## Errors in the calculation of new salary positions and performance premiums – 2017 MERIT exercise

Following the receipt of the letters dated May 12th announcing the qualification of their performance (MERIT 2017), and the notification of their salary slips for the month of May, several colleagues have come to us to enquire about the calculation of salary increases and performance premiums.

After verification, the Staff Association has informed the Management, in a meeting of the Standing Concertation Committee on June 1st, about errors owing to rounding in the applied formulas.

James Purvis, Head of HR department, has published in the CERN Bulletin dated July 18th an article, under the heading “Better precision (rounding)”, that gives a short explanation of these rounding effects. But we want to further bring you more precise explanations.

On the salary slips for the month of May, the calculations of the advancement and new salary positions were done, by the services of administrative computing in the FAP department, on the basis of the salary, rounded to the nearest franc, to which the advancement, a percentage of the midpoint salary of the grade and also rounded to the nearest franc, is added to obtain the new salary. Finally, the new salary position is a calculated by dividing the new salary by the midpoint salary of the grade.

In equations, this translates to:

Old_Position = Old_Salary / MidPoint

New_Salary   = Old_Salary + Round( Percentage_Advancement * MidPoint )

New_Position = New_Salary / MidPoint

Practically, the calculated difference between your new and old salary positions, i.e. your advancement, is tainted by rounding errors, and does not necessarily correspond to the values announced with respect to your performance qualifications: 0.35 % for a “fair” performance, 1.35 % for “strong” and 2.35 % for “outstanding”.

The calculation shows that, although the differences are real for salary positions, they are at most of 0.5 CHF per month this year for the salaries, that is without consequence on the salary paid by the Organization, which is rounded to the nearest Franc and is therefore correct.

Nevertheless, if left uncorrected, the errors can accumulate along your career and lead to substantial deviations on the long term.

And above all, there is a better and more precise way to calculate this!

In the spirit of the new career structure, the calculation should be made on the basis of the salary position, given as a percentage with three digits. The new salary position is then merely the sum of the old salary position and the percentage for advancement, as published and as a function of the qualification of your performance. It is only in the end that the new salary, rounded to the nearest Franc, is deduced from the salary position. Hence there is no propagation of rounding errors.

Old_Salary    = Round( Old_Position * MidPoint )

New_Salary   = Round( New_Position * MidPoint )

Clearly it is possible to find other means to calculate salary increases without losing precision on the long term and the solution suggested by HR in their article is a lead to follow.

The performance premium, paid annually, is calculated as a percentage of the midpoint salary of the grade, multiplied by 12.

The calculation of the Administration in 2017 relies on the calculation of a monthly premium, rounded to the nearest Franc, and then multiplied by 12:

Given that the premium should be calculated on the basis of the annual salary, and that rounding operations should come as late as possible in a calculation to retain precision, the formula should be: