Fundamental Stock Valuation in the Face of Stock and Option Grants

Imagine a company that pays only cash wages, and pays out all of its profits in dividends, and its yearly results are absolutely constant into the infinite future.

This company can be fundamentally valued by choosing a discount rate and summing the infinite geometric series of dividends to be paid out. For a 5% discount rate, and the first dividend payment of $1M total starting this afternoon, the present value of the total company would be :

$1M + $1M(0.95) +$1M(0.95 X 0.95) + ?

which is equal to $1M/(1 - 0.95) = $20M.

If there existed 1M outstanding shares, the present value of a single share would be $20.

If the company increased its cash wages, the profits and the dividend payouts would be smaller, and the total present value of the company would also be smaller, as would be the per share present value.

However, if the company instead granted shares to employees, the present total value of the company would still be $20M as all the payouts are unchanged.

The effect of the stock grants is to spread the payments out over more recipients, reducing the payouts per share (more shares).

For example, if the company granted enough shares each year to double the number of outstanding shares, then every per share cash dividend would be reduced by 50% from the previous year.

Thus the present value of a single share can be represented by an infinite geometric series using a ratio that combines the 5% discount rate and the 50% annual ownership dilution rate.

For a single share, the geometric series would be :

$1 + $1(.95 X .5) + $1(.95 X .5)(.95 X .5) + ?

or $1/(1-0.475) = $1/(0.525) = $1.90476.

As shown above, to calculate the present total value of a company, growth excluded here for simplicity,all you need to know is the future cash payments and the discount rate. If stock or option grants are made, you additionally need to know the annual rate of ownership dilution to calculate the present value of a single share.

NOTE: The rate of ownership dilution that must be used is the rate that would result in the absence of any share buybacks. Buybacks reduce the share count, but use up cash that otherwise would be paid out in the dividends.

Trying to convert the grants to a company expense leads only to garbage.

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Excellent summary. One

Excellent summary.

One could always keep going deeper and deeper to explore every way options and their accounting treatment, but you hit on the main point beautifully.

The press often treats stock option disclosures as some sort of dirty insiders' scheme. Option-based compensation plays a vital role in some companies, and I'll try to touch upon that later today at
South Park Pundit
.

(Shameless plug, but hey, no marginal cost to advertise here.)

http://stephenwstanton.blogspot.com

BTW, with very few

BTW, with very few exceptions, corporations should never pay cash dividends. Free cash flow should first be reinvested in the business to the extent there exists opportunites to generate returns exceeding the company's weighted averag cost of capital. Any exces cash should be used to buy back the company's shares.

In the "only cash wages"

In the "only cash wages" case, you draw the boundary of "the company" as not including what's given to the employees as compensation, so the company's value shrinks as the cash goes out.

In your accounting for the case of the company granting shares of the company to the employees, you draw the boundary to include what passes into the employees hands, so the company's value doesn't shrink as the shares go out.

What is the point in your definition that tracks one kind of negotiable pieces of paper but not another?

To try to make it as parallel as possible: two companies have identical vaults; each vault holds $1M in cash and $1M in unissued stock; both companies also have $1M in outstanding stock held by the owners. Come payday, company A hands out $500k in cash, and company B hands out $500k in stock. Company A's transfer cost the company $500k (because your "company"ness is defined as not attached to cash assets) but company B's transfer cost the company nothing (paraphrasing: your wording was that it's nonsense to say it's "a company expense") because your companyness follows the stock and now the employees are owners of something which is the same size as before.

Why is this a better definition than one where any transfer of ownership of any negotiable pieces of paper in the vault is treated the same way? Ordinarily, "the same way" would be as an expense; but another alternative would be to treat the cash transfer just as you treat the securities transfer, as a gracious gesture which does not affect the value of the company+assets, merely broadens its ownership...

"Trying to convert the grants to a company expense leads only to garbage." On the contrary: if one is trying to estimate the value of a single share of stock today (following it through future misadventures like dilution), trying to convert the grants to a company expense is a pretty sensible approach. It's not exact or easy; valuing securities, especially derivative securities, is inexact and hard. But you want a single bottom line for the value of owning a share, this seems to be basically the right choice.

Incidentally (still mulling over the "garbage" dismissal) a number can be garbage because it's factually wrong -- a real danger when trying to accurately value derivative securities, as the Long Term Capital Management geniuses reminded us not so long ago -- but it can also be garbage because it's laughably irrelevant. I don't think I need to make a case for why one would care about the value of owning a share of stock; countless textbooks and papers have been written on the problem of how to decide how much to be willing to pay for a share of stock, and countless careers have been spent doing it. You, however, might do well to present at least a sketchy case for why what you propose to track -- "the present total value of the company," washing away transfers of negotiable securities as irrelevant because the boundaries of "the company" are defined to follow the securities -- would be of practical value to anyone, or of theoretical interest to anyone other than the most tireless cataloguer of abstract concepts.

Also incidentally, trying to figure out the value of option-ish liabilities tends to be difficult, and the difficulty can lead to inaccurate earnings estimates (either unavoidably or by intentional accounting manipulation), regardless of whether the options are on securities or on other things. Consider, e.g., an automobile company selling its cars to rental companies, and driving the sales with a guarantee to buy back 18 months later at a pretty generous fixed price. Categories like "expense" don't fit tidily around that option-to-sell, but any accounting which excludes it means that the auto company's reported income for this year is bogus. This doesn't mean that optionish liabilities are necessarily a dirty insider's game, but does mean that when one wants to play dirty insider's games, they can be quite helpful. (Similarly, to various degrees, self-dealing, nepotism, commingling accounting between company units, poison pills, and placing a high value on hard-to-measure assets are not necessarily part of dirty insider's schemes...)

Also, by the way, I assume Wayne Wren's comment is intended to be conditional on the current differences in taxation of dividends versus capital gains, and not some universal economic truth which would have held in 1888 and will necessarily hold in all countries in 2008. If so, it's probably just as well to say so explicitly, since not every reader is likely to live and breathe tax law and accounting 24/7.

Wayne's comment was correct

Wayne's comment was correct in the sense that in most situations, when spare cash is available and reinvestment options would not clear the hurdle rate (cost of capital), stock buybacks are the most tax-efficient way to return money to shareholders.

Stock buybacks, in practice, are often done for the wrong reasons... Such as countering the net impact of option grants on the number of shares outstanding or driving up stock price through short term (and short sighted) manipulation of supply and demand.

In the long run, however, cash should be returned to investors. Under current law, buybacks are the best way to do it if done well (i.e. without driving up share prices artificiallly).

But "long term" could mean many decades.

Wayne, "BTW, with very few

Wayne,

"BTW, with very few exceptions, corporations should never pay cash dividends. Free cash flow should first be reinvested in the business to the extent there exists opportunites to generate returns exceeding the company?s weighted averag cost of capital. Any exces cash should be used to buy back the company?s shares."

This is A set of theories, but not a set that I would necessarily subscribe to. It is management's fiduciary responsibility to maximize shareholder value, whatever that may require.

Certainly a mere positive return on an internal investment is not to be preferred to a dividend payout that lets the shareholder make his own investments.

The buying of company stock on the market is often appropriate, but not at any price, and the appropriateness has nothing to do with any possible previous stock or option grants. Buybacks are often merely the means by which management inappropriately captures a majority of the free cash flow of a company while simultaneously masking from the shareholders the true extent of stock and option grants. Also, repurchases tend to drive up the share price, using shareholder cash, and thus make more option grants profitable for employees to exercise, further diluting shareholder ownership.

Regards, Don

Bill, "In the ?only cash

Bill,

"In the ?only cash wages? case, you draw the boundary of ?the company? as not including what?s given to the employees as compensation, so the company?s value shrinks as the cash goes out.

In your accounting for the case of the company granting shares of the company to the employees, you draw the boundary to include what passes into the employees hands, so the company?s value doesn?t shrink as the shares go out.

What is the point in your definition that tracks one kind of negotiable pieces of paper but not another?

To try to make it as parallel as possible: two companies have identical vaults; each vault holds $1M in cash and $1M in unissued stock ..."

I see where your misconception lies, and I will address it in due course.

First, whether employees are paid in stock, or cash, the employees are providing a service to the company, just like the pizza delivery man. In neither case are they an integral part of the company. In all cases their payment leaves the boundary of the company.

You have assumed that because the value of the company is not decreased by the payment of shares
that the shares have not really left the company. This is the misconception. A company cannot logically effectively own a part of itself. Any company shares that are possessed by the company itself, whether unissued or repurchased shares, have no more value than scrap paper, to the company itself.

There are two reasons for this. First, the company can create as many new shares as it likes without significant expense, so no existing shares possessed by the company can have any economic scarcity value. Secondly, any shares possessed by the company are really part of what is owned by the external shareholders, and thus have no effective reality. If a company possesses 1000 of its own shares and I own the remaining 1000, then I own 100% of the company no matter whether the company's possessed shares are destroyed or duplicated a million times.

Regards, Don