Peter. In my previous post to you early this morning I was wrong. Wasn't thinking. Apologies.
The appropriate value to use for cost to shareholders is *market* price minus strike price, discounted to present value.
Here the whole nine yards.
Look first at the exercise transaction:
The employee parts with Strike Price but gains a share. Then in selling to Our Shareholder (representing shareholders; plural; collective) gains Market price and parts with the share. Net change to the Employee is: Market price minus Strike price.
Shareholder starts out with the whole company. Then the company issues a share to the employee but gains the Strike price. Then Shareholder purchases the share at Market Price. Which leaves him down by Market Price but now owning all shares of the company, which itself is up in asset value by Strike Price. So Shareholder's total asset value has decreased by Market Price but, through complete ownership of the company, increased by Strike Price. Thus Shareholder gain is Strike Price minus Market Price.
Nothing in there about fair value. As you can see. Sorry.
In the meantime between issuing the option and exercise, purists will note that Shareholder also gains (or loses) whatever the company gains (or loses). And if Shareholder wants, can value the company as N+1 times Market Price. But that leaves Shareholder exposed to bubbles and things.
If we look closely, we see quite clearly that on top of whatever the company gained in the interim, Shareholders gain what employees gain at the moment of exercise, but that the signs are reversed. And if we assume that employees aren't as dumb as posts, we also know that Market Price is greater than Strike Price. So Shareholders experience a negative gain.
I call this negative gain a "cost", but you can choose to call it "gaining less than what they would have gained" if you like.
And this is precisely, exactly without a doubt or any need of estimation the cost of shareholder dilution in the moment of exercise. No doubt.
Teleport ourselves through time back to the moment of exercise then. How should we account for this upcoming dilution.
If one knew precisely what the market price was going to be the simple "Shannon Function" I use, reduced to present value of course, would be sufficient. However, we don't. Instead when looking forward, those who are smarter and more sophisticated than me know it's not so simple and want to be accurate to more than one decimal place.
Because to use the Shannon Function, I look at the future and say "the stock price will be up by $40". Well, say the purists, there's also a probability that it will be up by $0 or less, another that it will be up by $13 and a different probability that it will be up by $2,735 and every other number in between. And a few more besides.
So the purists want to go the long way* and account for these too. And they want precision.
What these gluttons for mathematical punishment want is an expectation value, which is the weighted sum of all of these possible values. Which we can get using the Black Scholes equation, or a variant. Which computes the expectation value of the gain (difference between strike and price) as a function of time and volatility and risk-free rate of return. Or one of a family of such critters developed more recently.
Anyway, whether one computes the Shannon Function or Black Scholes or any other critter, if we just add up the (present value) sum of these estimates of future dilution year by year by year, we have the present value, in dollars, by which future stock-option dilution is going to reduce the assets of Shareholders.
We also have this GAAP EPS thing which is a good proxy for profit. And if we just add up the discounted sum of these going forwards year by year by year we have the amount, also in dollars, by which profits are going to increase the assets of Shareholders.
And the second sum minus the first sum is how much Shareholders (plural, collective) will see their Asset value increase. Add that to present asset value, minus pending dilution from prior stock options (Using Shannon Function, Black Scholes or whatever), and we have a fair value for the company!!! Which we could then just divide by shares outstanding to get a fair price!!! Which might even be useful if one wants to think like an owner and estimate a market price from first principles.
Some bright spark might then note that the difference of two sums is the same as the sum of two differences.
And suggest that if we adjust EPS going forward by dilution going forward we end up with just one sum to do in order to come up with a price estimate.
And what has just fallen out of this chain of logic is the conclusion that a company with stock options is fairly valued alongside a company that doesn't IF earnings are adjusted for the expected dilutive cost of stock options, year by year by year. A kind of poetic justice: remember we showed that the dilution cost was the same as what employees gain? Well, subtracting this gain from EPS is kind of the same as if earnings are reduced by the amount of option compensation that employees can expect to receive. Cool.
Anyway, we end up in a place remarkably similar to the proposition advanced by S&P!!!
Gee... maybe my line of thinking has something to it after all? Can't possibly be true. Must be an accident. I'm just a lucky guy. Not knowing what I don't know as some smart alec had the wisdom <g> to insinuate. Or something like that.
Anyway, in defense of the folks who don't like the S&P proposal, I do note a few complications.
Foremost amongst these, the S&P proposal makes modelling the future EPS from the current EPS very very difficult because one has to do some complicated computations. Firstly a model of the business itself, and second a model of stock price dilution, and then add them together.
And then cycle this through and then come back with an estimated stock price (because that's what dilution depends on)... and iterate. And discount to present value, and sum... Very messy. Yeuch.
There is no way this can be done by taking a glance at the bottom line and multiplying by 37. Instead, folks will have to read and (shudder) understand the income statement.
And so it will pretty well render such ratios as PE and PEG somewhat meaningless. Really one would need to compute P = (PE - PD) because Earnings will follow one curve while Dilution Cost will follow another one.
Of course, this might turn out to be a good thing. Forcing people to look at numbers intelligently, instead of waving around 37 (or whatever) as a "fair" PE number without knowing how they came up with 37 except that it results in a share price they think looks right and they found some shred of evidence to support this conclusion (while dismissing all other evidence that suggests some other number).
Unfortunately this could usher in a return of pro-forma from the zone of the undead. And Qualcomm might respond by creation of a segment called QSO into which it packs all stock option stuff, and then issue four versions of its income statement (GAAP, GAAP ex QSI, GAAP ex QSO, and GAAP ex QSO and QSI), just to clarify things <ggg>.
Valuation will never be the same again!!!
Yes, there will also be some folk who fail to adapt. But that should merely accelerate the necessary economic darwinism and clear the market of folks who don't know what they are doing or who can't adapt to new rules. Roadkill lines the way on which the wheels of Progress spin.
But I do wish there was a better, easier way.
You seem to think there is. I keep seeing ambiguous reference to the notion that % dilution offers a better way. How do you go about working out the cost of this ongoing percentage dilution?
Let's say the enterprise has some assets. Then it's going to add to this pile of assets by earning a bunch of profit (and presumably not squandering it).
So we add all this series of numbers up, first dividing each by some future value discount factor that represents both the time value of money and a pinch of risk for good measure, and wrap it in goat entrails and come up with a present value.
We can call this "Fair Value" of the business itself. We want price per share.
Absent dilution it's pretty much straightforward to get fair price per share. You just divide the lot by shares outstanding and presto. Fair price per share.
But sadly, dilution is not insignificant. So we have to factor it in.
Since you and Clark are the experts in factoring in dilution, how about either of you take it from here to show the thread how it's done in the presence of ongoing dilution.
Can you do it without reference to the strike price of the options or the fair market value of the company while you are at it? I'm not sure that's possible, but I'm willing to give it full consideration.
'Cause as I said, the alternative gives a good answer, but it's very messy indeed.
John
* If the expectation value of an option is $3, this is the same as using the Shannon Function with a share price $3 above the strike price. It all kind of fits together with the concept of "I expect a return of x% from here" type thinking. Although mathematicians toes will probably curl at this statement, because an expectation value and a point value are indeed two different things.
P.S. I'm going to stick with the Shannon Function, because of * and because I really can't be bothered with five digits of precision where uncertainty in the underlying estimates clouds the first digit, let alone the next four. |
