The public data pertaining to SBS shares are somewhat confusing, and that’s putting it mildly. Even the 2002 prospectus introducing the American Depositary Shares (ADS, or ADR’s) did only add to the mystery. But we finally got some definite answers.

We were confronted with some confusing figures in researching SBS (which we published yesterday). Some data one comes across:

- 2008 eps (earnings per share) forecast on average $5.16 (Yahoo) and $5.72 (MSN)
- 2008 first half year eps $1.27 (MSN)
- 2007 eps in real is 4.6 (MSN)
- Total outstanding shares are 227.84M (The state has 50.3% of that)
- Total net profit in 2007 was 1,048.7M in real (MSN), which corroborates the 4.6 eps and the share count

However, what stuck in our throat was that earnings estimate for this year of US$5.16 per share from Yahoo. That just didn’t seam right. It would be more than 10 real per share, or more than 2 billion real in net profits while they did just under 6B real in revenue in 2007. 2008 could be better, but not that much better. We came up with two possible explanations:

- The eps estimates for 2008 are not in US$, they are in real. That would add up, sort off.
- The people doing the the estimations leave out the 50.3 public stake (the Brazilian state), perhaps because these are just a controlling stake without being an economic stake. That seemed already quite weird, but it would, in fact, also add up. We checked for the status of the state shares, and these are just common shares, so they do share in the spoils.

We concluded that the first possibility is way more likely, and considering that there were a few other anomalies in the public figures (look at Yahoo’s count for outstanding shares, for instance, at a curious 911,000!) we thought they just made a mistake. It happens.

It turned out that the ones who could have made a mistake were ourselves, however as somebody pointed to a third option, one ADS equals two common shares (listed in Brazil). That could indeed, once again, make the sums add up. So we’re looking into that, with some trepidation, as we didn’t come across any of this when we were reading stuff for our research.

So what we did is go to the prospectus for the ADS introduction in 2002. Here is what we found:

- Each American Depositary Share, or ADS, represents 250 common shares, from the 2002 ADR prospectus
- The common shares are listed and traded on the Sao Paulo Stock Exchange. On May 9, 2002, the closing sale price for our common shares was R$121.00 per 1,000 shares, which is equivalent to US$12.34 per ADS at the exchange rate in effect on that date.

Good to see that shares are still up from their 2002 levels! (not every company can say that, these days), but, more seriously, how does this fit in? Well..

- There are 227.84/250 = 911,360 ADS. So Yahoo was actually on to something when they gave (roughly) this number for outstanding shares which we initially found so curious.
- However, it doesn’t help that Yahoo then deducts a rather ridiculous market cap (15.27M, while the enterprise value on the same page is $2.35B!); shares short (475.85K, but this is somehow only 0.7% of shares outstanding) and an even more ridiculous eps of $529.50. You see, this is what we mean. Share count numbers (ADS and Brazilian shares) are used at random, giving a very confusing picture.
- The ratio of one ADS to 250 common shares doesn’t make sense, and anyway, since an ADS only gives the right to buy a certain amount of the common shares, we don’t see any reason not to base all calculations on the number of common outstanding shares, which happens to be 227.84M.

**The last angle we could think of is to see the Brazilian listing**. Well, it turns out we should have started with this because **here is, finally, the answer**. It turns out that the Brazilian shares trade on roughly equal prices in real as do the ADS in US$, which, considering the exchange rate (2.28 real per US$) can only mean that they trade two for one, meaning one ADS is only two common shares (the ones listed in Brazil).

That, in fact, warrants quite different conclusions from our article yesterday.

**The stock is twice as cheap as we thought**. Price/earnings ratio, even the trailing (2007) one is just 4.68, and since it so happens there are roughly two real per dollar (at least until recently, the real is losing steam as we speak) and apparently there are only half the number of ADS compared to the common shares in Brazil, it makes not that much of a difference if you express p/e’s in reals per brazilian common shares or US$ in ADS’s.- Somewhere between 2002 and now there must have been a change in the ratio of ADS to common share
- To avoid any mistakes, we still think it’s way better to calculate eps and p/e in terms of the common shares and not the ADS (which only represent rights to buy a certain amount of the common shares anyway)
- One comfort, we’re not the only one who made a mess of this, and unlike Yahoo, we got it right, in the end.. And it was Yahoo that send us into the wilderness anyway.

I am still quite confused. On the basis of your very complex calculations, could you kindly tell me what SBS’s PEG Ratio is right now?