rate of general inflation increases. 0

e. Interest rates rise; other things -
are constant. (e below)

(a) Lower safety stock will be required because delivery time is shortened.

(c) On the one hand, the need to stay competitive may require large inventories, but if the market gets competitive, sales may fall off and the need for inventories may diminish.

(e) EOQ and inventories are lower, since carrying costs are higher.

28-3 When money is tight, interest rates are generally high. This means that near-cash assets have high returns; hence, it is expensive to hold idle cash balances. Firms tend to economize on their cash balance holdings during tight-money periods.

28-4 a. Better synchronization of cash inflows and outflows would allow the firm to keep its transactions balance at a minimum, and would therefore lower the target cash balance.

b. Improved sales forecasts would tend to lower the target cash balance.

c. A reduction in the portfolio of U.S. Treasury bills (marketable securities) would cause the firm’s cash balance to rise if the Treasury bills had been held in lieu of cash balances.

d. An overdraft system will enable the firm to hold less cash.

e. If the amount borrowed equals the increase in check-writing, the target cash balance will not change. Otherwise, the target cash balance may rise or fall, depending on the relationship between the amount borrowed and the number of checks written.

f. The firm will tend to hold more Treasury bills, and the target cash balance will tend to decline.


SOLUTIONS TO END-OF-CHAPTER PROBLEMS



28-1 a. EOQ = = = = 3,000 bags per order.

b. The maximum inventory, which is on hand immediately after a new order is received, is 4,000 bags (3,000 + 1,000 safety stock). At $1.50 per bag the dollar cost is $6,000.

c. = + 1,000 = 1,500 + 1,000 = 2,500 bags or $3,750.
d. = 30 orders per year. = 12.1 » 12 days.

The company must place an order every 12 days.


28-2 a. C* = = . F = $27; T = $4,500,000; r = 12%.

C* = = $45,000.

b. Average cash balance = $45,000/2 = $22,500.

c. Transfers per year = $4,500,000/$45,000 = 100, or one approximately every 3.6 » 4 days.

d. Total cost = (r) + (F)
= (0.12) + ($27)
= $2,700 + $2,700 = $5,400.

If it maintained an average balance of $50,000, this would mean transfers of $100,000. There would be $4,500,000/$100,000 = 45 transfers per year. The cost would be 0.12($50,000) + 45($27) = $7,215. If it maintained a zero balance, it would have to make 360 transfers per year, so its cost would be 360($27) = $9,720.

SOLUTIONS TO SPREADSHEET PROBLEMS



28-6 The detailed solution for the problem is available both on the instructor’s resource CD-ROM (in the file Solution to FM11 Ch 28 P06 Build a Model.xls) and on the instructor’s side of the web site, http://brigham.swcollege.com.



MINI CASE



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 which the firm uses in its laptop computer. Each chip costs Webster $200, and in addition it must pay its supplier a $1,000 setup fee on each order. Further, 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 percent 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?

Answer: Inventory management is critical to the financial success of most firms. If insufficient inventories are carried, a firm will lose sales. Conversely, if excess inventories are carried, a firm will incur higher costs than necessary. Worst of all, if a firm carries large inventories, but of the wrong items, it will incur high costs and still lose sales.


b. What assumptions underlie the EOQ model?

Answer: the standard form of the EOQ model requires the following assumptions:

All values are known with certainty and constant over time.

Inventory usage is uniform over time. For example, a retailer would sell the same number of units each day.
All carrying costs are variable, so carrying costs change proportionally with changes in inventory levels.

All ordering costs are fixed per order; that is, the company pays a fixed amount to order and receive each shipment of inventory, regardless of the number of units ordered.
These assumed conditions are not met in the real world, and, as a result, safety stocks are carried, and these stocks raise average inventory holdings above the amounts that result from the "pure" 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.

Answer: Under the assumptions listed above, total inventory costs (TIC) can be expressed as follows:

TIC = total carrying costs + total ordering costs = CP(Q/2) + F(S/Q) (1)

Here,

C = annual carrying cost as a percentage of inventory value.
P = purchase price per unit.
Q = number of units in each order.
F = fixed costs per order.
S = annual usage in units.

Note that S/Q is the number of orders placed each year, and, if no safety stocks are carried, Q/2 is the average number of units carried in inventory during the year.
The economic (optimal) order quantity (EOQ) is that order quantity which minimizes total inventory costs. Thus, we have a standard optimization problem, and the solution is to take the first derivative of equation 1 with respect to quantity and set it equal to zero:

.









Now, solving for Q, we obtain:




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

Answer: EOQ = = = = 500 units.

When 500 units are ordered each time an order is placed, total inventory costs equal $20,000:

TIC = CP(Q/2) + F(S/Q)
= 0.2($200)(500/2) + $1,000(5,000/500)
= $40(250) + $1,000(10) = $10,000 + $10,000 = $20,000.

Note that the average inventory of custom microchips is 250 units, and that 10 orders are placed per year. Also, at the EOQ level, total carrying costs equal total ordering costs.

















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 per order?

Answer: 400 units:

TIC = CP(Q/2) + F(S/Q) = 0.2($200)(400/2) + $1,000(5,000/400)
= $8,000 + $12,500 = $20,500.

added cost = $20,500 - $20,000 = $500.

600 units:

TIC = 0.2($200)(600/2) + $1,000(5,000/600)
= $12,000 + $8,333 = $20,333.

added cost = $20,333 - $20,000 = $333.

Note the following points:

At any order quantity other than EOQ = 500 units, total inventory costs are higher than they need be.

The added cost of not ordering the EOQ amount is not large if the quantity ordered is close to the EOQ. For example, if the order size is 20 percent above the EOQ (600 units), tic increases by only $333/$20,000 = 1.67%.

If the quantity ordered is less than the EOQ, then total carrying costs decrease, but total ordering costs increase. At q = 400 units, carrying costs fall by $2,000 per year, but ordering costs increase by $2,500. The net result is an increase in total costs.

If the quantity ordered is greater than the EOQ, then total carrying costs increase, but total ordering costs decrease. At Q = 600 units, carrying costs increase by $2,000, but ordering costs fall by only $1,667, so the net result is an increase in total costs.






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 that Webster orders the EOQ amount.)

Answer: With an annual usage of 5,000 units, Webster's weekly usage rate is 5,000/52 » 96 units. If the order lead time is 2 weeks, then Webster must reorder each time its inventory reaches 2(96) = 192 units. Then, after 2 weeks, as it uses its last microchip, the new order of 500 chips arrives.

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?

Answer: There are two ways to view the impact of safety stocks on total inventory costs. Webster's total cost of carrying the operating inventory is $20,000 (see part d). Now the cost of carrying an additional 200 units is CP(safety stock) = 0.2($200)(200) = $8,000. Thus, total inventory costs are increased by $8,000, for a total of $20,000 + $8,000 = $28,000.
Another approach is to recognize that, with a 200-unit safety stock, Webster's average inventory is now (500/2) + 200 = 450 units. Thus, its total inventory cost, including safety stock, is $28,000:

TIC = CP(average inventory) + F(S/Q)
= 0.2($200)(450) + $1,000(5,000/500)
= $18,000 + $10,000 = $28,000.

Webster must still reorder when the operating inventory reaches 192 units. However, with a safety stock of 200 units in addition to the operating inventory, the reorder point becomes 200 + 192 = 392 units. Since Webster will reorder when its microchip inventory reaches 392 units, and since the expected delivery time is 2 weeks, Webster's normal 96 unit usage could rise to 392/2 = 196 units per week over the 2-week delivery period without causing a stockout. Similarly, if usage remains at the expected 96 units per week, Webster could operate for 392/96 » 4 weeks versus the normal two weeks while awaiting delivery of an order.


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

Answer: First, note that since the discount will only affect the orders for the operating inventory, the discount decision need not take account of the safety stock. Webster's current total cost of its operating inventory is $20,000 (see part d). If Webster increases its order quantity to 1,000 units, then its total costs for the operating inventory would be $24,800:

TIC = CP(Q/2) + F(S/Q)
= 0.2($198)(1,000/2) + $1,000(5,000/1,000) = $19,800 + $5,000
= $24,800.

Note that we have reduced the unit price by the amount of the discount. Since total costs are $24,800 if Webster orders 1,000 chips at a time, the incremental annual cost of taking the discount is $24,800 - $20,000 = $4,800. However, Webster would save 1 percent on each chip, for a total annual savings of 0.01($200)(5,000) = $10,000. Thus, the net effect is that Webster would save $10,000 - $4,800 = $5,200 if it takes the discount, and hence it should do so.


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

Answer: The EOQ model can still be used if there are seasonal variations in usage, but it must be applied to shorter periods during which usage is approximately constant. For example, assume that the usage rate is constant, but different, during the summer and winter periods. The EOQ model could be applied separately, using the appropriate annual usage rate, to each period, and during the transitional fall and spring seasons inventories would be either run down or built up with special seasonal orders.


j. How would these factors affect an EOQ analysis?

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

Answer: Just-in-time procedures are designed specifically to reduce inventories. If a just in time system were put in place, it would largely obviate the need for using the EOQ model.


j. 2. The use of air freight for deliveries.

Answer: Air freight would presumably shorten delivery times and reduce the need for safety stocks. It might or might not affect the EOQ.


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

Answer: Computerized control systems would, generally, enable the company to keep better track of its existing inventory. This would probably reduce safety stocks, and it might or might not affect the EOQ.

j. 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 switch from the production of one item to another at a minimum cost and quite quickly. This makes short production runs more feasible than under the old plant setup.

Answer: The trend in manufacturing is toward flexibly designed plants, which permit small production runs without high setup costs. This reduces inventory holdings of final goods.
k. Webster runs a $100,000 cash deficit per month, requiring periodic transfers from its marketable securities portfolio. Broker fees are $32 per transfer and Webster earns 7% on its investment portfolio. Can Andrea use the EOQ model to determine how frequently Webster should liquidate part of its portfolio?

Answer: The EOQ model can be applied directly to this problem.

EOQ = where F = $32, S = $12($100,000) = $1,200,000 worth of cash needed each year, and the carrying cost per dollar per year is 7%, which is the opportunity cost for investing that dollar.

EOQ = C* = .
So Webster should liquidate its portfolio in chunks of about $33,000. This translates to 1,200,000/33,123 = 36 times a year, or 52/36 = 1.44 or about every week and a half.