In France, there is a pair of companies, Bollore and Compagnie de l’Odet, both of which own over 50% economic interest in each other (but not over 50% voting power) through a complex puzzle of holding companies:
When the structure is simplified, the (somewhat simplified) result is:
Odet owns:
1 billion euros in net cash
70% of Bollore
Bollore owns:
81% of Odet
a net 10 billion euro other stock portfolio.
The remaining 19% of Odet and 30% of Bollore are held by other shareholders.
How would the companies be valued (book value) in such a case? Bollore’s value is at least that 10 billion, which they have in their stock portfolio, and 81% * Odet’s 1 billion, but should Odet’s 70% stake in Bollore also be valued somehow (it can’t be very much, of course).
A fun little puzzle. Could this be broken down in a way that the total value must be €1 billion net cash + €10 billion stock portfolio = €11 billion.
Naively, we would get
Odet: €1 billion + 0.7 * €10 billion = €8 billion
Bolloré: €10 billion + 0.81 * €1 billion = €10.81 billion
Total: €18.81 billion
But it was supposed to be €11 billion, from which we get a multiplier of 0.585 and the correct values are
Odet: 0.585 * €8 billion = €4.68 billion
Bolloré: 0.585 * €10.81 billion = €6.32 billion
While it might feel a bit odd at first that Bolloré’s value would be so much below that €10 billion stock portfolio, Bolloré does not actually own that stock portfolio; instead, Odet owns 70% of that stock portfolio (but Bolloré owns 81% of Odet, etc.), which again seems quite logical.
In itself, “merging” this whole entity is probably a good idea. But let’s perhaps rather look at it from the perspective of the remaining shareholders. Let’s simplify the situation a bit, and say that 1 share = 1%. So outside investors have 19 Odet shares and 30 Bolloré shares.
1 Bolloré share then directly owns 1/100 of that 10 billion stock portfolio and then indirectly 81% of Odet’s cash pile, and its Bolloré stake, which then again owns… etc.
The value of one Bolloré share must therefore be at least 1/100 * 10bn = €100m… but how much value does the chain ownership add on top of that?
If the companies were to merge, the combined firm would have that €11bn in total. I actually tried to crunch the numbers with that 58.5% split ratio (= Bolloré owners would get 58.5% of the combined company), but things don’t seem to add up correctly with that, as the current market caps of the companies are approx. 16bn (Bolloré) and 6bn (Odet), and while the market can be wrong, it’s unlikely to be that far off.
That’s exactly where the cross-holding complicates things. In reality, you would own that entire 11 billion euro entity 100% if you could somehow get your hands on that 30% of Bolloré (5 billion) and 19% of Odet (1.25 billion) = 6.25 billion worth of shares.
Perhaps in principle, but in practice, company boards make the decisions, and an individual shareholder would not be able to have the board replaced. Similarly, at general meetings, another company’s board is able to dictate decisions regardless of the opinions of individual shareholders.
In this case, if you actually look at the chart in that first post, you’ll notice that the family owns 50.2% or something like that of a holding company, which owns 50.1% of a holding company, which owns 50.3% of a holding company, which owns X% of Odet, etc. The family only has about a 9% “economic interest” in the company’s profits, but a controlling majority nonetheless. So in itself, voting power isn’t relevant here, because no one else can get it anyway
