The diluted EPS calculation is 50 years out of date

It will soon be the 50th anniversary of the publication of the Black-Scholes model for option valuation. The fair value of options has since been incorporated into several aspects of financial reporting. However, in the case of diluted earnings per share, the accounting still pre-dates Black-Scholes.

The treasury stock method for calculating diluted earnings per share only considers the intrinsic value of written equity options, such as warrants and employee stock options. We explain why this is a problem and the further reasons why the full economic value dilution resulting from these securities is not reflected in financial statements.

There is much to dislike about earnings per share, both as a measure of performance and, when part of a price earnings ratio, as a basis for equity valuation. The metric is both simplistic and complex in that it combines many different aspects of value in a single number. We have previously advocated that investors should focus on other performance metrics and valuation approaches, notably those based on enterprise value.1See our article ‘Enterprise value: Our preference for valuation multiples’. Nevertheless, as earnings per share is widely used by investors in practice, it is important that the accounting results in realistic metrics.

Basic EPS fails to allow for the ‘cost’ of written equity options

Most investors quite rightly focus on diluted rather than basic EPS. The problem with basic EPS is it makes no allowance for the impact of written options (and other potentially dilutive securities such as convertible bonds) on the earnings attributable to the parent company common shareholders. While other non-common share equity interests, such as non-controlling interests, are factored into basic EPS through an attribution of profit to minority shareholders, there is no similar profit attribution or other recognition of the ‘cost of capital’ of written options. This is the omission that diluted EPS is designed to correct. However, in our view, the dilution adjustment calculated under both US GAAP and IFRS is incomplete.

The calculation of earnings per share has remained largely unchanged since the first US GAAP standard was issued over 50 years ago. Both current US GAAP and IFRS can trace their roots to APB 15 issued in 1969 by the AICPA (the US standard setter at the time). There have been some subsequent modifications to the detail, but much of this has been a reaction to other accounting developments, such as changes in the accounting for convertibles and the introduction of the expensing of share-based payments to employees; the fundamentals of basic or diluted EPS have not changed.

In this article we focus on the diluted EPS calculation and specifically the treasury stock method applied to written options (the most common source of dilution). The problem is that this calculation is based on the intrinsic value not fair value of equity options.

Accounting for diluted EPS pre-dates the Black-Scholes model for option valuation

The treasury stock method predates the development of modern option pricing techniques. The well known Black-Scholes option valuation model was first published in 1973, well after APB 15 was first applied. Therefore, it is no surprise that, when initially developed, the diluted EPS calculation did not reflect the fair value of options.

But 50 years later option valuation is well established and fair value is widely used in other aspects of financial reporting, including the measurement of derivatives classified as assets and liabilities in the balance sheet, and in deriving the employment expense when options are granted to employees as part of stock-based compensation. Considering it is the fair value of equity options that creates economic dilution for common shareholders, we believe it is time to update the calculation of diluted EPS.  

The calculation of diluted EPS

Diluted EPS adjusts for the additional shares that may be issued in circumstances that are not under the control of the company. Future share issues at the discretion of the company, including the potential future grant of options, are not included in diluted EPS.

Most diluted EPS effects arise from written call options. These may be stand-alone, such as share warrants or employee stock options, or could be options embedded in other securities such as convertible bonds. There are two methods for calculating diluted EPS: the treasury stock method applied to stand-alone options and the if-converted method applied to convertibles2The accounting for convertible bonds under US GAAP, including the method for calculating diluted EPS, has recently been amended. For more about this topic, and why we believe US GAAP accounting does not faithfully reflect the true cost of convertible financing, see our article ‘Convertible accounting: New US GAAP inflates earnings’.. We do not discuss the if-converted method in this article; however, we believe that this approach also fails to fully capture economic value dilution.

In our view, the treasury stock method understates the dilutive effect of options, and therefore overstates diluted EPS. Indeed, we think there are three issues with the reported diluted share count that limits its relevance for investors:

  • The treasury stock method and its focus on intrinsic value.
  • The adjustment for unrecognised stock-based compensation.
  • The way that so-called ‘anti-dilutive’ securities are excluded from the calculation.

Treasury stock method – intrinsic value not fair value

Under the treasury stock method, the diluted share count is increased by the number of shares that could be issued if options are exercised, after adjusting for the shares that could be repurchased (i.e. bought back as ‘treasury stock’) using the exercise proceeds, based on the average share price during the period.

For example, assume a company has issued 1,000 5-year share warrants, each entitling the holder to purchase 1 share at a price of $10. The average share price during the year was $12. The amount paid to the company if these options are exercised is 1,000 x $10 = $10,000. This could be used by the company to repurchase 10,000 / 12 = 833 shares. The net effect is that the share count would rise by 1,000 – 833 = 167 shares.

Dilution effect = shares issuable – shares issuable x exercise price / share price

Dilution effect = 1,000 – 1000 x 10/12 = 167

The same result can also be obtained by dividing the intrinsic value3The intrinsic value of a call option is the higher of zero and the share price less the exercise price. Sometimes the exercise price is discounted for the time value of money, but this does not apply to the intrinsic value used in diluted EPS. of the options by the stock price. The dilutive effect under the treasury stock method is the common stock equivalents of the intrinsic value of options – the number of common shares with the same value as the intrinsic value of the options.

Option intrinsic value = 1.000 x (12 – 10) = 2,000

Dilution effect = 2,000 / 12 = 167

This illustrates why we say that the treasury stock method only allows for the intrinsic value and not the fair value of outstanding options.

Out of the money options do not increase the diluted share count

If the share price is below the exercise price, the above calculation would result in a negative value and the options would be regarded as anti-dilutive. However, because the options are out of the money, and exercise is unlikely, this reduction is ignored for diluted EPS purposes. The dilution effect is the higher of the above amount and zero, and diluted EPS can only ever be equal to, or lower than, basic EPS. The same result can be obtained by considering option intrinsic value. If the stock price is below the exercise price intrinsic value is zero and hence the common stock equivalents are also zero.

The treasury stock method is based on an assumed exercise of options, but this entirely ignores the main benefit of options – the option time value.

The treasury stock method ignores option time value

A holder of an equity call option benefits by being able to choose whether to exercise. If the stock price rises above the exercise price the option can be exercised and a gain realised. But if the stock price falls below the exercise price the holder can choose to not exercise and thus avoid a loss. This asymmetric payoff creates time value, which is what the Black-Scholes and other option valuation techniques are designed to measure. Of course, the holder must pay for this when buying the option (or providing employment services in return for receiving the option).

The asymmetric option payoff negatively impacts the common shareholders who have, in effect, written an option on part of their ownership of the company. In the same way that option holders benefit from optionality, the common shareholders have an equivalent cost.

Ignoring option time value creates misleading and illogical results

Assume a company issues warrants that are ‘at-the-money’ with the exercise price equal to the share price. Intrinsic value is therefore zero and under the treasury stock method no dilution is reported (basic EPS = diluted EPS). Indeed, the transaction would be earnings enhancing considering that the proceeds from issuing the warrants can be invested or used to repay other financing. For example, the proceeds could be used to buyback common shares and produce an immediate increase in both basic and diluted EPS.

However, this EPS accretion is illogical and misleading. If warrants are issued at a fair price, there can be no positive effect on shareholder value. The gain to shareholders from raising (and investing) the cash is offset by giving up value through writing the option. Therefore, the increase in EPS does not reflect the economics.

The problem is that the treasury stock method of calculating the diluted share count fails to allow for the fair value of the options.

A better approach to dilution – fair value common stock equivalents

We think the diluted share count should reflect the fair value of outstanding options. The fair value can be converted into ‘common stock equivalents’ by simply dividing the aggregate option fair value by the share price (instead of the intrinsic value effectively used in the treasury stock method). This number of common stock equivalents is then added to the basic share count. The option value and stock price should either be an average for the period or the value at the balance sheet date, depending on whether the diluted share count is used for periodic (e.g. EPS) or balance sheet date statistics.

Returning to our 5-year share warrant example above (where the option exercise price was $10 and the share price $12), if the volatility of the stock is, for example, 70%, the option value calculated using the Black-Scholes model is about $7.60 per warrant. Applying our fair value common stock equivalent approach, we obtain the following dilution.

Fair value of warrants = 1,000 x 7.60 = $7,600

Dilution effect = common stock equivalents = 7,600 / 12 = 633

This effect is nearly 4x the dilution calculated using the treasury stock method.

Of course, the difference is magnified where options are close to being at-the-money, and we also chose a high stock volatility input. But not unrealistically high – 70% is almost exactly the average volatility for Tesla over the last 3 years.

Tesla is a good example of a company where the dilutive effect of written options is material. In 2022 the diluted share count is 11% higher than the basic number of shares, with a commensurate difference between basic and diluted EPS. The dilutive effect in 2022 is lower than in the prior years, in part due to the lower stock price reducing the intrinsic value of the options

Tesla diluted earnings per share disclosures

Tesla 2022 10K

In our view, because the treasury stock method omits consideration of the time value of the Tesla options, the dilution disclosed above under US GAAP is understated. The impact is difficult to determine – Tesla has high stock volatility which increases the option time value, but this is mitigated by many of the outstanding options being significantly in-the-money during 2022.

Nevertheless, while it is challenging, we think that investors should seek to identify the fair value of non-common share equity interests when material. These should be included in enterprise value for EV based analysis and used to estimate the appropriate diluted share count for the direct analysis of common shares.

The unearned compensation adjustment

It is not just the treasury stock method that causes dilution to be understated. In our view, the adjustment to the exercise price for employee stock options is also problematic.

Unearned stock-based compensation increases the assumed ‘treasury share buyback’ and reduces apparent dilution

When applying the treasury stock method to employee options and restricted stock units, the unearned employment expense is added to the exercise. This increases the assumed treasury share buyback and results in a lower diluted share count. The unearned employment expense arises where stock-based compensation (SBC) does not immediately vest, and employees must provide further employment services before being able to benefit from exercising their options or selling shares.

For example, suppose a company issued 100 employee stock options 1 year ago that had a fair value at the time of grant of $10 per option or $1,000 in total. If the vesting period is 4 years only $250 of the grant date value would have been recognised as an expense (and as a credit to shareholders’ equity) in the previous year. The remaining $750 does not appear in the financial statements, although under US GAAP it is disclosed.

However, for EPS purposes, the employment expense related to past option grants that will be recognised in subsequent periods is added to the option exercise price – the employees must provide $750 worth of employment services (or $7.50 per option) as well as paying the strike price to exercise their options. If the exercise price is, say, $3 per option then the diluted share count adjustment would only be positive if the share price is above $10.50; the sum of the exercise price ($3) and the unrecognised employee stock-based compensation ($7.50).

The unearned compensation adjustment also affects the dilution for restricted stock units. In effect these have an exercise price of zero in cash terms, but the unearned component of the SBC expense is treated as a payment for these shares and therefore reduces the apparent dilutive effect.

We do not think the unearned compensation should be included in the exercise price. This is a pre-paid compensation expense and would be better reported as a prepayment asset with the full SBC issue recognised immediately and with no corresponding treasury stock method adjustment. The current approach unrealistically restricts EPS dilution, which is even further removed from the fair value of options that impacts equity investors.

Anti-dilutive securities are ignored

The diluted share count is only calculated and disclosed in the context of diluted earnings per share. The focus of the calculation is on the reduction of EPS if potentially issuable shares turn into actual issued shares. Consequently, any securities that are ‘anti-dilutive’ – those that would result in an increase in EPS – are ignored. Anti-dilution arises where the share price is below the exercise price and the net effect of applying the treasury stock method is therefore a reduction in shares. However, it can also happen if a company is loss making.

Share count dilution should not be ignored just because net income is negative

If the treasury stock method results in an increase in diluted shares but the company is loss making, the effect is to reduce that loss per share, which is regarded as anti-dilutive. However, we think this is misleading – the diluted share count is still higher.

The extract below illustrates this issue. Aridis Pharmaceutical is loss making and has a negative basic EPS. As a result, the warrants and stock options it has issued are all anti-dilutive, even though at least some (those that are in the money) would have been dilutive had the company been profit making.

The potential future share issues total 5.5m shares compared with 12.3m currently in issue. There is therefore clearly a current economic dilutive effect due to the fair value of these options. If the company becomes profitable, there will be EPS dilution. However, the accounting does not quantify this – the 5.5m is not the result of applying the treasury stock method nor is there any disclosure of our favoured ‘fair value common stock equivalent’, which makes the analysis of dilution for this company very difficult.

Aridis Pharmaceutical

Aridis Pharmaceutical 2022 10K

Adjusted (non-GAAP) diluted EPS may require a different diluted share count

The effect we describe can be particularly misleading when companies present adjusted (non-GAAP or non-IFRS) EPS metrics. If, for example, the reported basic EPS is negative (and therefore potentially dilutive securities are anti-dilutive) the diluted and basic share count are the same. However, if the adjusted EPS is positive, and what was previously anti-dilutive now becomes dilutive, the diluted share count should be different from the share count used for GAAP EPS. Because there is no accounting standard that governs adjusted per share metrics, we cannot be confident that all companies reporting non-GAAP EPS use the correct share count.

In our view, investors would be better served if financial statements just contained a diluted share count measure (both an average for the period and a period end amount) calculated using the fair value approach we advocate. Investors can then determine how this is best used in their analysis.

Enterprise value is a better approach

The problems with the diluted EPS calculation support our preference for an enterprise value based approach to equity analysis and valuation. A market enterprise value used in EV multiples should include the fair value of equity options and convertibles. Because the dilutive effect ,is captured in the fair value of these other equity claims, the market capitalisation component of EV should be based on the basic (not diluted) number of shares. In an EV based analysis the inadequacies of the treasury stock method become irrelevant.

The same applies to an enterprise to equity bridge calculation. After computing a business value using, for example, an enterprise DCF model, deduct the fair value of all non-common stock claims, including the fair value of equity options, before dividing by the basic share count.

Lack of fair value disclosures also makes enterprise value based analysis difficult for investors

We also think that the full fair value of outstanding employee stock options and restricted stock units should be included in EV, even though they are only partly reflected in the balance sheet. This is consistent with our comments above about how unearned stock-based compensation has the effect of understating the diluted share count.

The big problem for investors regarding enterprise value is that there is no requirement to disclose the fair value of outstanding equity options (including the bifurcated options embedded in convertibles reported under IFRS). We have previously advocated that this information should be a required disclosure – see our article ‘Enterprise to equity bridge – more fair value required’.

Is there any chance diluted EPS will be revised?

Don’t hold your breath …

Last year the IASB completed its most recent consultation4More information about the IASB’s third agenda consultation, including the conclusions and feedback documents, can be found on the IASB website. about its agenda. During the next 5 years it intends to increase its focus on digital reporting, further support consistent application and improved understandability of IFRSs, and to commence work in some specific areas that may ultimately lead to new or revised standards.

Little sign that the standard setters will embrace the fair value approach for diluted EPS

The IASB will start new projects on the accounting for intangibles and on the statement of cash flow, the shortcomings of which have been the subject of several our articles.5For example, see our article ‘When cash flows should include non-cash flows’. The IASB will also work with its new sister body, the ISSB6The ISSB or International Sustainability Standards Board was established in 2022 to develop international standards for the disclosure of sustainability related information., on climate related risks and how these should be reflected in financial statements, and if resources allow, will start work on improving segment reporting and the accounting for pollutant pricing mechanisms.

All these initiatives are welcome. However, much to our disappointment, earnings per share barely featured in the latest IFRS agenda consultation, and there seems to be little chance of reform anytime soon.7Although there has been no proposal to embrace fair value for the diluted share count, some years ago the IASB had the clever idea to modify earnings attribution which, in effect, would have produced the same outcome. In the Financial instruments with characteristics of equity discussion paper issued in June 2018, there was a proposal that part of profit and loss should be ‘attributed’ to outstanding options, based on the relative fair value of those options compared with the market capitalisation of common stock. This would deal with options in much the same manner as non-controlling interests in calculating basic earnings per share. The outcome in terms of earnings per share would be identical to what we propose in this article. Unfortunately, respondents to the discussion paper failed to see the merits of the approach and, although the IASB is still debating this subject, it seems unlikely there will be any change related to EPS or earnings attribution.

Insights for investors

  • The treasury stock method of calculating diluted earnings per share understates dilution by failing to consider the full fair value of outstanding options.
  • Just allowing for the intrinsic value of options can result in a misleading increase in diluted EPS when options are issued, even though no value is created by simply raising finance in this way.
  • The dilutive effect of stock-based compensation is reduced by including unrecognised compensation expense in the calculation of the assumed treasury stock buyback.
  • The concept of securities being anti-dilutive is misleading. All options create dilution in value terms, even if not under the treasury stock method, and dilution should not be ignored for currently loss-making companies.
  • The IFRS and US GAAP approach to dilutive EPS is long past its sell by date. Perhaps the 50th anniversary of the publication of the famous Black-Scholes model will persuade the standard setters to finally catch up.

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