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:
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
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):
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 of 30 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, the effort involved may be greater than that of a full inventory.
First of all, the quantity of the parts not moved during the physical inventory period must be physically recorded. However, sampling procedures can be used here. (AWV, 1980, p. 1f)
First, the parameters for the probabilities must be determined. Here 𝑝𝑢 is the lower and 𝑝𝑜 the upper limit for the error fraction (AWV, 1980, p. 6). Furthermore, 𝛼 is the risk of a rejected inventory in the case of a correct warehouse and 𝛽 is the risk of an assumed inventory in the case of an irregular warehouse (AWV, 1980, p. 7). (Odenthal, p. 28) speaks of confidence levels. Here 𝑉𝑜 = 1 – 𝛽 denotes the confidence that a non-compliant warehouse is found to be non-compliant, and 𝑉𝑢 = 1 – 𝛼 denotes the confidence that a correct warehouse is recognised as correct.
The lower the parameters 𝑝𝑢, 𝑝𝑜, 𝛼 and 𝛽 are chosen, the more stringent the test is (AWV, 1980, p. 16f). Obviously 𝑝𝑢 ≤ 𝑝𝑜 must apply.
The AWV provides in (AWV, 1980, p. 16) values of 𝑝𝑢: 1 – 2% and 𝑝𝑜: 3 – 10%. In (AWV, 1985, p. 21) these are given as 𝑝𝑢: 0.5% and 𝑝𝑜: 1%. (AWV, 1980, p. 17) also gives 𝛼: 5% and 𝛽: 5%.
(AWV, 1985, p. 23) recommends the full intake for high values, as well as “at