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Magazine

Correct arithmetic does not guarantee a sound decision

A calculation can be exact and still answer the wrong question. A fictitious indexation case shows this: the same index movement yields 7.3 points or 6.39%, and only one of these figures fits the clause in the lease. Traceable calculations therefore show not only the result but also the inputs, sources, units, reference dates and the rule by which the calculation was made.

Overlapping sheets with geometric diagrams and a metal ruler on a stone surface.
Editorial illustration · AI-generated

At a glance

  • Link every input to its source, unit and reference date; for an index, also to the base month and the base year.
  • Apply the calculation rule from the clause: in the fictitious example, 121.6 − 114.3 = 7.3 points, while the clause requires more than 10.
  • The business plan’s percentage calculation is correct (+6.39%) but tests a 5% threshold that does not appear in the lease.
On this page

First define what the number should say

“Is the index adjustment due?” sounds like an arithmetic problem. In fact it contains several questions: which clause applies in which version, which index was agreed, from which base month the change is measured, and whether the threshold is expressed in index points or in percent? Only once this is settled is it clear which number should be calculated at all.

In this article’s fictitious example, the subject is unit 3 of a commercial property. The question is whether the indexation clause in Section 5 of the lease has been triggered, not how rents across the entire property are developing. This restriction is not small print for the end but part of the result. It prevents a figure copied later from silently acquiring a broader claim, for example as an index assumption for an entire portfolio.

Bind every input to its source

For every number, its provenance and relevant professional characteristics should be established: document and version, page or cell, unit and reference date. For a price index, these include the name of the index, the base month, the comparison month and the base year of the index series. An index level without a base year is incomplete, because the same price movement yields a different number of points depending on the base year.

In the example, the inputs come from different documents. The fictitious lease for unit 3 states, on p. 6 in Section 5, the threshold of more than 10 points, the base year 2020 and, for the base month, the index level 114.3. The current level of 121.6 comes from the index series. The business plan contains a further figure, a threshold of 5%. It is a planning assumption, not a contractual source. In the example, the two amendments do not change Section 5; for a real lease, that is a separate review step.

Destatis · Merkblatt Punkteregelungen in Wertsicherungsklauseln

Apply the clause’s calculation rule

A deterministic calculation returns the same result for identical inputs and rules. What matters is which rule is applied. In its information sheet, the Federal Statistical Office (Destatis) distinguishes point-based clauses, under which an adjustment depends on a change by a certain number of index points, from percentage-based clauses. The percentage change is calculated using the formula given there: (new index level / old index level) · 100 − 100.

In the example, both approaches lead to correct but different figures. Under the point-based rule in Section 5, the index has risen by 7.3 points; the adjustment would only be triggered at a level above 124.3. Under the business plan’s percentage calculation, it has risen by 6.39% and has exceeded the plan’s 5% threshold, which lies at 114.3 · 1.05 ≈ 120.0. Both calculations are arithmetically correct. Only the first follows the lease.

Destatis · Merkblatt Punkteregelungen in Wertsicherungsklauseln

Illustrative example · fictional documents

Fictitious lease, unit 3, p. 6, Section 5: The rent changes in the corresponding percentage ratio as soon as the consumer price index (base 2020 = 100) has changed by more than 10 points compared with the base month. Base month 114.3, current level 121.6 (fictitious values). Under the lease: 121.6 − 114.3 = 7.3 points; the threshold has not been reached and is only triggered above 124.3. Under the business plan: (121.6 / 114.3) · 100 − 100 = 6.39%; the 5% threshold assumed there has been reached, and indexation from 2026 is planned. The validity of the clause and other units have not thereby been reviewed.

Review the selection independently of the calculation

The arithmetic check answers whether the chosen operation was performed correctly. The professional review asks whether it was the right operation with the right inputs. Does the base month correspond to the last actual adjustment? Is the current level a final value? Was Section 5 changed by an amendment? Does the base year of the index series used match the one named in the clause? None of these questions can be answered from the result of 6.39%.

The base year deserves particular attention. According to the Federal Statistical Office (Destatis), the consumer price index is revised every five years and rebased to a new base year; the change from base 2015 to base 2020 took place in February 2023. The result in points depends on the base year; the percentage change does not. If a clause names a different base year from the series used, a points check is not meaningful without conversion. A clear result title therefore records what was reviewed: “Threshold under Section 5 (points, base 2020) not reached” is more precise than “no index adjustment due”.

Destatis · Merkblatt Punkteregelungen in Wertsicherungsklauseln

Destatis · Umbasierung und Wertsicherungsklauseln

Hand over a verifiable result

A useful handover contains the input list with source references, the rule applied, the calculation steps and the result with its unit. In the example, it explicitly includes the contradiction: the business plan assumes indexation from 2026, which the lease does not support at the current index level. This discrepancy is the actual finding, not the figure 7.3.

Even if the threshold is exceeded later, the calculation remains a two-step process. The point-based rule determines whether an adjustment is made. According to the information sheet of the Federal Statistical Office (Destatis), the extent of the adjustment follows in a second step from the percentage change, if the clause, as in the example, provides for an adjustment in the corresponding percentage ratio. Whether the clause is valid and how it is to be interpreted remains a legal review.

RAIVA’s platform principle connects traceable results with sources and review steps. The values shown here are illustrative and establish no real leases, index levels or business outcomes. When information is missing, the result should contain an open question rather than concealing the missing certainty behind extra decimal places.

Destatis · Merkblatt Punkteregelungen in Wertsicherungsklauseln

About the author

Hermann del Campo

Co-Founder & CTO

Former Technical AI Lead within Deutsche Telekom Group with fifteen years in machine learning and production systems. He builds the technical evidence layer behind RAIVA.

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