Thursday, December 10, 2009

When regulators can’t do math: gas pipeline edition

The Federal Regulatory Energy Commission (the FERC) is charged – amongst other things – with regulating the rate of return on interstate natural gas pipelines.  Rates on these pipelines are by-and-large regulated so as to achieve a targeted return on equity.

Quite of its own volition the FERC has called for a judicial review of on three Midwestern gas pipelines including Natural Gas Pipelines of America (NGPL).  In its last rate case (1996), NGPL’s target rate of return was set at 12 percent. 

This is a peculiar review because – unlike past reviews – the review was called by the Commission itself and without a complaint from any of the customers using the gas pipeline.  [Customers for gas pipelines tend to be large oil and gas companies or large utilities and are usually not shy about calling for a review when rates are out-of-line.]

The FERC has argued – from publicly available documents – that the returns on the NGPL are (just) over 24 percent – and hence (and these are their words) are “unjust and unreasonable”.  They use lots of emotive language and have petitioned a judicial review to get the rates cut.  You can find the full document here.   A good press summary is here

To put it bluntly the FERC stuffed up.  It simply got the math wrong because it does not understand rates of return and depreciation – a staggering oversight for a body charged with regulating pipelines.  Worse – on the math presented – the rates on the NGPL should be increased in order to allow for the FERC mandated 12 percent return. 

This is a pretty nasty allegation – so I need to explain the basic mathematics of regulated returns.  I will start with the simplest of models that I can.

The simplest pipeline model

Imagine a pipeline that cost $100 to build.  It lasts 2 years.  The regulators have to allow the pipeline to recover an amount (say $x per year) so that the present value of $x per year adds up to $100. 

Now $x has to be more than $50.  Why?  Because over 2 years the pipeline has to recover at least the $100 that it cost to construct.  Depreciation alone is $50 per year – and having the pipeline recover only $50 per year would mean it made no profit.

We could (naively) presume that because $100 is employed the pipeline needs to make $12 per year profit in order to get 12 percent return.  So we would set $x at $62.  That unfortunately gives us a little too much return – because – in the second year the pipeline only has $50 of capital employed (they have recovered $50 through depreciation).  You can do the math here (and you assume for simplification that the cash is all received at year end) then the $62 received after year one would be worth $55.36 discounted at 12 percent and the $62 received in year 2 would be worth $49.43.  Add those up and you get more than $100. 

I used the “goal seek” function on Excel to work out the required annual return on the pipeline under the simplifying assumption that the annual payment is received in two equal increments.  I have linked the original spreadsheet (to convince you that I have done this correctly). 




In this case note that the required cash flow each period is $59.17c.  You can discount this if you want by 1/1.12 in the first year (getting $52.80) and by that squared in the second year ($47.17) and lo – these numbers add up to $100.

Now here is the clinch – which is that we know – by initial assumption here – that the return on equity for this project over its life is exactly twelve percent. 

But what is the return on average equity in the second year? 

Return on average equity in the second year!

The cash return in the second year is $59.17 cents.  [It needs to be that every year to provide a 12 percent return on equity over the life of the project.]   The pipeline depreciates by $50 per year over its two year life.  So the measured profit during the second year is $9.17 (the return less depreciation).

Capital employed commenced the second year at $50 (being the cost less the $50 of accumulated depreciation).  It ended the second year at $0 – as the whole pipeline had been written off by then.  The average capital employed for the second year is thus $25.  Given the stated profit is $9.17 the return on average equity for the second year – as recorded – will be 36.7 percent. 

This return will be observed even though the return on the project over its life is only 12 percent. 

There is nothing sinister about an observed 36.7 percent – and more generally there is nothing “unjust and unreasonable” in the observed returns of 24 percent of the Natural Gas Pipeline of America.  These returns are simply a mathematical artefact of the allowed return on equity of 12 percent over the life of the pipeline.   The observed ROE of 24 percent does not warrant a rate case – it is as to be expected.  Indeed as the pipeline in question is more than half depreciated I would have been surprised if the observed ROE was below 24 percent – and the 24 percent ROE does not represent a problem or a failure of regulation. 

What we have here is a regulator who has failed to understand the basic math of the business which they are meant to be mathematically regulating.

The deskilling of American regulators

I am no longer surprised at the general deskilling of American regulators.  This post demonstrates that the regulator – whose job it is to regulate the rate of return on gas pipelines – has no idea at all of the basic high school mathematical implications of that regulation.  I am used to SEC officials who can’t read a balance sheet or can’t see the Madoff fraud when it is laid out in front of them.  But the rot spreads more widely.  We have bank regulators who were blind or stupid and now we have utility regulators who can’t do basic math. 

A more generalised formula for what should be the observed returns on a pipeline

Warning – seriously wonky – here I do the math to show what the observed ROE should be.  You don’t need to read this – just accept the regulator has their math shockingly wrong.  But here is a way of working out precisely how wrong!

Being a nerd I thought I would help the regulator out with their math – and indeed it is not too hard to derive a generalised formula for the right observed return on a pipeline.  But hey – why bother when Wikipedia does it for you?  Wikipedia gives the present value of a stream of n paymnets of value A as follows:



PV(A) is the present value of the stream of payments – which in this case should be the construction cost of the pipeline

i is the rate of return – which in the case of FERC should be the regulated rate of return (12 percent), and

A is the annual cash return on the project, and

n is the number of years over which the project receives its return (which should be the depreciable life of the pipeline – or in the above example 12 percent). 

Now I would never use a formula out of Wikipedia without checking it (which I did by derivation) but for my readers I thought I should just plug in the above example – where the cost of the pipeline is $100, the annual payment is $59.17, i is the usual 12 percent and n is two years.  Plug the following into your calculator – it checks out just fine:


Now we can rearrange this standard formula to determine A:




Now we can also work out what the year-end capital employed (E) in year j of n is.  That is trivial – it is






Income in any year (Y) is equal to the annual payment less than depreciation.  In the formula below I just assume that the original cost of the pipeline depreciates in a straight line over n years.




Now the FERC is really obsessed by the observed return on equity on the pipeline (in this case about 24 percent).  But lets work out what the observed return on equity should equal:




You can rearrange and simplify this equation any way you like – I can’t really be bothered – I am lazy.  But hey we now have enough to work out what the observed rate of return should be.  Assume that the initial cost of the pipeline is 1 (it would cancel from top and bottom of the above formula).  The depreciation in the FERC document for the pipeline is 50 years – so n is 50.  The pipeline originally cost $3.728 billion but has accumulated depreciation of $2.273 billion – so we are in 35 of 50 – so in the above formula j is 35.  We are going to allow the regulated rate of return – which is 12% – so i is 0.12.  Plug this in and we get the following:




Just to check that I am not wrong I have done the same in a spreadsheet – which I have linked hereBut the lesson is that the observed rate of return should be 33.47 percent even though the project actually only returns 12 percent over the life of the project. 

An observed rate of return on 24 percent – the rate that FERC is complaining about – is too low.

FERC is right of course – the tariffs on these gas pipelines are “unjust and unreasonable” – they unjust and unreasonably low.  On FERC’s own numbers they are not adequate to provide the lifetime 12 percent return on equity that FERC mandates.

What are the options here?

I guess the easiest options for the owners of the pipelines are to allow the FERC numbers as to depreciation and capital employed to go to the judge uncontested.  They do not seem out-of-kilt with reality.  They then should present the math straight (and there are plenty of mathematicians who will do a better job than me) and they should ask for a rate increase! 

I do not think the judge will have any problem giving it to them.  But it is not the public policy objective here – and we wound up in this spot because of the mathematical incompetence of the FERC.  It is time to stop the rot at the FERC.

Stopping the rot at FERC

And it should stop relatively quickly.  Barrack Obama appears to have appointed a competent man to be the head of the FERC.  Whilst Jon Wellinghoff may have spent most of his career as an attorney he has – according to his CV – an undergraduate degree in mathematics (University of Nevada 1971).  He should be more than capable of checking the math in this post. 

I have contacted his office and given him a copy of this post.  Jon Wellinghoff endorsed and press released the review of the rates for the various gas pipelines.  He is however more than capable of withdrawing his request for a review.  Indeed I think he has to before the FERC is made a laughing stock as the SEC was after Madoff.

I will happily announce when he has reacted appropriately. 





PS.  The pipelines who would have had their returns slashed under this review include Northern Natural – which is owned by Warren Buffett’s Berkshire Hathaway.  I have not received or asked for a consulting fee but Berkshire holders (many of whom are my readers) should be sending their thanks...

PPS.  I am serious about the deskilling of US regulators.  I have spent only a few hours thinking about the mathematics and accounting of rate of return regulation in my life – and I spotted and roughly quantified this error within five minutes.  Regulators who do this all day every day should simply not make mistakes like this.


Anonymous said...

n is the number of years over which the project receives its return (which should be the depreciable life of the pipeline – or in the above example 12 percent).

I think you mean "2 years"

Anonymous said...

I have no idea what depreciation method they are using. You are assuming of course that straight line method is used. Or course if it was using accelerated method, then observed rate of return would have been even bigger. May be it's unit of production?

James B. Shearer said...

Interesting post but I think it shows straight line depreciation is inappropriate here. I think if you did it like a mortgage where the principal is reduced slowly at first and quickly at the end the rate of return would be constant throughout.

How are pipelines actually depreciated? And what happens at the end if it is still in use?

Unknown said...

Afternoon - Thanks for the interesting post.

One quick question;

How'd you get to the pipeline being in it's 35th year?



SG said...

Always interesting John.

FYI, the use of "unfair" and "unreasonable" is not intended to be emotive. They are actually US regulatory agency terms of art. Most regulatory enabling legislation employ the terms fair and reasonable as the standard to be met. As a result, the language in many agency rulings make reference to these terms in either their positive, or in this case, negative forms.

John Hempton said...

Jason- pipeline depreciated roughly 2% per year (FERC numbers).

Depreciation roughly 70% gross assets.

Put-em-together -pipeline is in 35th year.


Anonymous said...

Great analysis and IMO 100% correct. However after observing government agencies and prosecutors over the years what you most likely will see from FERC is a massive amount of cognitive dissonance and an inability to admit they were wrong.

stranger said...

these formulas are not used at this type of investment..becouse this is a Public Investment to determined by -zero base depreciation-means that costs could be melted long time before the finish time of debreciation.!

Unknown said...

Morning - thanks for your quick reply.

My only other question (after thinking a bit about it last night!) is;

I presume since you've used straigt line depreciation that this the method prescribed the FERC?



Anonymous said...

Is the difference that the regulator initially looked at what was fair and reasonable on an IRR basis, and now they're examining it from an NPV point of view?

The return allowed in the settlement in 1997 is below the required return, therefore the company would need to be compensated by higher returns in the later years for IRR to = 12% or NPV to = 0.

If everything is viewed on an NPV basis, then every year you should get depreciation plus your allowed return (in this case 9.71%) on your average capital employed. However, if you've under-earned the allowed return in the past, viewed as a whole, you need higher returns in the future to make up for your past losses.

It seems here the company had returns below the assessed cost of capital in the early years, and would have received higher returns in the future to compensate, except now FERC is saying "you're earning too much on the capital you have employed" without considering the losses previously sustained.

Anonymous said...


I don't know much about the way US regulatory "return on capital" is calculated, but your calculations assume that the goal is to get the desired return on AVERAGE over the projects's life.

While that would produce high ROA figures in the later later years of the project(s), it would show low ROA figures in the early years, and I'd question whether in our day and age regulated company management would accept this.

Isn't there some chance that they actually aim to get the target return year by year. If so, the return SHOULD be calculated on the written down value, with the rates (in real dollar terms) declining each year (or every few years as reviews take place).

What's that chance that this is the case with the pipelines?


Anonymous said...

The regulator has requested judicial review ... what is your point?

The entities concerned will submit a defense which will presumably reflect your math if it is correct .... are you a stockholder?

Anonymous said...

I think James B Shearer has it right: if they used economic depreciation then

ROI = IRR over the life of the project,

where "ROI" refers to ROI in each year.

In other words, the ROI will remain constant over time and will equal the project IRR.

Anonymous said...

this is hardly fair, gov employees stay in work by following procedures and following orders. This pipeline return stuffup was probably the brainchild of some 'smarter', higher political type. Those writing the report did as they were told. Knowing it was wrong (or perhaps misplaced). You should never assume that simple maths such as laid out, cannot be followed even in a common-sense way by the lay-worker or even factory hand. Stating they are so stupid, means you have missed asking the "why". The answer to this I imagine does not involve maths at all.
Enough of my blathering, came across this from the herald story. Great blog and a great effort in putting up ideas (even when anon nitpickers like me annoy). Thanks

Fungus the Photo! said...

January 2, 2010 9:39 AM

Then the government employees are complicit?

They should be able to blow a whistle to stop the denigration of the very public service in which they work?

As there is a lot of $ involved, it is quite possible that it is not incompetence at all, but kleptence!

Eureka said...

Provided that the $59.17 cash flow is returned to the investors at the end of the first year the equity will be $52.83 ($100+$12-$59.17). On that equity a further 12% will be earned to return $59.17 at the end of the second year ($52.83+$6.34-$59.17=0).

In the analysis the capital employed at the end of the first year, $50.00 is understated. Also, in the second year the average capital is calculated at $25 contrary to the initial assumption that cash flows take place at year-end and therefore understated.

Suppose that one could reinvest cash flows in a bank account also earning 12%. The balance sheet at year 1 would consist of a total investment of $109.17 (Pipeline $50 and cash at bank $59.17). By the end of the second year the bank account would have earned 12% $7.10. Together with the final cash flow, cash at bank would now amount to $125.98 and the investment in the pipeline will have been fully depreciated. Discounting the $125.98 at 12% for two years PV = $100.00.

The issues that are highlighted here are:

Cash flows rather than accounting allocations (depreciation) are discounted,
Capital employed is the residual claims of the owners/investors (or net investment in the project) which in this example is not equal to the depreciated value of the assets,
Timing of the cash flows should have been consistent, and
one cannot assume reinvestment of cash flows at a projects rate of return.

Unknown said...

Read through your post and glanced at your spreadsheet. One misunderstanding underlies your analysis -- the idea that the net income of the pipeline in year 40 must equal the net income in year 1. In fact, this never happens. Rates change over time, earnings change over time. Through capital expenditures, the asset base moves around unpredictably.

Think of it this way: initial investment $1000, 10 yr life, 10% ROE. 100% equity financing.
In year 1, the company is entitled to $100 of pre-tax earnings ($1000 * 10%). That is after the non-cash charge of $100 for depreciation (1000/10). So in reality, pipeline gets $200 of cash. At year end, company has $900 of equity remaining in the asset (think of the depreciation as a "return of capital" as opposed to a return on capital) and should be entitled to earn $90 in year 2. So in year 2, pipe gets $190 of cash... and so on. Notice that if you do this for 10 yrs, and discount the cashflows at 10%, the value of the cashflows = the initial $1000 investment.
At various points along the line, rate cases should be filed to determine how much the pipe is entitled to earn for the next year, and use an estimate of operating costs and volumes to work out a proper tariff.
Let's say 5 years in the company has not been reinvesting in the pipe and they still earn $100 of income. They will clearly be earning more than the $60 they are entitled to in that year, and shippers have cause to ask for lower rates.

FERC has its problems -- I personally differ w/ how they derive what the appropriate ROE is, and disagree w/ them initiating Section 5 rate cases when shippers don't initiate their own cases -- but they generally are pretty smart and pretty aware of the details involved here. Most rate cases involve both sides bringing in highly paid consultants to make their cases before a FERC Administrative Law Judge, who is typically highly skilled at sorting out the various arguments and regulatory arcana.

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