Contracts often need to reflect mathematical concepts, such as formulae, for determining price or price adjustments. Yet simple mistakes in these clauses can have costly results.

Interpretive Mathematics?

Take the salutary example of Chartbrook v. Persimmon[1], a case as relevant today as when it was first handed down in 2009. Here, a payment obligation was defined as:

"23.4% of the price achieved for each Residential Unit in excess of the Minimum Guaranteed Residential Unit Value less Costs and Incentives".

The parties took two very different interpretations of this clause, resulting in a difference of several million pounds. Whilst one of those interpretations appeared to be commercially reasonable, and the other not, the courts will interpret contracts literally, and rectification for "mistake" is difficult to obtain. So it was necessary to litigate all the way to the House of Lords (now the Supreme Court) just to establish what this clause actually meant.

Had the clause been drafted using a simple formula, the ambiguity would have been apparent immediately. You don't need to be Rachel Riley to understand that the following two formulae produce very different results:

(i) Price = 23.4% x (A – B – C)

(ii) Price = [23.4% x (A – C)] – B


A = price achieved for each Residential Unit

B = the Minimum Guaranteed Residential Unit Value

C = the Costs and Expenses.

Formula for success

The objectives of legal drafting are clarity, simplicity and the avoidance of ambiguity. In short, good drafting should minimise the risk of future dispute.

So be wary of contracts which rely wholly on long jumbles of words. If a picture can tell a thousand words, a formula can tell ten thousand.

Worked examples

The other notable point from Chartbrook was the absence of a worked example. Had the parties produced a worked example, the differences in interpretation would have been flushed out and clarified before the contract was signed – and years of expensive litigation would have been avoided.

You do the maths?

Whilst some contracts will contain mathematical concepts of such complexity that they can only be fully understood by other specialists (such as actuaries), a great many contracts contain relatively simple mathematical ideas.

Many lawyers "don't do maths". Yet, given the importance of these clauses, the lawyers need to work with the business and other relevant advisers (such as corporate finance) to ensure that anything which is drafted is accurate and sufficiently clear. Anything else just doesn't add up.