8. CONVERSIONS AND ROUNDINGS: RECOMMENDATIONS OF THE GENERAL COMMISSION FOR THE

A specific working group has been set up at the request of the chairmen of the main groups of the belgian General Commission for the Euro with a view to dealing with the problems of conversions and roundings. Its aim is to identify the main problems and formulate recommendations which can serve as a basis for the other working groups and also for enterprises which have to prepare for their changeover to the euro. These recommendations are therefore general in nature and may be supplemented depending on the progress made in the work within the Commission for the Euro.

A distinction has been made between the technical problems which will arise during the transition period, on the one hand, and those connected with so-called transparency roundings1, on the other. The following report deals only with the transition period. It seeks to explain the nature and scope of each problem identified and puts forward one or more recommendations.

The group is run by the secretariat of the Commission for the Euro and is composed of a representative of the Ministries of Economic Affairs and of Finance, the Chairman of the Commission for Accounting Standards as well as a representative of the Belgian Bankers' Association and of the National Bank of .

The following report is presented in seven parts :

1. The Council Regulation, based on Article 235 of the Treaty, on certain provisions relating to the introduction of the euro (Council Regulation (EC) No. 1103/97 of 17 June 1997). 2. Single conversions. 3. Cross conversions. 4. Reconstitution of the original amounts. 5. Reconciliation of the results. 6. Conversion of limits. 7. Accounting charging of rounding differences.

A copy of the document and additional information can be obtained from the secretariat of the Commission for the Euro, telephone number (02) 221.22.41 (fax : (02) 221.31.53).

1 Transparency roundings means conversions which are adapted so as to lead to an amount in which is easily usable. These conversions are therefore not solely mathematical. 8.1. COUNCIL REGULATION BASED ON ARTICLE 235 OF THE TREATY ON CERTAIN PROVISIONS RELATING TO THE INTRODUCTION OF THE EURO

Article 4

1. The conversion rates shall be adopted as one euro expressed in terms of each of the national of the participating Member States. They shall be adopted with six significant figures.

2. The conversion rates shall not be rounded or truncated when making conversions.

3. The conversion rates shall be used for conversions either way between the euro unit and the national units. Inverse rates derived from the conversion rates shall not be used.

4. Monetary amounts to be converted from one national currency unit into another shall first be converted into a monetary amount expressed in the euro unit, which amount may be rounded to not less than three decimals and shall then be converted into the other national currency unit. No alternative method of calculation may be used unless it produces the same results.

Article 5

Monetary amounts to be paid or accounted for when a rounding takes place after a conversion into the euro unit pursuant to Article 4 shall be rounded up or down to the nearest cent. Monetary amounts to be paid or accounted for which are converted into a national currency unit shall be rounded up or down to the nearest sub-unit or in the absence of a sub-unit to the nearest unit, or according to national law or practice to a multiple or fraction of the sub-unit or unit of the national currency unit. If the application of the conversion rate produces a result which is exactly half-way, the sum shall be rounded up.

Preliminary remarks

For Belgium, the conversion rate which will be fixed will have two figures before the point and four figures after it. It will be presented as follows : xx.xxxx. In the following examples, the conversion rate which has been applied (purely for the purpose of illustration) is : 1 euro = 40.2171 BEF). The conversion rate of each participating currency in relation to the euro will not be irrevocably fixed until 1 January 1999.

The problems of the conversions and roundings resulting from the changeover from the Belgian to the euro and vice versa must be envisaged differently depending on whether it is a matter of sums to be paid (invoices, notices of due dates, transfer slips, ...) and accounting operations, on the one hand, or of other amounts, on the other.

Article 4 of the Regulation, particularly points 1, 2 and 3 concerning conversion rates, concern all conversion operations, whatever their nature.

Article 5, which deals with the rounding after conversion, for its part, concerns only sums of money to be paid and accounting operations.

A conversion into the euro unit will therefore be rounded up or down to the nearest cent, and if the result is exactly half-way it will be rounded up to the next cent. A rounding which results from a conversion from the Belgian franc to the euro or from the euro to the Belgian franc does not pose any legal problem in so far as it is in accordance with the method described in the Regulation (Article 5).

By way of example, the BEF accounts of an enterprise must be converted into euros with two decimals after the point (eurocents). On the other hand, certain limits or certain thresholds which are published are akin to types of information which may follow specific rules and, for instance, be converted into euros or into thousands of euros.

8.2. SINGLE CONVERSIONS

BEF → EUR

The conversion of a BEF amount into euros is made by dividing the amount by the fixed conversion rate.

The result of the operation will be rounded, for amounts to be paid and accounting operations, to two figures after the point.

Amount in BEF/conversion rate = amount in euros

Example : BEF 1,250/40.2171 = EUR 31.0813 rounded to 31.08.

The European Regulation forbids the use of inverse rates. "Whereas 10" of the European Regulation in fact states that "the use of inverse rates for conversion would imply rounding of rates and could result in significant inaccuracies, notably if large amounts are involved".

OR

EUR → BEF

The conversion of a euro amount into BEF is made by multiplying the amount by the fixed conversion rate.

Amount in euros x conversion rate = amount in BEF

Example : EUR 31.08 x 40.2171 = BEF 1,249.95 rounded to 1,250.

The maximum error risk, per operation, resulting from a rounding corresponds to half the smallest unit into which conversion takes place, i.e.: - max. 0.5 cent upon a conversion into the euro (or BEF 0.20) - max. BEF 0.5 upon a conversion into the Belgian franc. Recommendations 1 and 2 concerning conversion of prices

The European Regulation provides for rounding, after conversion, only for amounts to be paid or accounted for (Article 5). Prices are not, therefore, explicitly referred to and the level of accuracy to which they should be redenominated in euros is the subject of the following two recommendations.

Recommendation 1

Barring an exception or exceptions to be determined by the Minister for Economic Affairs and that referred to in Recommendation 2, the same procedure as that appearing in Article 5 (first sentence) of the European Regulation shall be applied to the rounding resulting from a conversion connected with the double presentation of a price. In other words, for the conversion into euros of a price expressed in BEF, two decimals are to be used after the point. Thus, an item of information denominated in Belgian will retain the same accuracy when converted into euros.

Recommendation 2

The preceding recommendation may not, however, be sufficiently accurate for the conversion of certain prices, because an accuracy of two decimals after the point may be insufficient for the conversion into euros of prices which are relatively low but are applied to a large number of operations. The rounding difference which will result from the conversion of these prices into euros may be amplified by a substantial multiplier effect. For this reason the conversion into euros must be made with an additional accuracy of at least two decimals in relation to the amount in Belgian francs (for example, an amount of BEF 0.35 will be converted into EUR 0.0087).

This problem concerns, for instance, goods and services for which the nature of the contract requires the fixing of a unit reference value which is used as the unit of account in BEF. Notable examples of these are the unit values used for making out gas or electricity bills.

The total amount to be paid or accounted for, for its part, will be rounded in accordance with the method defined in Article 5, i.e., for the euro, to the eurocent. If the unit price is indicated on the basis of a higher unit of account (x10 or x100), the calculation itself will still be made starting from the basic unit of account.

Example2 : if the unit price of gas is BEF 0.22911 per MJ, this price expressed in euros will have to be EUR 0.0056968 per MJ in order to retain the same accuracy. Recommendation 3

The conversion of an amount expressed in euros, to be paid or accounted for, into Belgian francs shall be rounded to the franc in accordance with the method described in the European Regulation (Article 5), i.e. it shall be rounded up from BEF 0.50 upwards. In this respect the recommendation follows national practices.

8.3. CROSS CONVERSIONS

The European Regulation defines a calculation method which requires, for each amount to be converted, an intermediate conversion into euros with a minimum rounding to three decimals after the point. A different method may be used if it produces an identical result.

BEF → EUR →FRF

Example : BEF 1,000 → (1,000/40.2171) x 6.59993 → 24.865 x 6.59993 → FRF 164.11

or : BEF 1 → (1/40.2171) x 6.59993 → 0.025 x 6.59993 → FRF 0.16.

FRF → EUR →BEF

Example : FRF 1,000 → (1,000/6.59993) x 40.2171 → 151.517 x 40.2171 → BEF 6,093.57

or : FRF 1 → (1/6.59993) x 40.2171 → 0.152 x 40.2171 → BEF 6.11. → 0.1515 x 40.2171 → BEF 6.093.

2 This recommendation also applies to other products whose unit prices are relatively low - for instance, the price of a plastic plug, which is about BEF 0.30 and should be converted into EUR 0.0075. Note : With regard to the European algorithm, attention should be drawn to the fact that the choice of the number of decimals for the intermediate calculation in euros may influence the final result of the conversion. The examples presented above show that, while the method defined by the European Regulation may be suitable for the conversion of individual amounts, the choice of a larger number of decimals for the intermediate conversion may increase the accuracy of the final result of the conversion. It is therefore recommended that, for cross conversions made on the basis of a data processing program, the greatest possible accuracy should be maintained for the intermediate amount.

Furthermore, the European algorithm does not have as its purpose the calculation and indication of a bilateral conversion rate. These problems have been studied by the "Notes and Coins" working group of the Fin-Euro group of the General Commission for the Euro, which proposes the publication of bilateral rates in the case of Belgium in order to provide customers with sufficient information for their counter transactions.

Recommendation 4

Cross conversions carried out by means of a data processing program must maintain the maximum accuracy for the intermediate calculation in euro. Any other method which enables a result identical to that resulting from the application of the European Regulation may also be used. In the absence of a European initiative, the indication of the bilateral conversion rates of the currencies of the other countries of the Monetary Union vis-à-vis the Belgian franc will be the subject of a publication by the Commission for the Euro. These bilateral rates relate only to the information to be provided to customers for their counter transactions and will be arrived at from the conversion rates irrevocably fixed as at 01.01.1999. These rates will be calculated with an accuracy of at least six significant figures for the equivalent in Belgian francs.

8.4. RECONSTITUTION OF THE ORIGINAL AMOUNTS

BEF → EUR → BEF

Example : BEF 1,250 → EUR 31.08 → (1,249.947...) BEF 1,250.

As the accuracy of the amounts expressed in euros is greater than that of the amounts denominated in Belgian francs, an amount in BEF converted into euros can always be reconstituted in BEF.

EUR → BEF → EUR

Example : EUR 871.55 → BEF 35,051 → EUR 871.54.

Conversely, an amount initially denominated in euros and converted into Belgian francs might not be accurately reconstituted in euros. The error risk of reconversion into euros is at most ± 0.01 euro per amount.

Recommendation 5

A loss of accuracy of ± 0.01 euro may affect the reconstitution in euros of an amount to be paid initially expressed in euros and converted into Belgian francs. This difference must be allowed in so far as it results from the application of the European Regulation and cannot be invoked to dispute the correctness of a payment.

Note : This tolerance should also be incorporated in data processing programs, especially accounting programs, in order to avoid problems connected with the reconciliation of amounts. There are other data processing solutions, such as prescribing rounding of the intermediate amount in Belgian francs with one decimal after the point or storing the loss of accuracy in a memory.

Recommendation 6

In order to reduce any losses of accuracy due to conversion operations as far as possible, it is recommended that payment be made in the same currency as that of the invoice.

8.5. RECONCILIATION OF RESULTS

Although, according to the law of large numbers, roundings should offset each other, errors may nevertheless accumulate when payment transactions are carried out, on the one hand, and in the processing of information (particularly accounting information), on the other. Arithmetical operations on rounded amounts may amplify rounding errors. For this reason, the sum or the product of converted unit amounts may differ from the conversion of the total amount.

Examples : BEF EUR

1,250 → 31.08 1,300 → 32.32 500 → 12.43 600 → 14.92 ______(90.75) 3,650 → 90.76

In this case the sum of the various converted and rounded amounts does not correspond to the total amount of the addition when it has been converted and then rounded.

or

BEF 1,000 x 250 = BEF 250,000 → EUR 6,216.26 EUR 24.87 x 250 = EUR 6,217.5

Some organisations which write many invoices (big invoicers) have chosen to convert only the total amount of the invoice into the other currency. The payment order accompanying the invoice will always correspond to the currency in which the details of the invoice are denominated.

Recommendation 7

In order to avoid the problems which may result from the reconciliation between, on the one hand, the elements which are involved in an arithmetical operation and which are individually converted and, on the other, the conversion of the final result of the operation, it is recommended that only the final result be converted into the other denomination. It is always permissible for the enterprise to indicate certain amounts in both currencies for information purposes.

The conversion of statistical files poses a specific problem when it comes to reconciling the results, because all the data in the file have to be converted into euros, and this may lead to problems in reconciling intermediate or final balances and totals. These problems can be avoided if the conversion is applied first to the basic data of the file, while the various balances or totals are not converted but are recalculated from the basic data in euros.

Recommendation 8

For the conversion of statistical files or series, the conversion into euros must be applied to the basic data expressed in Belgian francs, rounded after conversion in accordance with Article 5 of the European Regulation. The balances and totals will be recalculated from the basic data converted into euros. If the results are also converted, either manual adjustments may be necessary in order to reconcile the results or the rounding differences will be retained unchanged in the statistical tables. The validation rules will have to be adapted accordingly. Historical data prior to 1999 which have already been published in BEF but which also have to be converted into euros for reasons of comparability of the data over time will be so converted on the basis of the irrevocably fixed conversion rates.

8.6. CONVERSION OF LIMITS

Some scales, limits or reference amounts might lack transparency after conversion into euros. Transparency roundings in euros are, however, liable to make the corresponding amounts in BEF less easy to grasp. Markets which will operate only in euros from 04.01.99 onwards (stock exchanges, interbank systems,...) will establish new scales or limits in euros, which will be the subject of a publication or a separate legal act.

Recommendation 9

In the absence of a publication or a separate legal act, limits, scales or other reference values shall remain denominated in BEF during the transition period. The conversion into euros shall be an arithmetical conversion in accordance with the European Regulation. In other words, for the conversion into euros of a limit in Belgian francs, with two decimals after the point.

A specific problem may arise for limits or intermediate thresholds which define tranches of amounts. In this case, in order to avoid rounding problems, the upper limit of a tranche expressed in euros is adopted, after arithmetical conversion, as the lower limit of the following tranche with the addition of 0.01 euro. For example, a limit of BEF 200 converted into EUR 4.97 and used as the upper limit of a tranche (or category) will be adopted as the lower limit of the following tranche with the addition of 0.01 euro, i.e. will be fixed at EUR 4.98.

For scales and limits used by the public authorities, it is recalled that these will continue to be in Belgian francs throughout the transition period.

Note In certain specific cases where these limits are ceilings or floors referred to, for instance, in certain legislative texts or certain orders (for instance stock exchange orders), the conversion into euros may be made in such a way as not to distort situations which may be at the margin. In some cases the conversion could be adjusted downwards for ceilings and upwards for floors. 8.7. ACCOUNTING CHARGINGS OF ROUNDING DIFFERENCES

Recommendation 10

At the request of the working group, accounting chargings of roundings have been the subject of an opinion expressed by the Accounting Standards Commission (Commission des normes comptables). In this opinion, the Commission proposes that all rounding differences be carried to a sub-account of the financial accounts (accounts 657 to 659 or 756 to 759 of a Minimum Standardised Accounting Plan), to be charged to the profit and loss account under Receipts or under Expenditure, depending on whether the balance is a credit or debit balance. If the enterprise opens several accounts for this purpose, the balances of these can be grouped together in the profit and loss account.