Stayer, I think your assertion is that my analysis is too...

That's absolutely correct, yes. That said, the same is true of SOL's ownership of BKW (and all their other investments - total tax liability is a little over a billion if I recall correctly). So if we're comparing the relative value of SOL vs BKW, there's a similar effect on both sides.

The difference it makes is that money sitting in SOL pays less than money sitting in BKW. And this was because SOL was trading at a premium to net assets while BKW was (and still is) trading at a discount to net assets. Of course what happened was that this was in large part corrected, with SOL holders losing wealth and BKW holders gaining some. In a perfectly functioning market, there would be more to come, on the basis that while SOL has fallen to approximately net assets, BKW has not risen much, and still trades at a discount to net assets. But perfectly functioning markets being found only in the shadow cast by flying pigs, I wouldn't hold your breath.

That said, to have not sold SOL in favour of BKW late last year and early this year is an opportunity lost. Even BKW itself made the historic move to sell some of theirs. For a period of time you could actually sell a thousand SOL shares and then buy BKW ending up with MORE than the thousand SOL shares you started with (and some free BKW assets to boot). Even if you think BKW is the less interesting investment, it's nonsense to say "I don't want to get more of my favourite SOL shares for free if it means I have to own all that nasty prime city-fringe real estate that BKW has"...

Taking this argument to its logical conclusion, imagine that a company is listed on both the ASX and the NZX. The shares are A$1 on the ASX, and A$0.50 (say NZ$0.55 on the NZX). Would you say "what difference does it make where your $ sits?"

It always matters where your money sits. Selling overvalued assets and buying undervalued ones is pretty much the definition of what we're all trying to do here.

Be careful also with your assertion that "they will never sell out of each others' shares". This did just happen. I'm not sure it will necessarily happen again soon, but, like me, the BKW board seems to have felt that SOL was so grossly overvalued that it was worth overturning nearly 60 years of tradition and selling the damn things. Frankly, I wished they'd gone further, paying out their SOL shares as an in-specie dividend to their shareholders. It's hard to know whether such an action might have crashed the SOL price, making the move useless. As it was they were only able to achieve about $26 while the market was north of $30, but I guess nobody with a $150M+ bank balance could be convinced to pay as much as the greater fools of the ASX.

Stayer, I think your assertion is that my analysis is too simplistic, in that I'm only looking one layer deep, thus:

BKW owns 39.4% of SOL, value $2.16bn
SOL owns 43% of BKW, value $1.1bn

...when in fact, one needs to take account of the circular nature of this, something along these lines:

BKW owns 39.4% of SOL, value $2.16bn
SOL owns 43% of BKW, value $1.1bn

BKW's $2.16bn ownership in SOL has, in turn, 43% ownership of BKW, value $928M.
SOL's $1.1bn ownership in BKW has, in turn, 39.4% ownership of SOL, value $433M.

(one could reiterate this indefinitely, but I'll stop here in the interests of sanity)

I.e., BKW's holding in SOL is made up in large part by holdings in itself. You could think of this a bit like treasury stock: the company buys its own shares and owns them. This increases the value of the company by the value of those shares. It could sell them and hold cash instead, or it could cancel (destroy) them, thereby reducing the number of shares on issue and increasing the value per remaining share (as the same assets are divided by fewer shares).

That this is the case does not, to my mind, change the calculation. BKW still owns 39.4% of SOL, and the market values that stake at $2.16bn. The fact that some of this value is BKW changes little. Some of the $2.16bn is a coal mine, some of it is a telco, some of it is Brickworks. What of it?

However, this does introduce some unusual price dynamics. Much like in the case of the company owning its own stock, when the price rises, the value of the company rises faster. Consider this:

Today you own 1000 BKW shares, value $17,100. Via this holding, you own 630 SOL shares. (Pause for a moment to contemplate that these alone are worth $14,400)... Each SOL share gives 0.27 BKW shares (149.8M BKW shares * 0.43 / 239.4M SOL shares). Today, that's worth $2908. This is part of the $14,400 that the market is determining that those SOL shares are worth.

Imagine that tomorrow BKW is worth $20. Your holding is worth $20,000, a gain of $2900. However, the value of the "treasury shares" (BKW shares owned by BKW itself via its SOL holdings), has also risen, from $2908 to $3402. A further $494.

Exactly the same would be true if the BKW/SOL cross-holding did not exist, and BKW simply owned the same ~25M shares in itself, say, because it had done an on-market buy-back.

This works the other way around too of course: when the share price of SOL rises, the value underpinning it rises faster, because it owns lots of itself via BKW.

The bottom line for me however is that despite this circularity and the unusual effects that it creates, you CAN simply establish the paper value of a BKW share by adding the value of the SOL shares represented by that BKW share. I.e., one BKW share gives indirect ownership of 0.63 SOL shares. Likewise, one SOL share gives indirect ownership of 0.27 BKW shares.

Ultimately what matters here is to answer the question: if all the assets behind this share were sold today, how much cash would I have?

Circular shareholdings such as this one are not particularly uncommon, and are practically de rigeuer in Korea where they are at the heart of the chaebol system of dynastic businesses including household names such as Samsung. Typically they come about because a small-ish holder seeks to maintain control of an empire which is expanding with other people's capital, as was the case with BKW/SOL. There is research to suggest that they create a number of problems, including lower long term returns to capital owing to the inability to re-allocate capital (particularly in a high capital gains tax environment), and that for similar reasons they depress recovery from economic recessions. They also, arguably, concentrate power, depriving minority holders of rights they would otherwise have. In the case of SOL/BKW, this point was tested in court, and found not to hold.

It's certainly an inelegant mess. With enough market participants failing to understand the mechanics, you can almost see how the BKW:SOL price ratio could get to the point where BKW's non-SOL assets would have a negative value. Almost.

I'd welcome anyone with a different point of view about the implications I've set out here to write up a rebuttal.