The **inventory sampling ** is, according to §241 Paragraph 1 of the German Commercial Code (HGB), an inventory simplification procedure approved since January 1, 1977 to replace the full inventory at the end of the year with recognised mathematical-statistical procedures. A distinction is made between extrapolation procedures using stratification and the sequential test.

The Institute of Auditors (IDW) published a detailed set of rules in 1981 and the Working Group for Economic Administration (AWV) also published supplementary explanations, to which we refer in our explanations.

**§241 para. 1 HGB**

“When drawing up the inventory, the stock of assets may also be determined by type, quantity and value using **recognised mathematical-statistical methods** on the basis of random samples. The procedure must comply with the **principles of proper accounting**. The informative value of the inventory drawn up in this way must be equivalent to the informative value of an inventory drawn up on the basis of a physical inventory.

This paragraph first of all allows **inventory sampling**. However, the following conditions are imposed for this:

- The
**inventory sampling**must comply with the principles of**proper accounting**. The Institut der Wirtschaftsprüfer (IDW, 1981, p. 61) lists this:**Completeness**

All storage positions must be recorded, all sampling elements must be “completely recorded and evaluated” (IDW, 1981, p. 61).**Correctness**

The sample elements must be evaluated correctly. According to the interpretation of the HFA, the accuracy of the physical inventory as such is guaranteed by a correspondingly high informative value of the**inventory sampling**.**Verifiability**

The planning and procedure of inventory sampling must be documented and comprehensible. The same applies to the calculations that ultimately lead to the results of the**inventory sampling**.**Individual entry of stocks and stock-reliable inventory accounting**

An individual entry cannot be made by**inventory sampling**. However, a book update that has proven to be reliable can be considered sufficient in this case. In particular (IDW, 1981, p. 62): “It is also sufficient if the inventory records are only kept by type and quantity during the year and a valuation of the individual items is carried out at the end of the year.”**Physical inventory of herds**

As the individual sample is of particular importance, the physical inventory must be carried out with particular care.

**Only recognized mathematical-statistical methods**may be used for**inventory sampling**: “Two main groups of methods are considered as recognized mathematical-statistical estimation methods for inventory sampling: the free mean value methods (simple or stratified) and the bound methods.” (IDW, 1981, P. 65)- “When applying mathematical-statistical test procedures for
**inventory sampling**, the initial hypothesis (null hypothesis) “reliable stock accounting” is tested directly against the alternative hypothesis “stock accounting not reliable” using a random sample.” (IDW, 1981, P. 66) - In particular, all storage positions must have “a calculable chance other than zero (IDW, 1981, p. 65) “and it must be a “random sampling procedure in the sense of statistical methodology” (IDW, 1981, p. 65).

- “When applying mathematical-statistical test procedures for
- The
**informative value of the inventory sampling must be the same as that of a normal physical inventory**: The requirements for inventory accounting are the same as for a continuous inventory. During the inspection, both the physical inventory as such and the recording of receipts and issues and quality reductions are examined. The**inventory sampling**procedure is checked for consistency before it is applied. An inspector is present during the physical inventory of the inventory sampling elements and checks them. Even if the total value of the warehouse is correct, the inventory can be rejected due to unreliable bookkeeping, even if the excess and shortage balance each other out. With regard to the total value, it must be determined with a confidence level of 95%, except for a deviation of 1%. With regard to an itemization, this must be done by means of a reliable book update. If the actual values deviate too much from the book values, i.e. if the inventory reliability is too low, the physical inventory must be rejected even if the total value is permitted. The physical inventory must also be rejected if there is a deviation greater than 3% with a probability of 95%. (IDW, 1981, p. 72f)

Simplified inventory procedures are also recognized by the Code of Obligations OR 9581 in **Switzerland** and the Corporate Code §192 para. 4 UGB in **Austria**.

In companies in Eastern European countries, the use of **inventory sampling ** is currently only possible if the accounting is carried out in the home countries Germany, Austria or Switzerland.

In all other **countries of the EU** clarification and coordination with the auditors and/or the tax authorities is required.

In addition to the above-mentioned generally applicable legal principles and the recommendations of the IDW for carrying out a physical inventory – and in particular an **inventory sampling** – organizational measures must also be taken to ensure the correctness of these transactions.

“It must be checked whether the population is clearly defined. In doing so, it must be taken into account whether – depending on the design of the internal control system – perishable, particularly valuable and other items not to be included in the sample are included in the sample”. (IDW, 1981, P. 76)

According to (IDW, 1981, p. 63): “Warehouses with inventory management systems of varying reliability should be treated as separate inventory populations”. It should be noted here that (IDW, 1981, p. 63f) “the individual elements may only differ from each other with regard to the characteristic value to be examined”. In any case, a clear delimitation of the population must be made before the **inventory sampling** is applied.

In order to exclude particularly high and particularly low values from the **inventory sampling** and thus reduce the risk of the physical inventory, a full inventory is carried out for the border areas. This includes, on the one hand, all physical inventory items without a target quantity and, on the other hand, the 5% most valuable items, which in most warehouses make up approximately 50% of the warehouse. In this way we meet the requirement defined in (IDW, 1981, p. 69): “In general, due to the “warehouse phenomenon”, a full inventory of 3 to 5% of the warehouse items will be sufficient to cover 45 to 50% of the total value of the warehouse collective”.

Each element of a population must have the chance to be selected in a random sample. The way in which elements are selected is determined by mathematical-statistical methods. For the sample size, the mathematical-statistical methods define a minimum with which the desired statement probability is maintained.

The randomness of the sample is also important in this context, since (IDW, 1981, p. 65) “only then can the rules of probability calculation be applied when evaluating the sample information.”

The mathematical-statistical sampling procedures generally assume a theoretical distribution model. The mathematical-statistical statement is then only correct if the underlying distribution model is fulfilled when the inventory is calculated on a sample basis. Therefore, you must check whether the requirements for the procedure used are met both before drawing the sample and after evaluating the sample. A documented structural analysis of the population and the sample can provide valuable information for this purpose. The procedures […] usually require the model of normal distribution ” (IDW, 1981, p. 67)

In (IDW, 1981, p. 65) is given for the drawing of samples:

“A prerequisite for the application of all mathematical sampling procedures is that the individual elements of a sample are randomly selected from the individual elements (storage positions) of a precisely defined population (storage collective) […]. This means that

- in the case of so-called unstratified random selection, each stock item must have the same non-zero chance of being included in the sample selection or
- in the so-called stratified random selection, each stock item must have a calculable, non-zero chance of being included in the sample selection

The selection procedure may be a lottery, random number procedure, systematic selection with random start, final number procedure, etc.”.

So there is the free random selection and the stratified random selection.

With regard to the total value, this must be determined with a confidence level of 95% except for a deviation of 1%.

The Institut der Wirtschaftsprüfer (IDW, 1981, p. 68) describes a number of 100 samples as minimum: “In the mean value estimation, for example, the sample size should generally not be less than 100 sample elements in the case of stratified extrapolation and 250-300 sample elements in the case of bound extrapolation”.

According to the Arbeitsgemeinschaft für wirtschaftliche Verwaltung e.V. (AWV, 1978, p. 20), 2% of the total size of 𝑁 is also regarded as the minimum for the size of the sample 𝑛: “For the size of the sample n from the items which are taken and evaluated by random sampling […] the principle of minimum [sic] for n from N 2% of the items normally applies for safety reasons.”

“Due to the extrapolation of the results obtained by the random sample, increased demands must be made on the recording work. The physical recording should therefore be planned, carried out and monitored with particular care”. (IDW, 1981, P. 62). Always full recordings should be made (IDW, 1981, p. 63):

- “perishable items
- particularly valuable objects
- Objects with a tendency to uncontrolled shrinkage
- badly stored items
- Negative positions
- positions which have not been moved at least once a year, provided that the physical recording is necessary to determine their value”.
- Items which (IDW, 1981, p. 63) “are no longer or not yet stored (dummy items).”

In addition, (IDW, 1981, p. 69) provides that the most valuable 3 to 5% of the warehouse should be fully stocked “in order to cover 45 to 50% of the total value of the warehouse collective.”

If the actual values deviate too much from the book values, i.e. if the inventory reliability is too low, the inventory must be discarded even if the total value is permissible. The physical inventory must also be rejected if there is a deviation greater than 3% with a probability of 95%. (IDW, 1981, p. 72f).

“If a mathematical-statistical test confirms the null hypothesis (“inventory accounting reliable”), the inventory accounting can be taken over as the starting point for the inventory. However, even in this procedure, this is only permissible if there is no doubt about the informative value of the inventory accounting (functionality of the internal control system, number and amount of individual differences, etc.).” (IDW, 1981, P. 75).

Sequential tests are suitable for warehouses where the accuracy is very high. The sample size ideally corresponds to the minimum sample quantity (depending on parameters – usually 35 items), independent of the total quantity of stock items. If there are deviations from the target quantity, additional samples must be taken and the sample quantity is increased. You should note this, since the effort involved is theoretically unlimited. Therefore, in an unfavorable situation, this can be higher than the effort required for a full inventory.

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