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# PayPal and valuation of [0.4 x sqrt(T) x vol] Employee Stock Options

PayPal has recently released its Q1 earnings, results worth investigating if interested in spotting the latest trends in the [electronic] payments industry. Being PayPal a growing company with complex dynamics of established businesses, it also offers the chance to summarize critical views that investors can adopt to make a difference valuing businesses and spotting opportunities. A few months ago I wrote about __The Hidden Math of Share Buybacks__, a corporate practice that depending on the implementation can affect the value of investors’ holdings either way. The earnings of PayPal allow us to discuss an argument presenting similar complexity and technicality: **Employee Stock Options (ESO)**. ESOs are interesting because they are related to add-backs, those usual adjustments made on the reported earnings of the business to obtain the cash-flow and the valuation of the investment. Employee Stock Options also suggest us to think in terms of probability & statistics. __We will be pushed to think about the deepest principles of corporate finance, something that could exponentially increase our critical abilities.__ In this post, we will make a brief intro, and we will then dive into some interesting and intuitive math.

__1.3 - INTRO: Are corporate earnings properly reported to investors? Giving public companies the benefit of the doubt, probably “yes”__

The value of a company is the collection of the money it can generate, discounted for the time owners have to wait for receiving cash, and lowered by the liabilities the business must repay before letting owners enjoy the proceeds. The first crucial point investors have to agree on is what constitutes the present and future cash-flows. While that could result easy for small businesses, and almost immediately identifiable through the tax return and bank statement, when it comes to medium and big companies things are usually not that easy. The latter type of business has multiple singularities any given year (i.e. investments, lawsuits, M&A, accidents of some sorts, etc.). It is tough to separate one-time expenses [and sometimes revenues] from the repeating ones affecting the long-term and intrinsic value of the company.

*Note: we will not differentiate here between “expenses” and “expenditures”, based on the actual disbursement of cash. We will treat those terms as interchangeable, and we will explicitly state whether we are implying actual cash in and out of the bank.*

A public company [and audited private ones] must report earnings according to regulated standards, GAAP rules in the USA. Usually, the management of the company presents also non-GAAP numbers with the objective to customize the numbers to its specific business. That often results in adding back some expenses based on factors that we will summarize with the following two types of add-backs:

1. * Paid-in-cash “accidents”*: examples of this add-backs are lawsuits and their legal expenses – please note that the accounting of lawsuits is a bit complex, being possible to be required to report related expenses or liabilities before the actual payment happens. A company may add back this type of expense classifying it as a one-time accident not to be incorporated by investors on their long-term view of the earning capability. The lawsuit example was chosen for its intuitive nature, much more complex cases are possible. Investors should make a call on whether those are really one-time accidents. It is tough to give general and technical rules on these expenses, investors should rely on their specific knowledge of the industry and determine whether similar expenses are likely to occur repeatedly because intrinsic of the industry.

2. * Non-cash expenses:* examples of this add-backs are Employee Stock Options (ESO). These are expenses not immediately paid in cash, and often without clear terms of payment and amounts. This type of add-backs are perhaps a bigger stretch than the first one: just because a company does not pay something immediately, it does not necessarily mean it never will, even when the terms and the amount of the payment are not clear. However, there is the case for this second group of common add-backs to be evaluated a bit more technically and generally than the first type. That is what we are about to do.

Depending on the degree to which the company markets its non-GAAP numbers improved by the add-backs, it can either provide investors with useful information or it can confuse them on the actual potential of the business. A positive view of the issue could be the following: companies are probably often right in presenting better views of the cash-flows; they may be trying to show investors their actual __liquidity potential__ rather than the __long-term earning__ one. They may be trying to say the following: *“… about all the expansion projects we are telling you about, do not worry about our liquidity, for our actual cash-flow is better than the reported earnings thanks to some expenses we haven't paid yet; therefore we can afford to pay now for additional investments, and have our future reported earnings to benefit from them ...”*. Framed in that way, non-GAAP pictures and adjusted cash-flows do have their point.

*Please note: the second type of add-backs, non-cash expenses, are in part added-back because of GAAP regulations. Being non-cash, they are naturally added back in the official Cash-Flow Statement of the company which has to match the final net change of the bank account. However, we are discussing here those cases where companies stretch and oversell the final cash-flow arriving at some “non-GAAP cash-flow”, with the risk of confusing investors. If the reader has ever gone through the financial reports of investment companies (insurance, public private-equity companies, etc.) s/he would probably know how the complexity of those documents can at times result non-intuitive. Again, this post does not imply bad intentions and does not want to generalize.*

__2.3 - Even though companies properly report results, the technicalities of some arguments make them tough to handle? Let us go through the math of ESOs__

Employees Stock Options are integrations to employees’ compensation that are not immediately paid in cash. ESOs assign employees the future option to purchase shares of the company at discount. The calculation of the real expense for the company is not trivial: blocks of granted options usually vest in time, and from that moment on, employees have the option to exercise them and purchase actual shares at discount. The conversion to shares dilutes the ownership of all other owners because of more shares outstanding on the open market diluting the Earnings Per Share (EPS) - as we will see below, “diluted earnings”, accounting for the additional shares that convertible options would produce if instantaneously exercised, is just a minimal improvement. Finally, the actual cost of the shares that companies issue to employees has an uncertain cost because it can depend on the price at which they repurchased them from the open-market - among the objectives of share buybacks there is the intent to build inventory for future re-issuance to employees.

A simplified accounting of ESOs is the following: after employees are granted options, as the contracts vest in time, the associated expense is recorded on the P&L and their Payment-In-Kind (PIK, payments not made in cash), is recorded as a form of [hybrid] equity on the Balance Sheet – in some cases, it must be recorded as a liability. The cost is associated with an estimate of the Fair Value (FV) of the option, a number related to the “strike” of the contract (the agreed-on price at which the employee will be allowed to purchase shares). If and when the employee decides to exercise the options, on the Balance Sheet there is a correspondent increase of the cash paid-in by the employee to the company to receive the shares at discount, and the migration of the [hybrid] equity previously recorded toward two actual equity accounts, “equity” and “paid-in premium” – the premium will reflect any discrepancy between the previous record and the final settlement.

We just saw how options affect the balance sheet, income statements, and the earnings of the company. If that expense is then added back to build a non-GAAP Cash-Flow, and we use the result to build the cash-flow profile in time and final valuation, we risk overestimating the value of the business - as we mentioned above, ESO costs are added back even just to build the GAAP Cash-Flow. Let us see this through the PayPal example.

PayPal at the end of 2020 had earnings for the year of **$4,202M** or about $3.5 EPS (Earnings Per Share) – I used FY20 earnings over Q4 average outstanding shares from the Q4 earnings. Among the costs of the year, there was $1,472M associated with vesting options. The after-tax equivalent, at about 20% tax-rate, is $1,178. If we added that expense back, we would get a cash-flow of **$5,380** which is about 28% more than the original earnings.

*Note: we are adding back the after-tax number because we assume we would pay taxes on the extra profit without that cost. That is correct if we are building a cash-flow for valuation purposes; in a similar way, real applications would also have to subtract CAPEX and investment in Working Capital, and they would probably imply an add-back for D&A etc. However, if the objective was to tie to the net-change in the bank or the number in the GAAP cash-flow statement, we would have to add 100% of the expense which was not paid in cash ... if the reader finds this confusing, please disregard, for the point stays the same.*

While that higher $5,380 could be useful to show the higher liquidity potential of the company compared to what reported earnings would suggest, any type of valuation based on that cash-flow would result in estimates which would probably be too optimistic. Is the company never going to pay [somehow] that cost? We could fix part of the problem considering Price-Over-[Diluted]Earnings. At the end of 2020, PayPal had about **1,191M** of common shares outstanding. At the same time, the potential dilution effect of the convertible options was about 24.3M additional shares, say about 2% dilution potential. The original Earnings-Per-Share were $4,202M/1,191M=**$3.53** EPS, and the diluted ones would be $4,202M/(1,191M+24.3M)=**$3.46** diluted EPS. The same numbers based on the non-GAPP cash-flow would be respectively $5,380M/1,191M=**$4.52** adjusted EPS and $5,380M/(1,191M+24.3M)=**$4.43** adjusted and diluted EPS. It is easy to check that the major difference is due to the nominator, especially in this case where options-related expenses are particularly high compared to the earnings.

Which number should we use in our valuation of the investment?

__3.3 - Is $3.46, which accounts for both the cost of issuing options and the dilution effect, the best and conservative view? Probably yes, but that is still likely to be wrong__

The cost of options compensation that we find among the GAAP income statement and earnings is posted at Fair Value (FV). What does it mean? The Fair Value of options contracts is usually the result of calculations like Black-Scholes. Without entering the details of the differential equation behind that model, we can use a simple formula shortly approximating the result of Black-Scholes for At-The-Money options (ATM) - options whose strike (agreed-on purchasing price) is equal to the current market price of the underlying [stock], which is often the case for ESOs. That equation is the following:

0.4 * sqrt(T) * Vol

*Note: the approximation has some assumptions like zero interest rates etc… The interesting reader can research further.*

The second term of the formula above is the square root of the time to expiration of the contract, and the last term is the volatility of the underlying [stock]. The formula is implying that the option has 50% chances of ending up profiting from the movement of the underlying (i.e. share going up in price). Moreover, since the stock will move up and down similarly to a random walk, it is likely to do so proportionally to the Volatility of the underlying [stock], which in turn has to be scaled by the time at our disposal (i.e. multiplied by the square root of the time according to the standard deviation of a normal distribution). Basically, we are quantifying the top half of picture 1.

*Note: 0.4 in the formula is not an error (i.e. it should not be 50%) … a hint to the reasoning could be the following: assuming a normal distribution, 1 sigma move (1 volatility move up and down) is like saying that about 68% of the times we will be within that value, while we want the share to move as much as possible in the positive direction. Again, the interested reader can find the details.*

So, during the vesting period of granted options, a company would register the related cost at its FV, usually considering the current price of the stock, its volatility, and the time to expiration of the contract. Is that valuation of the actual cost that the company will suffer really “fair” [or, good]? It depends. It depends in part on how good our estimate of the volatility of the underlying is. It also depends on the real statistics of the specific underlying and how much they differ from the theoretical normal distribution.

__CONCLUSION: So, what should we do? We cannot even be sure of the initial expense posted by the company on the GAAP Income Statement? Let us try to answer by wrapping everything up__

Stock option compensation is not easy to handle because of uncertainties at any step. The cost initially posted on the Income Statement is the first approximation due to the estimation of the Fair Value. Any other further step in the manipulation of numbers is likely to add uncertainty. While companies present GAAP and non-GAAP cash-flows where the cost of option compensation is added back, it could be a good practice for corporate valuation to still use a cash-flow [however we build it] penalized for the cost of vesting options (i.e. keeping the cost of vesting options posted in the Income Statement, without adding it back to our cash-flow). As we just saw in the previous paragraph, that is not exact either; however, not being possible to predict the future, it could be the lesser of all evils. Moreover, considering diluted shares rather than the outstanding ones, is likely to be an additional optimal practice - though the company is likely to be re-purchasing them at the same time.

Therefore, yes, in the simplified example of PayPal discussed above, this post would suggest $3.46 to be the best choice.