## Monday, February 27, 2012

### Working Capital – Inventory Economic Order Quantity

Today we explore a little more closely the analysis of inventory consistent with our Cash Conversion Cycle metrics and the particular nuances of inventory and its impact on our risk and cost of capital (discussed in last week’s “Working Capital – Finance and Inventory”post).

Economic Order Quantity
One of the first equations we run across when discussing inventory is the Economic Order Quantity. This calculation balances per batch costs with ongoing carrying costs of the inventory in order to determine when additional inventory should either be:
·         Ordered, as the case in raw material for a production process, or a distributor or retail operator, or
 Figure A
·         Produced – in the case of scheduling production runs to satisfy customer demand for a product
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The Economic Order Quantity formula is shown in Figure A.
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Figure B shows the result of this calculation if we have a firm with a demand of 120,000 units per year (D), each with a value of ²100 (C), a carrying cost of 50% (k), and a per batch cost of ²1000 (S), then our optimal order quantity is about 693 units.
 Figure B
One practice that separates a good analysis from a poor one is the process of finding ways to validate or “prove out” the results. I call this process triangulating, since we rely on more than one process to move us toward our objective.
 Figure C
In this case, we can validate our result by simply calculating the costs under different order scenarios. Figure C shows the costs in the previous example under four different reorder scenarios near the 17.3. We note that the lowest total cost in this analysis is 17, followed by 18, with the others being higher. Since 17.3 is between 17 and 18 but closer to 17, this comparison is consistent with the results of our Figure B.

The Benefits of the Economic Order Quantity
The primary benefit of the Economic Order Quantity formula is its simplicity. The entire calculation and result obtained in Figure B took a total of 6 cells in a spreadsheet. It does not get much simpler than that!
While there are drawbacks to this formula (which we will discuss next), for many routine, low value items, it might not make any sense to go any further than this type of calculation. For instance, six cells in a spreadsheet might be a great way to order pencils or paperclips (though even that much analysis might be too much!).

The Drawbacks of the Economic Order Quantity
The underlying assumption in the Economic Order Quantity formula is that pace of the material is even throughout the year. In many cases, this is not realistic. A US retailer using this method will be substantially overstocked during the summer since a large part of retail sales is related to the Christmas holiday season.
In addition to pace, there is linearity in the formula which can also be problematic. Costs (both per batch and per unit) are fixed and do not vary. This is often not the case in real-life. At some point a new person needs to added to the warehouse staff if inventory levels get too high, so the cost function can be step-wise rather than linear. Or there will be economies of scale in some of the other costs, like insurance.

The Hidden Traps in Economic Order Quantity
In addition to the disadvantages, there are other “traps” which might be present in the calculation, primarily related to the difficulties that are sometimes present when attempting to make accounting information actionable from a finance perspective.
When we consider a concept such as carrying costs, the cost of the inventory infrastructure will be allocated to the inventory and included in any accounting perspective of carrying costs.
Yet, once our warehouse is built, this and the cost that go along with it is “sunk” from a continuing investment perspective, but it will not show up that way in a fully allocated accounting calculation.
For instance, if we have a warehouse that we heat and keep lighted at ²100 per year, we will spend this ²100 no matter whether there are 10 items in the facility or 100. Let’s say our per item cost of inventory is ²100. So if we carry 10 items on average per year our inventory costs ²1,000, and our carrying cost rate will be 10%. If we keep 100 units, it will be 1%.
Because this carrying cost charge is in the EOQ formula, it will impact the Q that ends up being calculated.
Yet, re-stating what was said at the beginning of the example, we will spend ²100 no matter what. As such, the optimal Q for our firm can only be calculated if we can remove that data.
In addition to carrying charge, often our inventory will include other sunk or immaterial-to-the-Q-calculation items in its cost, for reasons we have discussed in other posts – such as actual vs. standard costing, the breakdown of direct manufacturing vs. overhead, and the allocation of both thereof.

Key Takeaways
The Economic Order Quantity formula can serve, in certain circumstances, as an efficient means of ensuring that we invest the correct amount of funds into this working capital category. However, we need to be mindful of adjustments to the data we have on hand in order to ensure that the formula includes only economically relevant decision factors.
Questions
·         What has your experience been with the Economic Order Quantity formula?

1. My son is in need of a resource right now… He has homework in economics, and I think this would be of great help to him. I want to help him, but I've been away for weeks. Would it be okay to share this to him? :D Thanks a lot!

1. Yes, good luck!

2. We live in a complex world where technology rapidly changes on a continual basis, so I agree that a key benefit would, in fact, be simplicity.
-Jackie @ Inventory System

1. Jackie,

Einstein said "A scientific theory should be as simple as possible, but no simpler."

Maybe we should use that statement for inventory systems as well!

3. This comment has been removed by a blog administrator.