Warrants Dilusion

[orit]

Hi David,
I really need your help is understanding,I was trying to figure out by myself but with no success unfortunately:
when a company issues warrants to employees, it gives the employee the right to purchase shares @ a specific strike price.
When the employee exercised, basically the company increased its equity by this amount.
The employee doesn't pay any premium for this warrant,
1. what is it exactly the warrant issue cost, who pays for it?
2.In respect to the delusion -The company basically increased its equity by the number of warrants multiplied by the strike price(lets assume that 1 warrant=1 share) and the delusion is the outcome of reduction in shares holding percentage for the existing investors. can you please explained the notion behinf the calculation of the warrant dilusion
Thanks a lot,
Orit

 

[David Harper CFA FRM]

Hi Orit,

I consulted to companies for years on options, it's quite a deep topic. One issue is, what kind of dilution are we talking about; ie, an ATM option has zero intrinsic value, so to account for its fair value is to introduce an "economic" dilution into a (more standard) cash flow dilution. I can tell you that the assumption behind your question is true in practice: neither companies nor analysts have easy ways to account for the dilution (I spent years with FAS 123, which is actually a third perspective on dilution, you can look at cash flow, economics or accounting; here is an old 7-part tutorial I wrote for investopedia on ESO dilution: http://www.investopedia.com/features/eso/#axzz2MtZjwb4n )

But, as a simple pass, I'd refer to Hull's formula is 14.10, where he says (and, truly, I am confident Hull knows he's being simplistic, this is a simple model) the share price after exercise = [N*S(T) + M*K]/(N+M), where M = # shares O/S and N = # of options issued with strike @ K.

So consider the case where options are granted ATM; e.g.,
N = 1,000 shares O/S
S = $20
s.t. company market cap = $20,000 before options

Then company grants 100 options ATM
M = 100
K = 20

Assume unrealistically they are exercised ATM:

• company market cap grows to 20,000 + 100*20 = 22,000,
• but divided by new shares of 1,100 --> share price unchanged at $20.00; i.e., market cap grows but shares purchased at fair price so stock price unchanges

say instead share price increases to $25 and then options are subsequently exercised:

• before exercise market cap = 25*1,000 = $25,000 equity market cap; over 1,000 shares = $25/share
• after exercise, market cap = $27,000 but over 1,100 shares for implied "dilution" of share price down to 27,000/1,100 = $24.55

this is simple but, as far as it goes, directionally true. We can note:

• This shows that the strike (K) does get paid; in practice, over 90% of US ESO as cashless which means that the employee gets the net shares; e.g., if you held the above 100 ITM options (S=25, K=20), then (neglecting tax) your cashless exercise would just net you a "grant" of 20 shares because you use 80 of your received shares to pay the exercise: (100*20)/25 = 80 shares pay for excise. This proves there is real dilution: 20 shares have been granted for free, so the existing shareholders are paying by the +20 share increase. This ignores taxes so is wrong in the specific.
• So far this does not include time value; that's non-trivial, FAS 123 accounting aspires to incorporate fair value. Like the rest of fair value (ESO accounting lies within a broader framework), the minute you attempt fair or economic value, you introduce variability (even subjectivity; e.g., BSM assumptions) into the model, epically! We noticed as consultants that some companies would favor binomial over BSM for ESOs because they could dramatically reduce the accounting expense, e.g.
• the cash flows are different, too, and importantly impacted by taxes. Specifically, the company enjoys a very real cash inflow from the exercise proceeds (it's almost a free lunch cash flow wise; basically existing shareholders are sending cash to the company). So, tech companies offset this with share repurchases; most of Cisco's historical repurchases have been motivated by ESO dilution.

I hope that's a good start,

 

[ShaktiRathore]

Hi there
Warrants issued causes the dilution of the shares. They are given to the employees for performance. Since in the end the shares value gets diluted due to increase in effective no of O/s shares the shareholders holding the shares already in the company pays for them. Thus in the end its the shareholders that get penalized for the issuance of the warrant.
let no of warrants be 50 with total shares O/s 250. Total equity at current market price of 10 is 250*10=2500
Now when warrants exercise price be 8. Suppose all 50 warrants are exercised then the total o/s shares increases to 250+50=300.
Total equity position becomes 2500 plus 50*8 from the warrant holders. So total equity is now 2500+50*8=2900
The share price gets diluted to 2500+8*50/300=2900/300=9.67.(treasury approach)
otherwise we can simply divide the total equity by the total new shares formed after the warrant is exercised i.e. total equity/300=2500/300=8.33[dilute shares]

thanks

 

[David Harper CFA FRM]

Hi Shakti,

Thanks! Your math (Treasury method) is consistent with Hull's formula; i.e., share price after exercise = [N*S(T) + M*K]/(N+M)

Such that, in your example, if the strike price of the options instead were 10, that is S = K, then 3000/300 would (efficiently) imply no dilution.

That's where it get's interesting: the treasury method, per an accounting conservatism, can only include ITM options.
But are ATM ESOs dilutive? I'd say, yes, of course they are! Roughly according to their time value, they have a cost approximately equal to their nonzero value. Hence the "economic" interpretations that, imo, are inevitably model-dependent (under FAS 123 due to the earnings charge element, I can produce widely varying option costs for otherwise identical grants), thanks

 

[orit]

Thank you David and Shakti for your comprehensive explanation.
David I read the related link you referred me to,thanks you very much it helped me understand it from the point of you I'm familiar with - finance
1. The calculation of the dilution when the option is ITM - is understood.
2. Can you plesae make one more clarification: why do you multiply the option price with (number of shares/number of warrant)?
Thanks again,
Orit

 

[David Harper CFA FRM]

Hi Orit,

sure thing, but i am not sure to which you refer?
In my follow-up to Shakti's example, I was using Hull's: New share price = [N*S(T) + M*K]/(N+M)
With Shakti's: N = 250, S(T) = 10, M = 50 options with strike (K) = 10 (ATM).
New share = (2500+10*50)/300=3000/300=$10; ATM implies no dilution under Treasury method (which does not consider the cost of time value; is not fair value cost)

 

[orit]

Hi David,
I'm referring to the example in the excel files - 4.b.2, in this example you show there is a warrant delusion when the stock price equal to the strike price.
Thanks

 

[David Harper CFA FRM]

Hi orit,

Oh, okay, yes the XLS implements Hull's subsequent example, which goes further than the formula both Shakti and are using (in an non-obvious way: by multiplying BSM option value). The formula attempts to incorporate the full value (time value) that i've been saying is absent above. If you use the XLS with Shatki's numbers, just to highlight the difference, then we get:

• before options (i realize we are calling these warrants, but imo warrants attach to securities; these are ESOs), we have 250 shares * $10 = $2,500 market cap
• then grant 50 options (ESOs) with K = 10 (ATM). Let's assume option value is $1.00 per option
  (Note that ATM options have zero intrinsic value and the $1.00 fair value is entirely time value)
• Hull's "economic" approximation, as opposed to the "pretax cash flow" approximation above, has the premise (just an assumption) is that the company's total (equity) market capitalization is unchanged by the options. In short, no free lunch, the options are perfectly dilutive according to their BSM cost
• Under that assumption, $2,500 unaffected market cap = ($9.83*2500 existing s/h) + ($0.83*50 ESO holders). His math ensures the 2,500 is preserved. for example, if we increase volatility, option cost goes higher and the diluted share price would decline. This is different than the more simplistic discussion above as we are now (in the XLS) using the BSM price of the option, not just the intrinsic value. Specifically, ATM options under this approach are dilutive to existing SH by reducing their share price

thanks,

 

[orit]

Thank you, David,I'm referring to my initial question:
the only thing I can't figure out is why you multiply $1 by 0.83 which is basically the ratio of the existing s/h out of the total equity ( s/h + warrants)
Maybe I'm putting too much time and energy to understand it..

 

[m123mikmik]

@David Harper CFA FRM CIPM - With regards to this thread, how likely is a warrant question going to be on the exam? Thanks so much!!

 

[David Harper CFA FRM]

Hi @m123mikmik

It's a good question. The relevant AIM is "Identify the complications involving the valuation of warrants." However, the complication and nuances that attach to, especially, employee stock option (ESO) render this topic (in my opinion) unlikely to be tested. And I cannot recall seeing a question on this topic, in a very long time. In the case of an ESO, the "complications" include the tax treatment and cash flows (not in the reading) and, more importantly, the dilution caused by grants. In financial analysis, there are different views on how best to quantify this dilution, so I can't really see the exam having an ability to go beyond the complication as dilution. More precisely, in some approaches, it's an iterative or circular calculation so, at worst, the complication is "dilution which is hard to figure due to possible circularity" circularity being that the ESO grant causes dilution which decreases the value of each share and the impacts the value (and net cost) of the option granted so in economic reality the option impacts itself! (as the above thread shows, I think). I hope that explains why I think it's virtually impossible to really query this AIM at the moment. Thanks!