Smith Barney Math

I'm trying to work out the mathematics of the proposed joint venture between Citigroup and Morgan Stanley, and what it does for Citi's balance sheet, using stories from the FT and Bloomberg.

According to the FT, Citigroup has 15,500 brokers; according to Bloomberg, the companies have 22,000 brokers between them. Let's be charitable to Citigroup and assume that Citi's brokers are worth just as much, on a per-broker basis, as Morgan Stanley's. And let's further assume that the FT is right and Morgan Stanley is going to pay Citi $2.5 billion for a 51% stake in the joint venture. How could that correspond to the $10 billion gain Bloomberg says that Citi would book?

If the joint venture simply merged on an all-brokers-are-equal basis, then Morgan Stanley would own 6,500/22,000 or 29.5% of the joint venture. So if it ends up with 51%, or 11,220 brokers, that means it's essentially buying 4,720 brokers from Citigroup for $2.5 billion. Which values each broker at about $530,000.

At that valuation, the entire joint venture would be worth $530,000 times 22,000, or $11.65 billion. Citi will have received $2.5 billion in cash, and would own 49% of the joint venture, worth another $5.7 billion, for a total of $8.2 billion.

If that's the case, how on earth can Citi gain $10 billion "from writing up the value of Citigroup's Smith Barney brokerage unit to the new price set by the deal"? Smith Barney might not be worth a lot on Citi's balance sheet right now, but it's surely worth more than $0.

And this puzzles me, too:

The gain of $5 billion to $6 billion after taxes would flow into Citigroup's capital...

After taxes? What taxes? I thought that Citi had managed to lose so much money of late that it has enormous tax losses which essentially mean it's not going to pay any taxes for the foreseeable future. But now Bloomberg's implying that 40% to 50% of the $10 billion gain on Smith Barney will have to be paid in taxes -- which seems like a ludicriously high tax rate at the best of times.

Is there something I'm missing here? Are Smith Barney brokers actually worth more than Morgan Stanley brokers? Are some of the numbers wrong? Or is this just a case of journalists getting different numbers from different sources, and not stopping to ask whether they play nice with each other?

Update: A reader points out that the Bloomberg article does talk about "a $20 billion joint venture", and only "as much as" $10 billion in Citigroup gains. So maybe we can work backwards from the $20 billion number? That would value the joint venture at about $900,000 per broker, on average.

But let's say that the Citi brokers are worth only $800,000 each, while the Morgan Stanley brokers are worth $1.2 million apiece.

In that case, the joint venture before any cash payment would be worth $800,000 times 15,500 on the Citi side, or $12.4 billion, and $1.2 million times 6,500 on the Morgan Stanley side, or $7.8 billion. Total: just over $20 billion, with Morgan Stanley having a 39% stake. In order to raise its stake to 51%, Morgan Stanley would need to buy another 12%, and 12% of $20 billion is $2.5 billion.

That would explain the $2.5 billion. After receiving the cash, Citigroup would also have 49% of a $20 billion joint venture, worth $9.8 billion. So altogether it would have $12.3 billion, and depending on the current book value of Smith Barney, a large chunk of that might find its way into write-ups.