It's the exclamation point, probably. Photographer: Andrew Harrer/Bloomberg
It's the exclamation point, probably. Photographer: Andrew Harrer/Bloomberg

Yahoo Inc. is a public company consisting of a portfolio of

  1. whatever you think Yahoo is,
  2. a 35 percent stake in a separate but similar publicly traded company called Yahoo Japan, and
  3. a 24 percent stake in a separate, different, soon-to-be-publicly traded company called Alibaba.

My Bloomberg View colleague Matt Klein ran the numbers in March, and non-Bloomberg-affiliated Matt Matt Yglesias ran them again today, and the numbers tell you that 2+3 > 1+2+3, as it were: Yahoo's Alibaba and Yahoo Japan stakes add up to be worth more than Yahoo is worth. Meaning that Yahoo's actual business -- Yglesias calls it "Tumblr and Flickr and the iOS weather app that I love and all the news sites and the mail and the fantasy sports stuff" -- is worth a negative amount of money, something like negative $13 billion today.1

One obvious question is, how can that be true? 2 The actual Yahoo business -- call it "Core Yahoo" -- still makes hundreds of millions of dollars a year in profits, which theoretically belong to shareholders. A thing that pays you positive hundreds of millions of dollars a year shouldn't be worth negative billions of dollars.

Of course, profits that theoretically belong to shareholders aren't necessarily paid out to shareholders: Yahoo pays no dividend and has a ... checkered management history, so you could easily take the cynical view that Yahoo will plow those profits back into a declining business, be completely mismanaged, run the business into the ground and leave shareholders with nothing. Fine! But:

  • Unless the probability of that outcome is 100 percent -- a rare thing in this life -- then Core Yahoo should have some positive value; and
  • Shareholders can never be left with less than nothing, so even if the run-into-the-ground scenario is 100 percent likely, Core Yahoo should be worth zero, not billions of dollars less than zero.

So the puzzle remains.

Now, there was a significant sleight of hand in that last argument. Core Yahoo can easily be worth less than zero: It could switch from making profits each year to making huge losses each year. If Core Yahoo has those losses as part of the broader Yahoo Inc. public company, Yahoo Inc. will have to pay to cover the losses. It can do this by selling off some of its Alibaba shares or whatever, reducing the amount of valuable Alibaba left for Yahoo's public shareholders. So Core Yahoo could in fact have a negative value to Yahoo's shareholders, by reducing the amount of Alibaba that they effectively get.

On the other hand, if Yahoo were divided into three separate public companies -- call them Core Yahoo Inc., Yahoo Japan Holdings Inc., and Yahoo Alibaba Holdings Inc. -- then Core Yahoo Inc. would have no claim on the Yahoo Japan or Alibaba shares, and so could never be worth less than zero to its shareholders.

I guess this is fairly obvious, but it leads you to a general theory of the conglomerate discount, which is that a business can be worth less than zero (to shareholders), but a company can't be (to shareholders). I once tweeted this, but it also seems to be a real thing; here is a paper formalizing it.3 And it's true of good businesses as well as bad ones, since every business has some probability of ending up with a negative value. Google makes a lot of money now, but there's some nonzero probability that the present value of all of its future cash flows as an enterprise will be negative (driverless car rampage, trillions of liability, etc.). But its stock value can't go below zero.

A fun question is, as fiduciaries for shareholders, should Yahoo's directors split into three separate companies to maximize value? If YJHI and YAHI are worth around $9 billion and $40 billion, and Core Yahoo Inc. is worth around, I don't know, one penny, then just doing some corporate restructuring should create $13 billion in free shareholder value. Why not do that? Some thoughts in the usual place. 4

But the broader point is that you shouldn't be too quick to blame either business incompetence or investor irrationality for the negative value of Core Yahoo. Core Yahoo isn't worth less than zero because investors don't know it exists, or because the expected value of its future cash flows is really negative. Core Yahoo is worth less than zero because it's an arithmetic residue of taking a bunch of businesses with very public price tags on them and applying a conglomerate discount.

That discount isn't really about the viability of the core business; it's about the fact that investors don't have direct access to any of the individual businesses, but have to buy them in packaged conglomerate form where any gains on the business they want can be wiped out by losses on the ones they don't. And that's as true of Alibaba and Yahoo Japan as it is of Core Yahoo: 5 Each of those businesses would, as a matter of arithmetic, be worth more on its own than it is in Yahoo. Each share of those businesses that Yahoo owns is worth less to Yahoo shareholders than a share that those shareholders own directly.

But every business everywhere would, as a matter of the same arithmetic, be worth more on its own than it is as part of a bigger company, which is why you always get a lot of people asking that companies break themselves up. Usually, though, the companies can come up with a plausible (and often correct!) argument that the businesses enhance each other as a business matter enough to overcome the disadvantage that they have as an arithmetic matter. Google's driverless car business would have more theoretical option value as its own company, but it also probably wouldn't exist as its own company, so there's a good reason to keep it within Google.

The weird thing about Yahoo is just that the other businesses are so visibly separate, and moving so inexorably off on their own. It's not entirely fair to blame Yahoo's core business for that, but it is the most obvious place to put the blame.

1 In ugly table format, just to be different:

Source: Filings, Bloomberg.
Source: Filings, Bloomberg.

2 It's possible that it's not, of course, as the math relies on analysts' estimates of what Alibaba will be worth when it goes public in the U.S. later this year, and perhaps those analysts are wrong. Certainly there is a wide range of estimates; this Bloomberg News article quotes one analyst putting Alibaba's value at $200 billion. But there's also a huge margin for error; the breakeven Alibaba value -- the value at which Yahoo's core business is worthless, given today's Yahoo and Yahoo Japan market caps -- is about $113 billion. So the initial public offering would need to go pretty terribly to imply any actual value in Yahoo's business.

3 From the abstract:

We show that a conglomerate can be regarded as an option on a portfolio of assets. By splitting up the conglomerate, the investor receives a portfolio of options on assets. The conglomerate discount arises because the value of a portfolio of options is always equal to or higher than the value of an option on a portfolio.

The stock of a levered company is like an option on the assets of that company, with a strike price equal to the debt. Options are worth more when the volatility of the underlying asset increases, and the volatility of a basket of not-perfectly-correlated assets (Core Yahoo, Alibaba, Yahoo Japan) is less than the volatility of the individual assets, since sometimes their moves cancel each other out. You'd rather own options on the values of the three individual assets than own one option on the sum of their values.

4 One straightforward obvious answer is that Alibaba is in the middle of its IPO process and a Yahoo restructuring might distract from that -- and that the best way to unlock the Alibaba value is to let it trade and then figure out what to do. Presumably Yahoo will sign a lock-up promising not to get rid of its Alibaba stake for at least six months or so after the IPO, further delaying any potential spinoff. (I mean, I would argue that Yahoo could just spin off Core Yahoo, leaving current Yahoo Inc. to just hold Alibaba and Yahoo Japan, but I'm obviously not in charge.) But, like, a year from now? Some sort of separation seems worth looking into if Core Yahoo still has a negative value.

Another possible answer is tax. Yglesias says, "some of this is likely attributable to tax effects. If Yahoo fully liquidated its stake in Alibaba and then tried to dish $40.32 billion out to its shareholders, Uncle Sam would end up taking a healthy cut." You could avoid that by just dividending the Alibaba shares themselves to shareholders; my guess is that that couldn't be done as a tax-free spin-off but it should avoid corporate-level tax and just be taxable as a dividend to shareholders. The top dividend tax rate is 20 percent, so that creates at most $10 billion of tax liability against the $13 billion of shareholder gain, even ignoring the fact that many holders are tax-insensitive. (And, again, you could imagine a more creative solution like spinning off Core Yahoo and leaving Alibaba behind, or splitting into three separate holding companies, which might reduce the tax burden at the cost of some sort of complication discount.)

Then there are all the bad reasons. If you're a director or officer of Yahoo the conglomerate, you'd rather run (and get paid like you run) a $36 billion company than a one-penny company, or whatever Core Yahoo would actually be (single-digit billions? More?). So there are obvious personal-interest reasons to resist a shareholder-value-maximizing, but size-reducing, transaction.

Incidentally, Dan Loeb's 2011 activist campaign at Yahoo included arguments for unlocking the value of Alibaba and Yahoo Japan, but at the time he estimated that Alibaba was worth $25 billion and that Core Yahoo had some positive value, so he didn't give it the focus it might get now. Perhaps post-Alibaba IPO we'll see Carl Icahn look into this; his luck with separating businesses is due to improve.

5 A little less in that they're their own limited liability companies, though that's not a conceptual objection. Just think of the enterprise of managing the Alibaba shares for Yahoo as its own business; it could find a way to have a negative value ("Guys, let's take out a huge margin loan!").

Perhaps a bigger problem is that the sensible formalization of the conglomerate discount, as the difference in value between a basket of options and an option on a basket, relies on there being some debt. Yahoo has $5 billion of cash and marketable securities and $2.3 billion of long-term liabilities, so negative net debt. Again, this is not a conceptual problem exactly: just think that Yahoo has $2.3 billion of debt and four risky businesses, (1) managing its cash, (2) managing its Alibaba shares, (3) managing its Yahoo Japan shares and (4) its actual business. But it's weird; the size of the conglomerate discount should increase with debt (more debt = more option value = more value to lose), and here debt is low-to-negative.

To contact the writer of this article: Matt Levine at mlevine51@bloomberg.net.

To contact the editor responsible for this article: Zara Kessler at zkessler@bloomberg.net.