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The danger posed by geometric progressions 20 January 2015

We were taught about progressions, or series of numbers, at school.  They come in two varieties – arithmetic progressions and geometric progressions.  An example of an arithmetic progression is 3, 6, 9, 12, where the next number is obtained by adding a number (or subtracting it).  These are benign.  An example of a geometric progression is 4, 16, 64, 256, where the next number is obtained by multiplying by a number (or dividing by it).  In the context of real life, these are anything but benign.

You can see why by playing with a calculator (type CALC into the search box on your PC).  Key 3, +, +, =, =, = … to show the arithmetic progression above.  Each time you press the equals sign, you move one stage – but even after ten repetitions you have only reached 33.

Now try the geometric progression, by keying 4, x, x, =, =, = …  After ten repetitions you are at a figure that exceeds 4 million (technically it’s 411 (4 to the power of 11).

You can see a geometric progression at work by folding a piece of paper.  After the first fold there are 2 layers, then 4, 8, 16, 32.  You soon have so many layers that folding becomes first difficult, and then impossible.  The story of grains of rice on chessboard squares is another example of a geometric progression.

Wikipedia says that the formula for calculating the n-th term of a geometric sequence with initial value a and ratio r is

a_n = a\,r^{n-1}.


Why is this important?

Why is this important?  Two reasons really.  First, it’s really important when drafting an index-linked rent review provision that you don’t end up with a geometric progression, otherwise the rent will go through the roof (once inflation returns, which I’m sure it will do).  Important from the tenant’s point of view, anyway.

Secondly, it is key to understanding the problem in the many leases that feature in the case of Arnold v Britton, which is to be heard by the Supreme Court on 26 January 2015.  The leases – of chalets in a holiday park in the Gower in South Wales – contained a provision in this (or very similar) terms:

“To pay to the Lessors without any deductions in addition to the said rent as a proportionate part of the expenses and outgoings incurred by the Lessors in the repair maintenance and renewal of the facilities of the Estate and the provision of services hereinafter set out the yearly sum of Ninety Pounds and value added tax (if any) for the first year of the term hereby granted increasing thereafter by Ten Pounds per Hundred for every subsequent year or part thereof.”

It isn’t immediately obvious, but the phrase in italics constitutes a geometric progression, with the figure rising by a multiple of 1.1 every year.  The annual increase is not £10 but 10%, which makes all the difference in the world.

A typical lease, for a term of 99 years, was granted in 1977 when the service charge cost was £90.  It is now in the region of £3,000.  By the time the lease expires, it will be over £1 million [£90 x 1.198, using the formula above, which equates to just over £1,025,000] .  The tenants are saying that cannot be what the parties intended, but both Morgan J and the Court of Appeal have (without enthusiasm) found for the landlord.  The clause requires the tenants to pay a sum unrelated to the landlord’s actual costs of providing the services.  Worse, the tenants do not have the protection of section 19 Landlord and Tenant Act 1985 (which requires service charge costs to be reasonably incurred), because that applies only to a charge that “… varies or may vary according to the relevant costs.”

Davis LJ in the Court of Appeal sympathised with the tenants, saying (at [56]):

“Any conclusion that means the holders of these particular leases are (currently) required to pay over £3,000 per annum for the relatively limited services provided for these holiday chalets, and with potential remorseless compounded increases thereafter, is not at all attractive.  I am well aware of that.  But, as I have sought to show, it is the result of the bargain made: and the court cannot properly, under the guise of a process of interpretation, introduce new and other terms to mend a bad bargain: which is, in reality, what the court is being asked to do.  To do so would involve distortion of all correct legal principles. Whatever the hopes and aspirations of these lessees, understandable though they may be, the court cannot simply come up with some “fair” result irrespective of the terms of the contract and in the absence of any claim for rectification.  Moreover, Mr Daiches [counsel for the landlord] was entitled to point out that the “merits” may have looked very different had inflation continued in the interim at rates corresponding to those experienced in the late 1970s: and do in fact look very different in the version of the lease containing the triennial increase.”

The reference to inflation rates may puzzle younger readers but in the 1970s inflation rose to frightening levels, caused initially by a huge increase in the cost of oil in 1973.  This website (chosen at random) says that inflation in 1974 was 16%, rising to over 24% in 1975.  Except for one year, it did not fall below double figures until 1982.  So any suggestion that the parties to leases granted in the 1970s cannot have intended an increase of 10% in the costs every year is not sustainable.  (Other leases were granted in later decades, and the same argument does not apply to those, so some form of rectification may still be sought.)

It seems to me that the Supreme Court has to reverse the Court of Appeal’s decision.  It is clearly inequitable that the tenants are having to pay the landlord increasing sums for providing the same services, with no correspondence between the amount being paid and the cost of the services being provided.

I think the tenants’ best hope is that the Supreme Court interprets the offending clause as an agreement to repay the landlord what it actually costs the landlord to provide the services.  The clause itself is strange: if the amount that is to be paid by the tenant is not related to the costs incurred by the landlord, why include the phrase “a proportionate part of the expenses and outgoings incurred by the Lessors in the repair maintenance renewal and the provision of services hereinafter set out” ?  Morgan J in the High Court puzzled over the same question – but it is clear that half of the clause is redundant, and the two halves are mutually exclusive.  Either the reference to the services or the calculation of the sum is inappropriate.  Morgan J decided that the clause made no sense if the reference to the sum of £90 (and increasing) is ignored, and the Court of Appeal agreed (on principles of interpretation, if not the parties’ merits).  This helpful article by Nikolas Ireland of Forsters summarises the first instance decision well.

So we now need the good sense of the Supreme Court to end the tenants’ misery by interpreting this provision as a covenant to repay the landlord the costs of providing services, while ignoring the pernicious geometric progression contained in the second part of the clause.  Lord Neuberger is part of the five-justice court that will hear the case, so I am confident that a way will be found for justice to be done.  Fiat justitia ruat caelum, I say.


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