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I’m a sucker for a little puzzle and I guess this Knight-Getco-Virtu thing qualifies, so let’s just bop around doing some silly arithmetic about it. Knight, the trading firm that slow-burn blew itself up this year, is looking for buyers, and Getco and Virtu seem to be those buyers. On the table we have:

- An offer from Getco to buy half of Knight’s shares for $3.50 in cash and leave the other half outstanding in a new merged Knight-Getco, and
- A rumor of an offer from Virtu to buy all of Knight’s shares for $3.00 in cash.

Virtu’s deal is worth $3.00, I guess. Getco’s deal is more complicated, but it’s got to be worth … at least $1.75, no? Plus whatever a (half of a) share in the new company is worth. What is that? Well it’s a proportionate amount of

- Whatever Knight is worth,
*plus* - Whatever Getco is worth,
*minus* - The cash that is paid out to cash out half of the shares, all
*divided by* - The number of shares in newco.

Plus synergies, etc., which are probably a thing. Rapacious prop traders + naive retail order flow = synergies!

Anyway you can start on the Getco deal’s value by mathing out tangible book value numbers. The offer implies (1) that Knight’s tangible book value is $1,189mm^{1} and (2) that Getco’s tangible book value is $735mm.^{2} Take that and subtract $539mm paid out to Knight shareholders and you get a tangible book value of newco of $1,385mm. Divide that by the 395mm-ish newco shares outstanding and you get, magically, $3.50 per share, because that is the number they are solving for.

So if both Getco and Knight are worth exactly their tangible book value, then the deal is worth what it says it’s worth (ignoring synergies, and also 69mm newco warrants that Getco’s shareholders are getting). If not, then not. For instance, again ignoring the warrants and synergies:

- If KCG is worth $3.50 per share (107% of TBV), what Getco’s paying for half of it, and Getco is also worth 107% of TBV, then Getco’s deal is worth $3.67 per share.
- If KCG is worth $2.49 per share (71% of TBV), where it traded pre-rumor on Friday, and Getco is worth its tangible book value, then Getco’s deal is worth $3.14 per share.
- If KCG is worth $2.49 per share (71% of TBV), and Getco is worth 71% of its tangible book value, then Getco’s deal is worth $2.88 per share. You might discount this one, as Getco has not recently exploded and so may not deserve the discount that Knight has, though of course that may just mean that the exploding is in its future.

I would think that’d sort of bound the value, more or less, though again it ignores the warrants.^{3} My favorite math, though, is that if if KCG is worth $3.00 per share, what Virtu’s supposedly offering for it, and Getco is worth its tangible book value, then Getco’s deal is worth $3.38 per share, which is pretty much where it’s trading now. In other words, if (1) you think that Virtu values Knight appropriately and (2) Getco’s GAAP accounting values Getco appropriately, then (3) you should take the Getco deal over the Virtu one and (4) you should think it’s worth about what the market thinks it’s worth. So that’s nice.

Getco-Knight arithmetic [Google Docs]

Rival Suitors Vie for Knight Capital [WSJ]

Quick Thoughts On The GETCO – Knight Capital Group Story [Kid Dynamite]

1. *You can get that either from the 10-Q (Assets minus Goodwill minus Intangibles minus Liabilities, divided by diluted shares) or from Getco’s offer, which notes that $3.50 is a 7.4% premium to Knight’s tangible book value. See math here.*

2. *Because, again per Getco’s offer, “Knight’s tangible book value would accrete to $3.50 per share pro-forma for the Merger,” and since you have the number of shares you can solve for the tangible book value provided by Getco.*

3. *There are roughly two ways to think about the warrants, viz. (1) roughly Black-Scholes them and then subtract them from the value otherwise available to shareholders, or (2) be all “look, jerks, the warrants are only worth something if the shares end up worth more than $4, and then you’ll be thrilled, relatively speaking. Very relatively speaking.” I’m all for fake-o Black-Scholes, generally, but I feel like (2) is more legit in the quasi-cash-out-merger context.*

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Matt, where's the damn NPV math?

-Guy who is now screwed.

12 other people are also on the Getco-KCG Google docs…

Anonymous User 21,

You'd look so fine

On cell E-9,

Your pink square

Made me dilute my shares,

I only wish that my goodwill has not peaked.

– Anonymous 'Missed Connections' Quant

Always love the spreadsheets. spreadsheets > charts unless spreadsheets include charts, then you know, whatevs.

Matt, any views on the Olam/Muddy Waters dispute? Whichever side your charts back I'd bet would win.

:) same here