Estimating Inventory-Related Relevant Costs and Their Effects

Learning Objective 3 Identify the effect of errors that can arise when using the EOQ decision model and ways to reduce conflicts between the EOQ model and models used for performance evaluation

• errors in predicting parameters have a small effect on costs
• by making the two models congruent

How do Glare Shade’s managers calculate the annual relevant inventory-related costs, such as the relevant carrying, stockout, and ordering costs?

We start by discussing the relevant inventory carrying costs of $5.20 per unit per year, which consist of the relevant incremental costs plus the relevant opportunity cost of capital. What are the relevant incremental costs of carrying inventory? Only those costs, such as warehouse rent, warehouse workers’ salaries, costs of obsolescence, costs of shrinkage, costs of breakage, and costs of insurance, that change with the quantity of inventory held. The salaries paid to clerks, stock keepers, and materials handlers are irrelevant if they are unaffected by changes in inventory levels. Suppose, however, that as inventories increase (decrease), total salary costs increase (decrease) as clerks, stock keepers, and materials handlers are added (transferred to other activities or laid off). In this case, the salaries paid are relevant costs of carrying inventory. Similarly, costs of storage space owned that cannot be used for other profitable purposes when inventories decrease are irrelevant. But if the space has other profitable uses or if total rental cost is tied to the amount of space occupied, storage costs are relevant costs of carrying inventory.

What is the relevant opportunity cost of capital? It is the return forgone by investing capital in inventory rather than elsewhere. It is calculated as the required rate of return multiplied by the per-unit costs of acquiring inventory, such as the purchase price of units, incoming freight, and incoming inspection. Opportunity costs are also computed on investments (say, in equipment) if these investments are affected by changes in inventory levels.

In the case of stockouts, the relevant incremental cost is the cost of expediting an order from a supplier. The relevant opportunity cost is (1) the lost contribution margin on sales forgone because of the stockout and (2) the lost contribution margin on future sales forgone as a result of customer ill will.

The relevant ordering costs are only those ordering costs that change with the number of orders placed (for example, the costs of preparing and issuing purchase orders and receiving and inspecting materials).

Cost of a Prediction Error

Predicting relevant costs is difficult and seldom flawless, which raises the question, “What is the cost when actual relevant costs differ from the estimated relevant costs used for decision making?”

Suppose Glare Shade’s relevant ordering costs per purchase order for UX1s are $200, but the manager predicts them to be $100 when calculating the order quantity. We can calculate the cost of this “prediction” error using a three-step approach.

1. Step 1: COMPUTE THE MONETARY OUTCOME FROM THE BEST ACTION THAT COULD BE TAKEN, GIVEN THE ACTUAL AMOUNT OF THE COST INPUT (COST PER PURCHASE ORDER). This is the benchmark—the decision the manager would have made if the manager had known the correct ordering cost. Using $D=\text{13,000\hspace{0.17em}units of UX}1\hspace{0.17em}\text{per year},$ $\mathrm{P}=\$200,$ and $C=\mathrm{\$}5.20\hspace{0.17em} \text{per unit per year},$ the best action is to purchase 1,000 units in each order (from section The Economic-Order-Quantity Decision Model).

1. Glare Shade’s annual relevant total costs when the $EOQ=1,000$ units are

1. Step 2: COMPUTE THE MONETARY OUTCOME FROM THE BEST ACTION BASED ON THE INCORRECT PREDICTED AMOUNT OF THE COST INPUT (COST PER PURCHASE ORDER). In this step, the manager calculates the order quantity based on the prediction (that later proves to be wrong) that the ordering cost is $100. Using $P=\mathrm{\$}100,D=\text{13,000}$ units of UX1 per year, and $\mathrm{C}=\mathrm{\$}5.20\hspace{0.17em} \text{per unit}$ per year, the economic order quantity is as follows:

1. However, the actual cost of the purchase order is $200. Consequently, the actual annual relevant total costs when $D=\text{13,000}\hspace{0.17em}\text{units\hspace{0.17em}\hspace{0.17em}per\hspace{0.17em}year},$ $Q=707\hspace{0.17em}\text{units},$ $P=\mathrm{\$}200\mathrm{,}$ and $C=\mathrm{\$}5.20$ per unit per year are as follows:

1. Step 3: COMPUTE THE DIFFERENCE BETWEEN THE MONETARY OUTCOMES FROM STEP 1 AND STEP 2.

1. The cost of the prediction error, $316, is 6% of the relevant total costs of $5,200. Note that the annual relevant-total-costs curve in Exhibit 21-1 is somewhat flat over the range of order quantities from 700 to 1,300 units. That is, the annual relevant cost is roughly the same even if misestimating the relevant carrying and ordering costs results in an EOQ quantity of 1,000 plus 30% (1,300) or 1,000 minus 30% (700). The square root in the EOQ model diminishes the effect of estimation errors because it results in the effects of the incorrect numbers becoming smaller.

In the next section, we consider a planning-and-control and performance-evaluation issue that frequently arises when managing inventory.