Rounding off numbers in commitments calculations
Financial commitments, Operating lease accounting commitments and Additional accounting commitments are calculated very precisely. The calculation will always take the exact numbers into account. The amounts are calculated without rounding off the numbers. This means that fractions are stored in the memory and will be used in every next calculation step. Only the last amount is rounded off, based on the remainder of the latest calculation.
If an amount of 1,000 euros has to be paid in 12 months, the amounts are calculated as in the below example. If the system would round off each amount individually, all amounts would be rounded off to 83.33 but this doesn’t add up to 1,000 at the end. By adding the remaining fractions, the system will now add 1 to the last digit of the amount if the sum of remainders is >= 1.
The remainder is changed with -1; this algorithm will be repeated until the end. The remainder at the end will be used to round off the latest amount. If the sum of the remainders >= 0.5 after the last calculation, 1 is added, else nothing is added. The same applies if the sum of the remainders will be <= -1 and <=-0.5.
Month | Payment per month (1,000 euros per year) | Payment+Remainder fraction | Remainder fraction | Sum remainder |
|---|
January | 83.33 | 83.33+1/3 | 1/3 | 1/3 |
February | 83.33 | 83.33+1/3 | 1/3 | 2/3 |
March | 83.34 | 83.33+1/3 | 1/3 | 1 (==>-1) |
April | 83.33 | 83.33+1/3 | 1/3 | 1/3 |
May | 83.33 | 83.33+1/3 | 1/3 | 2/3 |
June | 83.34 | 83.33+1/3 | 1/3 | 1 (==>-1) |
July | 83.33 | 83.33+1/3 | 1/3 | 1/3 |
August | 83.33 | 83.33+1/3 | 1/3 | 2/3 |
September | 83.34 | 83.33+1/3 | 1/3 | 1 (==>-1) |
October | 83.33 | 83.33+1/3 | 1/3 | 1/3 |
November | 83.33 | 83.33+1/3 | 1/3 | 2/3 |
December | 83.34 | 83.33+1/3 | 1/3 | 1 (==>-1) |
Because a calculation based on fractions is very precise, the performance will drop if the calculations take a lot of steps; the fraction of the remainder will be based on exponentially large numbers.
To avoid performance issues, the rounding off of calculations for financial lease accounting commitments and for the present value is not based on the calculation with fractions. Some numbers are rounded off in intervals. For the present value calculation, the system will round off the interest percentages per period. Based on the calculated present value, the depreciation is calculated based on big fractions, as these are easy calculations. The interest percentages for calculating the interest, based on the liability / receivable for every accounting period, will also be rounded off. Since rounding off is based on a very large number of digits, it will have no impact on the outcome and it will improve the performance significantly.