RSPT – A Fair Valuation Based on True Value of New and Existing Mines

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Following on from the interest generated by his last post, Mule Stable regular Zebra (James Glover) returns to the subject of the Resources Super Profits Tax in another guest post.

In a previous post I explained how the formula for the RSPT (Resource Super Profits Tax) was derived by considering the Government to be a 40% silent investor in any mining project. I showed that the correct deduction from the return on investments is indeed GBR (Government Bond Rate), as proposed, not a higher rate that includes a “price of risk”. One important thing I missed in this analysis, however, was whether the investment amount (I) was the correct basis for valuing the Government’s new 40% “investment”. I aim to show that the correct variable should actually be the Market Value of Assets (MVA) and as such the appropriate deduction from profits is several times (maybe as much as 4 times) higher for established mines.In the example given based on the mining industry “price to earnings ratio” of 14 the RSPT would only be 9% of earnings. I should emphasise this is not about having separate formulas for new and existing mines but correctly taking into account the fair, market based, price the Govt should pay for it’s 40% share of the earnings.

For new mines MVA = I (where all “=” signs should be taken to mean “approximately equal” to head off the pedants) so the proposed tax is correct in this case.

The Government says that in return for this tax take they are taking downside risk as well as upside benefit. One of the criticisms of the RSPT is that the Government is effectively nationalising 40% of ongoing mines and the GBR deduction is irrelevant as there is no serious downside risk. In the framework I propose the Government is not currently proposing to pay a fair price for this “nationalisation”. If the fair price of the Government’s stake is taken into account then the tax from existing mines is considerably lower than proposed. It may be as low as 9% of earnings. This does not require a backdown by either the miners or the Government, although the Government’s tax take might be less than forecast

If the Government is going to nationalise 40% of a mine – at a fair price – then it needs to effectively pay 40% of the Market Value of Assets (or MVA) for the mine. For new mines the Investment = Equity + Debt is pretty much set at this value. The Government RSPT tax is then:

Tax = 40% x (Earnings – GBR x MVA)

The first term is the Government’s 40% share of the earnings (here taken as Earnings before Tax). The second term is the deduction for the interest that recognizes that the funding of the Government’s share is undertaken by the mine at the Government Bond Rate or GBR. There is no good reason for the Government to pay less than the market value of this asset or MVA. For a new mine just starting up MVA = I, the investment amount, so

Tax = 40% x (Earnings – GBR x I)

If ROI = Return on Investment = Earnings/I then we can write this as:

Tax = 40% x (ROI – GBR) x I

which is the proposed RSPT formula.
For an ongoing mining operation with established operations and contracts, the market value will exceed the book value several times over. I am going to take the very simple assumption that MVA = Price ie the market value of the assets is the market value of the equity. This ignores leverage and is probably too simplistic. Price is based on share price and the number of outstanding shares. In terms of PE-ratio (the ratio of Price to Earnings as determined by the share price) we can write

Tax = 40% x Earnings x (1 – GBR x PE-ratio)

Compared to the original formula the deduction is 40% x GBR x PE-ratio x Earnings. Alternatively we can write this as 40% x GBR x I x MBR where MBR is the Market to Book ratio = MVA/I. So the original Govt funding deduction is just multiplied by MBR. The current formula assumes implicitly that MBR = 1. For existing businesses eg. banks MVA/BVA can be as high as 4 (which is BHPs current value). This gives a very simple deduction in terms of % of earnings, rather than Investment/I, of 40% x GBR x PE-ratio. Note that this is really the same formula for new and existing mines; it just makes proper allowance for the true value of established mines.

So what is the fair deduction for existing mines? It obviously varies with share price and hence market conditions. For mines which are privately held we need a proxy based on publicly traded stocks. The PE-ratio for traded mining stocks is currently about 14. So now, using GBR=5.5%, the fair deduction for the Govt’s nationalised share for existing mines is not 5.5% (as many erroneously claim) or 22% (allowing for a 25% ROI) but 31%! Note this deduction is off the 40% so the total RSPT tax on earnings would be 9%.

So under a scheme based on a fair deduction for existing mining assets the tax should be:

RSPT = 40% x Earnings x (1 – 5.5% x 14) = 9% x Earnings.

After 30% company tax this represent a total tax of 38%. Even if we don’t know what the PE-ratio would be for mines which aren’t publicly traded we can use an industry based proxy for the mines whose stocks are publicly traded. Currently this is in the range 13-14. If I was the miners I’d be pretty happy with that. Maybe they should have taken a closer look at the RSPT before opposing it. All the miners have to do is get the Govt to accept it should pay a fair value for its stake and the framework I propose makes that transparent.

Eliminating the irrelevant

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After going to all the trouble of explaining the “classical” analysis of the Tuesday’s Child problem, here I will explain why I think that analysis ends up with the wrong answer.

This will get into the nuts and bolts of the mathematics of probability again, but I will start with some of the questions which led me to rethink this problem.

In her Math Blog, Tanya Khovanova approaches the problem in a very interesting way. Paraphrasing Tanya, if Mr Smith tells you that one of his two children is a boy born on Tuesday, you will (if you accept the classical reasoning) revise the probability of two boys from 1/4 to 13/27. But, you would do the same if he said the boy was born on Wednesday, or indeed any day of the week. So if he said he had a boy born on *$$*@day (his voice was muffled and you couldn’t quite catch which day he said), wouldn’t you then revise your probability to 13/27 too? After all, you’d make that revision regardless of what day he actually said! If so, couldn’t you then revise the probability to 13/27 even if he doesn’t mention a day of the week and just said he had a boy? This clearly makes no sense and suggests there is a problem with the classical analysis.

The crux of the problem is that if Mr Smith is volunteering information, he could just as easily have spoken of a day other than Tuesday. Indeed, he may have said ‘I have two girls’, ‘Anyone for tennis?’ or ‘The UK doesn’t have a solvency problem the way Greece does’. The situation is very different if you are asking the questions of Mr Smith. If you ask him whether he has a boy born on Tuesday, he is restricted to saying ‘yes’ or ‘no’. At least, that’s the case if you allow the one big assumption I am making here, namely that whatever Mr Smith says, he is telling the truth (even about macroeconomics).

So, exactly how the information is revealed makes a difference. That in itself is well understood, but at this point many people will simply give up saying that there are too many options open to Mr Smith so it is impossible to come to any sensible conclusions. So, they will either give up on the problem or rephrase it to one that can be answered, such as where you ask the questions of Mr Smith, as I did in the Tuesday’s Child post. But, if you rephrase the problem, you are solving a different problem and giving up on the original one. What I will argue here is that all those options open to Mr Smith do not matter at all. Mathematically we can eliminate “irrelevant” options and come up with a perfectly defensible solution to the problem.

To ease into the mathematics, I will go back to Gardner’s simpler two boys problem:

Mr Smith says, ‘I have two children and at least one of them is a boy.’ What is the probability that the other child is a boy?

Before trying to answer that, I will instead ask if Mr Smith had two boys, what is the probability that he would say ‘I have two children and at least one of them is a boy’. It is impossible to say: there are so many other things he could have said instead. But what if I asked about the probability that Mr Smith would say ‘I have two children and at least one of them is a boy’. Again it’s impossible to say, so instead I will ask how does that probability compare to the probability of him saying ‘I have two children and at least one of them is a girl’? I would argue that, by symmetry, these two probabilities have to be the same (whatever they may be). As soon as you accept that, the classical solution falls apart.

Now for the mathematics. To save a bit of space I’ll use X to denote the event “Mr Smith says, ‘I have two children and at least one of them is a boy’.” and I will write Y for “Mr Smith says, ‘I have two children and at least one of them is a girl’.” In mathematical terms, my symmetry argument is that $P(X | BG) = P(Y | BG)$ , even though we don’t know what either of these probabilities are. This is the sort of reasoning I will use to calculate the conditional probability:

$P(BB | X) = P(BB)\frac{P(X | BB)}{P(X)}$

Even though I will not be able to calculate either the top or the bottom term of this fraction, I will be able to calculate the ratio. To do this, I will use an equation I call “eliminating the irrelevant”. For any events A, B and Z, if A is a subset of Z and Z is independent of B then a bit of algebra will show that.

$\frac{P(A | B)}{P(A)} = \frac{P(A | B\cap Z)}{P(A|Z)}.$

I can apply that to the current problem by setting $Z = X\cup Y$ as long as Z is independent of BB. While we have not been told that is the case, it would seem to be an extremely reasonable assumption. If you think of all the other things Mr Smith might have said, is there any reason to assume that he would be more likely to say something other than X or Y simply because he had two boys rather than two girls? I don’t think so. It’s certainly possible that there could be a link, in much the same way that a coin could be biased, but in the absence of any other information we would start by assuming heads and tails are equally likely.

Note that Y by itself is not independent of BB, nor is X. What I am arguing is that the fact that Mr Smith has two boys (BB) does not affect the likelihood that he will say either X or Y as opposed to something else entirely.

The formula above thus allows us to calculate the conditional probability we are after as follows:

$P(BB | X) = P(BB)\frac{P(X | BB\cap Z)}{P(X | Z)}.$

In one fell swoop, we have eliminated the irrelevant alternatives for Mr Smith and now have something we can work with, even though we will never know what the probability of X actually is!

The top line of the fraction is straightforward. If Mr Smith is restricted to X or Y and has two boys, only X is possible, so $P(X | BB\cap Z) = 1$ . The bottom line requires a bit more work. As in the last post, we can break it up into disjoint alternatives:

$P(X | Z) = P(X | Z\cap BB) P(BB) + P(X | Z\cap BG) P(BG) +P(X | Z\cap GB) P(GB).$

Note that I have taken the liberty of dropping one term here as I know that $P(X | Z\cap GG)=0$ . By symmetry, since Mr Smith is restricted to X and Y, $P(X | Z\cap BG)=\frac{1}{2}$ and the same applies for the GB term. So, we now have

$P(X | Z) = 1\times\frac{1}{4}+ \frac{1}{2}\times\frac{1}{4} + \frac{1}{2}\times\frac{1}{4} = \frac{1}{2}.$

Now we’ve got everything we need and so

$P(BB | X) = \frac{1}{4}\times\frac{1}{\frac{1}{2}} = \frac{1}{2}.$

So instead of the classical conclusion that the probability that Mr Smith has two boys is 1/3, we have arrived at a figure of 1/2. The key to this result is that when we ask Mr Smith whether he has at least one boy, the probability that he says ‘yes’ is the same whether he has BB, BG or GB. When he makes an utterance of his own accord, although we don’t know what the probability values $P(X | BB)$ , $P(X | BG)$ or $P(X | GB)$ are, I am contending that $P(X | BB)$ is double the other two (because in those cases he could have volunteered information about a girl). So, when Mr Smith volunteers that he has at least one boy, he is giving more information to us than if he simply answers ‘yes’ to our question.

The same reasoning will also give a probability of 1/2 for two boys in the Tuesday’s child case (there you would set Z to cover the 14 options for Mr Smith of saying one of boy/girl and one of Monday/Tuesday/Wednesday, etc).

To sum up, if Mr Smith volunteers ‘I have two children and at least one is a boy,’ then the probability that he has two boys is 1/2, whereas if you ask him ‘do you have two children and at least one boy’ and he answers ‘yes’, the probability that he has two boys is 1/3. Likewise, if he volunteers that he has a boy born on a Tuesday, the probability that he has two boys is 1/2 but if you ask him whether he does and he says yes, the probability of two boys is 13/27.

This gives the satisfying (and, I think, intuitive) result that the day of the week does not matter and Tanya’s paradox of a muffled word changing the probabilities is resolved.

Tuesday’s Child

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Following on from the teasers in the probability paradoxes post, here is a closer look at “Tuesday’s child”. While it may not strictly be a paradox, it still has the rich potential for generating controversy. In fact, I don’t agree with what could be called the “classical” analysis of the problem. Here I will look at this classical approach and save my own interpretation for a later post.

A warning: this will be the most mathematical post on the blog to date, so it is not for the faint-hearted!

All of these probability paradoxes hinge on the notation of conditional probability. Conditional probability is the probability of one event given that another event has occurred. As a simple example, imagine roll a dice and A denotes “rolling a six” and B denotes “rolling an even number”. Then the probability of rolling a six is 1/6, but the probability of rolling a 6 given that I roll an even number is 1/3.

Now, before getting onto Tuesday’s child, I will go back to the simpler paradox, which I introduced in the Martin Gardner post. Note that throughout this post I will assume that girls and boys are equally likely and I will ignore identical twins (no offence to identical twins, of course!). I’ll quote from Gardner’s “Mathematical Puzzles and Diversions”:

Mr Smith says, ‘I have two children and at least one of them is a boy.’ What is the probability that the other child is a boy? One is tempted to say 1/2 until he lists the three possible combinations of equally probable possibilities – BB, BG, GB. Only one is BB, hence the probability is 1/3. Had Smith said that his oldest (or tallest, heaviest, etc.) child is a boy, then the situation is entirely different. Now the combinations are restricted to BB and BG, and the probability that the other child is male jumps to 1/2.

Without going into my reasons in this post, I don’t agree with Gardner’s solution to the problem as he posed it. But, with a little tweak, I would agree. If instead you ask Mr Smith whether he has at least one boy among his two children and he says ‘yes’ (as opposed to having him volunteer the details), then the probability that he has two boys is 1/3.

I’ll tweak the Tuesday’s child problem in the same way for now. Imagine the problem is now as follows:

Mr Smith has two children. You ask whether he has at least one boy born on a Tuesday. He says ‘yes’. A lucky guess perhaps, but now you wonder what the chances are that Mr Smith’s other child is also a boy.

At this point, we could enumerate all the possible combinations of children and weekdays of birth. All up there are $2\times 7\times 2\times 7 = 196$ possibilities. Looking through that list, we would then scratch all of those that do not have at least one boy born on a Tuesday. In the list that remains, look at the proportion made up by families with two boys. Try it and you’ll find your revised list has 27 combinations in it and 13 of them have two boys, so the probability we are after is 13/27.

For me, that looks a bit much like hard work, so instead I would call on a bit more of the mathematics of conditional probability. Feel free to stop reading now if you don’t have the stomach for even more mathematics!

Mathematically, conditional probability is defined as follows:

$P(A | B) = \frac{P(A \cap B)}{P(B)}$
where the left hand term denotes the “probability of A given B” (and P denotes “probability of”). The top term on the fraction is “A intersection B”, which simply means that both A and B occur.

I will denote by X the “event” that Mr Smith said ‘yes’ to the at least one boy born on Tuesday question (the inverted commas are there because “event” is actually a technical term in probability). The probability we want to calculate is

$P(BB | X) = P(BB) \frac{P(X | BB)}{P(X)}$

Starting with the conditional probability on the top of this fraction, if we have a two-boy family, the answer to “do you have a boy” will certainly be “yes”, so we need to know the probability of at least one of the boys having a Tuesday birth date. There are 7 possible birthdates for each child, giving 49 possibilities. Of these, 7 have a Tuesday for the elder child and 7 for the younger, but this double-counts the case where both were born on a Tuesday, so we have:

$P(X|BB) = \frac{13}{49}.$

One way to calculate the probability of X itself is to break it down into different possible gender combinations:

$P(X) = P(X \cap BB)+P(X\cap GG)+P(X\cap BG)+P(X\cap GB).$

Here I am using the fact that probabilities of “disjoint” (non-overlapping) events add up, i.e. $P(A \cup B) = P(A) + P(B)$ if A and B are disjoint. Using the conditional probability formula, this gives:

$P(X) = P(X | BB) P(BB)+P(X | GG) P(GG) +P(X | BG) P(BG)+P(X | GB) P(GB).$

Now the probability of the boy in a mixed gender family being born on a Tuesday is 1/7 and the probability of having boy-girl or girl-boy are both genders is 1/4. Combining this with the fact that the probability of a boy born on Tuesday is zero in a two-girl family and what we already know about a boy-boy family know gives us

$P(X) = \frac{13}{49}\times \frac{1}{4} + 0 + \frac{1}{7}\times\frac{1}{4} + \frac{1}{7}\times\frac{1}{4}= \frac{13 + 2\times 7}{49}\times\frac{1}{4} = \frac{27}{49}\times\frac{1}{4}$

Putting this all together, we have

$P(BB | X) = \frac{1}{4}\times\frac{13}{49}/(\frac{27}{49}\times\frac{1}{4}) = \frac{13}{27}.$

While you are waiting for the next post with an alternative interpretation, you might want to think about Gardner’s two boy problem a bit more. In order to get to the classical conclusion that there is a 1/3 chance Mr Smith has two boys then you effectively have to assume that if he had one boy and one girl, he would definitely say ‘I have two children and at least one of them is a boy’ and not ‘I have two children and at least one of them is a girl’. Does that really make sense?

UPDATE: Here is a spreadsheet which simulates the classic version of the Gardner problem (i.e. assuming that you ask Mr Smith the question), and here is an alternative analysis.

Probability Paradoxes

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Probability is tricky.

If you are one of those people who likes to say “I was never any good at maths at school”, your response to this would be “of course!”. But probability seems to be tricky for mathematicians too, even for mathematicians who teach probability.

I have always loved probability paradoxes and clearly remember spending most of a train-trip to Edinburgh almost 20 years ago debating the famous Monty Hall problem (see below).

Now I’ve been thinking about paradoxes again. It all started with a passing reference to the two boys paradox in my recent post about the passing of Martin Gardner. Commenting on that post, Bob Walters (who was in fact my honours supervisor a long time ago) drew my attention to his own reflections on that paradox, which opened a can of worms for me. I’ve been obsessing on the topic ever since.

Rather than jumping straight to my conclusions, I thought it would only be fair to give readers a chance to think things through themselves first. So in this post, I will simply state a few well-known probability paradoxes and discuss my own thoughts on each of them in future posts. Feel free to share your thoughts in the comments.

Tuesday’s Child

Bob’s post alerted me to a variant of the two boys problem that has been generating a lot of discussion (here, here, here and here among other places). Appropriately enough, all of this discussion emerged from the most recent Gathering for Gardner, a conference on mathematical puzzles held in honor of Martin Gardner.

So here is the puzzle.

A man says to you “I have two children, one is a boy born on a Tuesday”. What is the probability the man has two boys?

This is a more complicated version of the original puzzle where the man simply says “I have two children, one is a boy”. Classically, the answer to this one is that the probability of two boys is 1/3. The argument is that there are four equally likely probabilities to start with: Boy-Boy, Boy-Girl, Girl-Boy and Boy-Boy*. The statement rules out Girl-Girl, and Boy-Boy is one of the three equally likely remaining possibilities.

I say “classically” because I no longer agree with this reasoning. I’ll explain why in a later post, and for now I’ll just pose another question. Is there any difference between the scenario in which you ask the man “do you have at least one boy?” and the scenario in which the man simply volunteers the information? I think there is a difference and understanding this difference is the key to the puzzle. As for Tuesday’s child, does the day of the week have any bearing on the probability?

Monty Hall

This is perhaps the most famous of all probability paradoxes. It derives its name from the host of an old American TV game show called “Let’s Make a Deal”. Here’s how the problem was posed in a letter to the “Ask Marilyn” column in Parade magazine.

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

Should you switch? Does it matter? When the problem appeared in Parade, it generated an enormous volume of mail, arguing both ways. So, if you think the answer is obvious, it may be worth thinking again!

The Envelope

This is perhaps the trickiest problem of the three.

You are given the choice of two sealed envelopes and told that they both contain money, and that one envelope contains exactly twice as much as the other. You pick an envelope and open it, discovering that it contains, say, $20. You are then given the option of keeping the $20 or switching envelopes.

It is suggested that there is a 50% chance that the other envelope contains $10 and a 50% chance that it contains $40 and that your expected pay-off is therefore 0.5 x $10 + 0.5 x $40 = $25 if you switch. Is this reasoning correct and should you therefore change envelopes?

If that reasoning is correct, doesn’t it also mean that you should switch if the first envelope contains $30 or $500? In which case, why even bother opening the envelope if you know you are always going to switch?

* Here I’m assuming that human babies are equally likely to be boys or girls, which is probably not quite true.

Rolling Stone vs Triple J

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Last month Rolling Stone published a revised list of the 500 Greatest Songs of All Time. The last version of the list was published in 2004 and, while the update brings the count of 21st century songs from 3 to 28, there have not been too many significant changes. The top ten songs remain the same.

TrackArtist

1	Like a Rolling Stone	Bob Dylan
2	(I Can’t Get No) Satisfaction	The Rolling Stones
3	Imagine	John Lennon
4	What’s Going On	Marvin Gaye
5	Respect	Aretha Franklin
6	Good Vibrations	The Beach Boys
7	Johnny B. Goode	Chuck Berry
8	Hey Jude	The Beatles
9	Smells Like Teen Spirit	Nirvana
10	What’d I Say	Ray Charles

Rolling Stone Top 10 Songs

The Beatles still have more tracks in the list than any other band.

	Artist	Song Count
1	The Beatles	23
2	The Rolling Stones	14
3	Bob Dylan	13
4	Elvis Presley	11
5	U2	8

Rolling Stone Top 5 Artists

But what interests me most is what this list has to say about Rolling Stone, its readers and the compilers of the list. A while ago I wrote a post about Triple J’s Hottest 100 of All Time where I noted that the Triple J’s list was heavily skewed to the 1990s. This chart shows the distribution by decade.

So how does the Rolling Stone list compare? Here is its distribution.

The difference between the two should be clear, but just to labour the point, here are the two distributions side by side (and converted to percentages since the Rolling Stone list has five times as many songs in it).

Rolling Stone vs Triple J by Decade

I suppose it should come as no surprise that the baby-boomers love their 60s and 70s music and the Gen-Ys love their 90s music. But, having spent my formative music-listening years in the 80s, I cannot help but feel that decade is under-represented by both charts. Or is that an accurate reflection of the quality of music in the 80s?

And another question: how likely is it that this post will end up in the headlines of Bubblepedia? Fortunately, not very.

Data: the list was obtained from here, a reference obtained from the Wikipedia entry. I fixed some typos, added years and loaded the data into a Google docs spreadsheet. Let me know if you see any remaining errors.

No move expected by the Reserve Bank

Vale Martin Gardner

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I was saddened to hear today that Martin Gardner has passed away at the age of 95. Born in 1914, Gardner was a prolific and gifted writer. He is best known for his mathematical and scientific writing, but he also dabbled in magic and philosophy. His The Annoted Alice is perhaps the ultimate edition of Lewis Carrol’s Alice in Wonderland.

For many years he wrote a column on “Mathematical Recreations” in Scientific American, which I read avidly as a child. These columns gave me endless pleasure, solving puzzles, constructing tetraflexagons and hexaflexagons and pondering probability paradoxes.

I am sure it was reading Gardner that I first came across the peculiar “second child paradox”. While perhaps not strictly a paradox, it is at least a little counter-intuitive and goes something like this. Imagine you bump into an old friend you have not seen or heard from in years who tells you she has two children and one of them is a boy. What are the odds that she has two boys? Since the possibilities are Boy-Boy, Boy-Girl, Girl-Boy, the answer is 1/3. But if she had told you she has two children and the oldest is a boy, the odds that she has two boys are 1/2!

Of his science writings, my favourite is The Ambidextrous Universe (now in its third edition), which explores left and right “handedness”–the difference between an object and its mirror image–and its role in the physics of the universe. In exploring the notion of mirror symmetry, Gardner asks the strangely puzzling question why does a mirror reverse left and right but not up and down?

Gardner also gave me my first exposure to the debunking of pseudo-science. In 1952 he wrote “Fads & Fallacies in the Name of Science”, which takes on an eclectic mix of peculiar beliefs ranging from flat-earthers to UFO-logists, from bizarre beliefs about pyramids to ESP and from Forteans to medical quackery. But the chapter that has really stayed with me since reading Fads & Fallacies almost 30 years ago is the one on dianetics, the “science” behind Scientology.

In this chapter, Gardner describes the notion of an “engram”. According to adherents of dianetics, the unconscious mind has a habit of making recordings of painful experiences. These recordings, particularly those made as a child or even in utero, have a tendency to cause problems later in life. Of course, trained “auditors” can help identify and purge troublesome engrams. As Gardner notes, engrams seem to be susceptible to bad puns:

An auditor reported recently that a psychosomatic rash on the backside of a lady patient was caused by prenatal [engram] recordings of her mother’s frequent requests for aspirin. The literal reactive mind had been feeding this to her analytical mind in the form of “ass burn”.

As a skeptic, Gardner would look askance at anyone claiming to be able to predict the future, but it is a pity his own powers of prediction were not more accurate:

At the time of writing, the dianetics craze seems to have burned itself out as quickly as it caught fire, and Hubbard itself has become embroiled in a welter of personal troubles.

Sadly, Scientology is not only still around, it is probably stronger than it was back in the 1950s.

Science, mathematics and skepticism all continue to be very important to me, and I suspect that Martin had no small part to play in sowing their seeds in my mind many years ago. There are many others like me he has inspired and, along with his enormous catalogue of publications, that inspiration is a wonderful legacy.

Following one link too few…a mea culpa

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My last post, Are Australia’s banks about to collapse?, took Steve Keen to task for a presentation on the dire outlook for Australia’s property market and its banks. However, a commenter has pointed out that it was not Steve’s presentation! Moreover, the final slide of the presentation, which is in very poor taste, appears to have been added by Business Insider.

How did I get that wrong? By following one link too few. Here is a quote from the Business Insider article where I found the presentation:

according to this presentation from economist Steve Keen, courtesy of Mish’s Global Economic Analysis

Following the link to Mish’s Global Economic Analysis gets a bit closer to the truth (“on his blog” not “by him”):

Australian economist Steve Keen addresses that question and more in a presentation on his blog How to Profit From the Coming Aussie Property Crash (and Banking Crisis)

At that point I made the mistake of not following the final link to Steve’s blog and instead read the presentation. Slide 3 was a familiar one I had seen in various forms and by then the notion that Steve had written the presentation was firmly implanted. The style should have given me pause for thought as it is extraordinarily hyperbolic.

If I had followed the final link, as indeed I should have done, I would have found a post entitled “Excellent presentation on Scribd on Australian housing” the following on Steve’s blog:

This presentation was noted by a blog member today. Take particular note of slides 21-20 which compare the balance sheets of US and UK banks to that of one Australian bank, the Commonwealth.

How to Profit From the Coming Aussie Property Crash (and Banking Crisis)

So who did write the presentation? Who knows, but it was uploaded to Scribd by someone called Karenina Fay.

In any event, while Steve may think it is an excellent presentation and I clearly do not, he did not write it and hence this a mea culpa. I apologise for following others in incorrectly attributing this presentation to Steve and I have edited the original post. I will also be endeavouring to click that last link in future!

Are Australia’s banks about to collapse?

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UPDATE: In this post I repeated Business Insider’s mistake of attributing the presentation I criticise to Steve Keen. While Steve considers it an excellent presentation, he did not write it and I apologise for not confirming the source before publishing this post. I have now struck out the incorrect attributions. My criticisms of the presentation itself still hold, which is why I am leaving the post up in its edited form.

Steve Keen and his forecasts of a property market collapse have received plenty of local media coverage over the years. Now he has come to the attention of the international press as well.

In April, Keen hiked to the top of Mount Kosciuszko after losing a bet about the direction of property prices with Macquarie Bank strategist Rory Robertson. This event was enough to prompt an extensive review of Keen’s concerns in the New York Times. Curiously, Robertson himself did not receive a mention, despite winning the bet.

Now the US business site Business Insider, which has a penchant for drama, has published one of Keen’s presentations a presentation, incorrectly attributed to Keen, under the headline “Here’s What You Need To Know About The Major Property, Debt, And Banking Crisis Brewing In Australia”.

One of Keen’s central concerns is the size of private sector debt in Australia. This is a legitimate concern and should receive more focus than misguided fears about Australian government debt. However, I am far less pessimistic than Keen about the outlook for Australian property prices.

As for the Business Insider presentation, Keen takes his concerns it goes too far, to the point of unsupportable alarmism. The final slide of the presentation is evidence enough of this, not to mention being in extremely poor taste. This slide appears to have been added by Business Insider! If that is not enough to convince you, I will consider just one of the arguments offered by the anonymous author Keen.

On slide 22 of the presentation, he writes:¹

Look at CBA 2009 annual report—Leverage ratio is almost 20 times (total assets of $620.4 billion against $31.4 billion of equity). Of $620.4 billion of assets, $473.7 billion are loan assets. If around 6.6% of CBA’s loans go bad (any loans not just mortgages), 100% of its shareholder equity will be wiped out!!

(the bold italics are not mine, they appear in the presentation). Here the implication is something like “6.6% is not very much. Wow! CBA could easily collapse!”. But, that line of thinking does not stand up to even moderate reflection.

Crucially, we must understand what “going bad” means for a loan. It does not mean losing everything, which is in fact very rare for most types of bank loans.

Over half of CBA’s are home loans and these are secured by the property that has been mortgaged. According to their half-year presentation², based on current market valuations, the average loan-to-value ratio (LVR) for CBA’s portfolio is 42%. This means that, on average, the value of the property is more than twice the loan amount. This gives the bank an enormous buffer against falls in property prices. Of course, this average conceals a mix of high and very-low LVR loans. Even assuming that loan defaults occurred on a higher LVR section of the portfolio, say with an average LVR of 70%, and allowing for Keen’s oft-quoted figure of a 40% decline in house prices, CBA would still only lose 14% on their defaulting loans³. Even then, this does not take into account the fact that, like other lenders, CBA takes out mortgage insurance on loans with an LVR of more than 80%.

But we can be more conservative still. In their prudential standards, the banking regulator APRA considers a severely stressed loss rate on defaulting home loans to be 20%. To suffer actual losses of 6.6% in their mortgage portfolio, CBA would have to suffer a default rate of at least 33%! This would be astonishingly unprecedented. Currently, the number of CBA borrowers late on their mortgage payments by 90 days or more is running at around 1%. Most of these borrowers will end up getting their finances back in order, so for actual defaults to reach 33% is inconceivable. A default rate of a “mere” 2% would be extraordinary enough for CBA.

As for the rest of the $473.7 billion, it includes personal loans, credit card loans, business loans and corporate loans. The loss rates on some of these loans can be higher than for mortgage portfolios, but losing everything on every defaulting loan is still highly unlikely. So to suffer 6.6% in actual losses on these loans, defaults would have to run at a far higher rate. Furthermore, since the dire prognosis for the banks is rooted in the view that the property “bubble” is about to burst, presumably the argument would not simply be based on everything other than the home loan portfolio collapsing.

If property prices do fall sharply and our economy has another downturn, will bank earnings be affected? Of course. Are they teetering on the brink of collapse? Of course not.

¹ While there is a footnote on the slide referencing this post, what is not made clear is that the whole paragraph is a direct quote rather than Keen’s own words. Presumably he agrees with it though!

² Page 84.

³ If property prices fall to 60% of the original value, the loss on a 70% LVR loan would be (70% – 60%)/70% = 14.3%.

Resource Super Profit Tax Everything Correctly Explained (R.S.P.T.E.C.E.)

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This guest post from Mule Stable regular Zebra (James Glover) delves into the details of the proposed Resources Super Profits Tax.

The Australian Government (hereby known as the Govt) has proposed a Resources Super Profits Tax (RSPT) for mining companies. Superficially it appears to be a 40% tax on all profits (measured by Return On Investment or ROI) in excess of the Govt Bond Rate (or GBR, the interest rate at which the Govt borrows money, over the long-term).

The key points of this article are:

1. The GBR is the correct threshold level for RSPT,

2. If the Govt increases the threshold above GBR this will represent a subsidy of miners by taxpayers,

3. The RSPT will benefit small and marginal mining projects to get finance through partial Govt backing of risks.

So for example suppose miner Mineral Wealth of Australia (MWA) invests $1bn in the Mt Koalaroo Iron-Ore mine. MWA is a wholly owned subsidiary of Silver Back Mining (SBM). In the year following they make $200m profit or a return on investment (ROI) of 20%. If the GBR = 5.5% then the 40% RSPT means a tax revenue to the Govt of Tax = 40% x (20%-5.5%) x $1000m = $58m.

This seems very straight forward. It appears that the Govt is saying that GBR represents some “fair” level of return and anything in excess of this is a “super profit” to be taxed accordingly. Not at the normal company tax rate of 30% but a “super tax” rate of 40%. This is how it has been presented by both sides in the media. Arguments against the RSPT have focused on whether the GBR as a “risk-free” rate is the appropriate benchmark for a risky profit stream. Indeed it is not but in fact this isn’t what the RSPT is about. For example normally taxes on profits have no negative impact on the Govt if the company loses money. In the case of the RSPT though the Govt has stated that 40% of any losses can either be claimed back from the Govt (as a refund) or carried over to other projects.

So what is the RSPT? A good way to consider it is if the Govt took a 40% stake in MWA as a “silent partner”, leaving SBM with a 60% stake. In this case we would expect the Govt to contribute $400m of the investment costs (raised presumably through issuing bonds at the GBR or equivalent). In return it would get 40% of the profit. The Govt return would therefore be 40% of the profit less the cost of funding its 40% investment ie Tax = ROI x 40% x I – GBR x 40% x I = 40% x (ROI – GBR) x I.

This appears to be the formula that the Govt has presented to calculate the RSPT and in this derivation it is quite straightforward. However the Govt appears to be getting something for nothing since it isn’t actually stumping up the $400m in investment capital. So what’s going on? A clever piece of financial engineering that’s what. The Govt avoids raising the capital itself (and hence have it be counted as Govt debt) by getting the project to raise it on the Govt’s behalf.

(You can easily skip the next paragraph if you aren’t interested in the details of mine financing costs)

Whilst MWA raises 100% of the $1bn in capital the Govt appears to get the upside (and potential downside) as if it has contributed $400m without doing so. Money for old rope you say. However consider MWA not to be the stand-alone mining company SBM, but the joint venture beween the Govt and SBM. Suppose MWA borrows $1bn in capital at its Project Funding Cost (or PFC). This PFC will be lower than the SBM’s Miner’s Funding Cost (or MFC) as the Govt is now backing 40% of all liabilities. In fact in an efficient market we deduce PFC = 60% x MFC + 40% x GBR. If MWA then allocated these funding costs accordingly it would charge the Govt its share, risk-weighted, not PFC, but GBR. If the GBR = 5% and MFC = 8% then we expect PFC = 6.8% not the 8% if SBM was the sole investor. Under this arrangment SBM’s cost of funding (in % terms) its effective 60% share of the joint project is the same as its stand alone cost of funds, as it should be.

An argument against raising the threshold above GBR is that this will effectively lower the miners’ cost of funds, the difference being borne by the Govt and hence us taxpayers. No wonder miners are arguing so vehemently for the threshold to be raised. In fact it can be shown that raising the threshold to 11%, as some propose, and using a GBR of 5.5% would effectively reduce the miners’ cost of funds by a whopping 3.67%! If you want a formula for the Miners’ Taxpayer Subsidy(MTS) it is: MTS = 2/3 x (Threshold – GBR) in terms of the miners’ funding cost discount (paid for by the taxpayers remember); or MTS = 40% x I x (Threshold – GBR) in $ terms. For the Koalaroo mine this would represent $22m of funding cost transferred from the mining company SBM to the taxpayer. That’s you and me. You don’t see that in their ads.

From the Govts perspective the advantage to them is that the investment does not sit on their balance sheet but the project company MWA’s and in effect SBM’s balance sheet. From a financial engineering point of view all this makes perfect sense. Having said that, it was precisely this sort of clever off-balance sheet flim-flammary that got Greece (and Lehman’s et al) in trouble. We need to make absolutely sure it is properly accounted for.

Update: Several commenters have pointed out the effect on mine financing of the RSPT. Specifically with the Govt backing 40% of any losses smaller stand-alone projects will find it easier to get project finance. As discussed above the funding cost will be lower with the Govt’s partial backing. The operating profit (so called EBITDA) of the project is unchanged so this makes them more, not less, viable. This is at odds with what the miners have been saying. Even existing projects with refinancing clauses in their loans should find it easy to convince their lenders to reduce their interest payments. For large global miners such as BHP-Billiton, who issue bonds, it will be harder to disentangle the Australian RSPT benefit to their overall cost of funds and hence spreads. But the market should over time price this in with lower spreads on their bonds. With a reduced cost of funds miners will be able to leverage their existing equity across more projects and make up for the 40% the Govt now takes out of individual profits (and losses) through the RSPT.

Update: Tom Albanese, CEO of Rio Tinto was on Inside Business on ABC on Sunday May 30. It is interesting that in arguing against the RSPT he referred to the unfairness of the Govt coming in as a 40% “silent partner”, and not about the GBR threshold. He clearly understands the true nature of the RSPT. While it was self-serving he emphasised (in my terminology) the determination of Investment or “I” for existing projects. Depreciation comes into it but some of these projects are decades old and it would an accountant’s dream/nightmare to work out the correct value of I to base the Govt’s GBR deduction on. He also questioned the “principle” (his word) of the Govt forcibly coming in as a “silent partner” on projects which are clearly profitable going forward, having survived to this point. After all they are not compensating mining companies for mining projects that failed in the past. I’m afraid I have to agree with this point, though I think it is more complex than I currently comprehend. It is good to see the RSPT being debated for once without the disinformation we have seen from less eloquent opponents. After all the Govt did say at the beginning that it was these sort of aspects of the RSPT they were prepared to negotiate on, not the 40% and not the GBR threshold.

UPDATE: Zebra looks at a fair value approach to the RSPT.

Stubborn Mule

Obstinately objective