A Note on Stock Options and Corporate Valuation

A Note on Stock Options and Corporate Valuation Bernhard Schwetzler * Many listed companies offer stock option plans (SOP) to their managers as part of a performance-based compensation package. For financial analysts the impact of stock option plans upon corporate value is often difficult to estimate. Also the procedure how to properly account for SOP in the valuation process is an issue. This note highlights the most important problems and tries to give some technical advice for the incorporation of SOP in the valuation procedure. * Prof. Dr. Bernhard Schwetzler WestLB Chair Financial Management CCT Center for Corporate Transactions HHL Leipzig Graduate School of Management

1. Shall we care about SOP when calculating corporate values? Yes, we should because - options given to the managers otherwise could have been sold on the marketplace and the firms would have realized the sales proceeds, - SOP may substitute salary that otherwise would have been paid as cash to the managers, - in some cases (especially in growth firms) SOP are significant in size related to the market cap of the firm, - even if you don t care about SOP in the valuation procedure you should have an idea about the necessary assumptions that would allow you to ignore SOP. 2. How to value a SOP Let us start with the question how to properly value a SOP at the grant date (as we will see this does not necessarily give us the right answer on the question about the impact of a SOP upon the equity value of the firm). This question has been a major issue for accountants. As a SOP gives the managers the right to purchase shares of their company at pre-specified conditions within a certain time frame, the major accounting standards propose the application of option pricing models for the calculation of the value of the SOP. SFAS 123 (R) share based payment recommends standard Black-Scholes or Binomial-models as a starting point for the calculation of the grant-date fair value; IFRS 2.17 also refers to generally accepted valuation models. The grant-date fair value is then to be distributed over the requisite period, i.e. the number of years until the vesting date. There are some SOP-specific reasons that might require some adjustments to the standard option pricing models: - SOPs are not tradable on a stock exchange, - SOPs cannot be exercised by the manager before vesting date, and - SOPs expire if the manager leaves the firm before the vesting date. Due to this reasons the value of a SOP is usually argued to be significantly lower than the standard option pricing formula would suggest. There may be some other reasons that may make it rather complicated to calculate the fair value of the SOP: - The SOP may be structured as an outperformance model against some capital 2

market index (in order to avoid windfall gains and losses). In this case, you (or the accountant that is to calculate the value of the SOP) will have to use some more advanced models for the valuation (e.g. Garbade-model for pricing exchange options). - In some cases, the strike price of the option is increased by a certain amount if the manager does not exercise this year. - Empirical evidence suggests that managers exercise their options earlier than theory would recommend; the reason for this is that managers have a significant fraction of their wealth tied up in their program. Thus, the overall risk to their personal wealth is higher than that of a well diversified investor. To sum up, the valuation of a SOP may become a rather tricky thing for the accountant calculating the grant-date fair value. Being an external financial analyst, you are in a lucky position being able to rely on the results of this procedure: the amount showing up as an expense in the annual report of the firm. Can we directly refer to the grant-date fair value of a SOP for the purpose of corporate valuation? Unfortunately not because - the result just refers to the grant date. As important input factors for the value of the option may change over time (e.g. the stock price (underlying) or the time to maturity of the option), the value of the option will change as well. - the impact of a SOP upon corporate value will crucially depend on the relative cost and benefits against a cash wage payment. Knowing just the cost of a SOP does not tell us anything about these factors. 3. How to assess the value impact of future grants Especially when using DCF-based valuation models you will be concerned with the problem to assess the impact of future grants of SOP upon the value of the corporation. Here there is a convenient way to ignore the SOP in the valuation procedure: just assume that the relative cost and benefits of SOP against cash wage net out to zero. This assumption allows you to make projections for the management s total compensation including both cash payments and future grants of SOP without having to address the problem of the uncertainty of the absolute size and other important features of the future grants: no matter how big the grant will be, it will always substitute an equivalent amount of cash payments. Given the options to be valued with their fair value at any future grant date there will be no difference 3

between a future cash payment and a future option grant of the same size. In any case you will have to take future grants into account when making your projections for the total management compensation. If you have the chance to rely on future P&L projections that already contain expenses for future option grants, this is fine. But you have to watch out and adjust the figures if the amount is already distributed over the years until the vesting date: the assumption above states that the total amount of the annual grant will be substituted by cash payments. 4. How to asses the value impact of past grants Past, sunk, and therefore irrelevant? One may think that SOPs granted in the past are sunk cost and thus irrelevant for corporate valuation, but unfortunately this is not the case: as the firm is the writer of the call, any change in the options value will affect the value of its equity. An increase in the call s value decreases the equity value and vice versa. 1 Over the lifetime of the option, input factors for the valuation may change significantly. The most important factor is the stock price as the value of the underlying: an increase in the stock price increases the value of the option and by doing so reduces the value of the equity. The table below shows the change in input values and the according changes of the options value for the 1999 tranche of the SOP of EPCOS, a Germany based high-tech firm listed at Frankfurt stock exchange (we used a standard BS model for simplicity): Date 14.10.1999 (grant) 11.2.2000 (high) 26.11.2002 (low) Strike 35,6 35,6 35,6 Stock price 31,0 177,0 15,0 Volatility 70% 70% 70% Risk less rate 5,16% 5,35% 3,93% Dividend 0 0 2,25 adjustment (PV) Time to maturity 7 6,666 5 Value Call 21,2 157,20 4,89 The table shows that changes in the share price are triggering huge changes in the 1 This argument presumes that the firm did not yet cover the call by purchasing the underlying stock. This is especially the case if the firm serves the option by issuing new shares. 4

value of the outstanding options. As the firm itself is the writer of the options an increase from 21,2 to 157,2 in option value must negatively affect the value of its equity. This effect is independent from the wage substitution the SOP has had at the date granted: - If the SOP did not substitute any wage, then the options with a fair value of 21,2 have been given away for free to the managers. As the firm is the writer of the option, it is still negatively affected by the increase of the options value. - If the SOP fully substituted wage, then the managers received an option with a value of 21,2 instead of a 21,2 payment in cash. At the date when granted the SOP thus has been neutral to shareholder wealth. On the other hand the firm is changing the cash payment against a contingent liability of the manager: any increase in the liabilities value negatively affects the value of the equity and vice versa. The consequence of the second point is that the argument of the relative cost neutrality is not going to allow us to ignore SOP granted in the past when calculating corporate values (as this was the case for options to be granted in the future). The change in the options value can become significant even for large firms: For the example of EPCOS AG the BS value of the entire SOP outstanding dropped from around 48 mill. in dec. 2000 to 1,5 mill. in nov. 2002. The following chart shows the value of the entire SOP between 2000 and 2002 (thick line and right hand scale relate to the share price, left hand scale to the total SOP value): Wert der AOP der EPCOS AG 50.000.000 200 45.000.000 180 40.000.000 160 35.000.000 140 Wert 30.000.000 25.000.000 20.000.000 120 100 80 15.000.000 10.000.000 5.000.000 0 14.10.99 14.12.99 14.02.00 14.04.00 14.06.00 14.08.00 14.10.00 14.12.00 14.02.01 14.04.01 14.06.01 14.08.01 14.10.01 14.12.01 14.02.02 14.04.02 14.06.02 14.08.02 14.10.02 60 40 20 0 Datum Kumuliert AOP GJ 2000 AOP GJ 2001Tr 1 AOP GJ 2001 Tr 2 Aktienkurs 5

The example highlights the need to recalculate the value of the SOP granted in the past based on the market parameters valid on the date of the valuation. The only arguments perhaps justifying to avoid this effort are lack of materiality (if the value of the SOP is small against the firm s market cap) and a constant value of the SOP since grant date (in this case you can rely on the values at grant date). Now presume that the size and value of the SOP is large enough to be material and that there is evidence that the value of the options has changed significantly since grant date. What information does an external financial analyst need to recalculate the value of SOP granted in the past? Some of the data serving as an input for a standard option pricing model 2 are easily observable: volatility, underlying stock price, and risk less rate can be observed or derived from capital market data. 3 Usually, the options of a SOP are granted at the money, the average over some trading days stock price before grant date serving as strike price. Getting the strike price and the exact grant date for the options granted the current year may sometimes be difficult if the firm has issued options in several tranches throughout the year and just reports the average strike price for all options granted the current year in the annual statement. It may become rather cumbersome and sometimes impossible for an external financial analyst to disentangle the information given in the notes in order to get the exact grant dates and strike prices for each SOP tranche. In this case, the only option left is to use the average strike price reported and combine it with some appropriate average grant date (say, 1 st july) and estimate the value of SOP granted in the past based on these data. As the DCF-valuation concentrates on the projected future cash flows of the firm (including the future grants of SOP) it takes an additional step to account for the contingent liability caused by the options outstanding from past granted SOP to get the fair value of the firm s equity. This is done by deducting the current fair value of the past SOP s. 2 If the re-evaluation of the SOP granted is performed by an external financial analyst, the use of standard option pricing models can be justified. 3 In the case of an outperformance option against a market index volatility and index itself can also be calculated and observed resp.. 6

6. FAQs 1. When trying to properly ignore SOP why not simply pointing to capital market efficiency and arguing that the share price will fully reflect any value impact caused by past and future grants of SOP? The argument is different for the share price and the fair value per share: of course the fair value of the SOP should also be reflected in the current share price, if the market is efficient. But the fair value based on DCF does not yet take the impact of SOP granted in the past into account, so you as financial analyst have to by deducting the fair value of the SOP. 2. There are several ways for the firm to deliver the underlying stock if the option is exercised: physical delivery by the firm is arranged by either the company buying back own stock and selling it to the managers or (the more common case) by the firm creating new shares via capital increase and issuing it to the manager. On the other hand, many programs organized as stock appreciation rights (SAPs), realize a cash settlement by the company paying the intrinsic value of the options as cash to the managers when exercising. Does the way how the firm delivers the underlying affect corporate value? The answer to follow concentrates on the impact upon shareholder wealth; different tax treatments, social security issues and accounting treatments of the three different delivery options are ignored. Let us start by comparing the buyback and deliver option against the cash settlement (here the number of shares is not affected by any of the two procedures). Obviously, there should be no difference between the two as the loss/negative cash flow for the firm is the same in both cases: buying back the stock at the market price and selling it to the managers at the lower strike price realizes the same negative cash flow as paying out the intrinsic value as cash. It is a bit trickier to compare the two options mentioned against the case of newly issued shares because the number of shares outstanding will be higher in the latter case. Managers pay the strike price into the company and get newly issued shares. If the total equity value of the firm is increasing by exactly the amount of cash flowing into the firm, then there will also be no difference in the value per share for the different options: the cost for the shareholders of the managers exercising the options is the difference between the current share price and the strike price paid by the managers as the cost for issuing the 7

shares too cheap. The total value of equity in the future will be different: in the latter case total equity value will be higher by the additional cash paid into the firm as the total strike prices. 3. The convenient way to ignore future SOP grants discussed in (3.) relies on the assumption that the net cost of a SOP are equivalent to a cash wage payment. Empirical evidence suggests that this is not the case: managers value 1 in cash significantly higher than an option with a fair value of 1. That means the cost of SOP for the firm are higher than the value attributed to the SOP by managers. Does not this blow up the convenient way to ignore future SOP grants? While it is true that the cost of a SOP for the firm are higher than the perceived value of the SOP by the managers, there may still be a way to save the argument in (3.) by relating it to the net of cost and benefits: The higher cost of the SOP against a cash payment may be offset by the higher incentive it provides for the managers to increase the value of the company. So if 1 value in cash wage are equivalent to, say, 1,30 in SOP value the higher cost of the SOP will be compensated if, due to better alignment of managements and shareholders interest and higher effort, the value of the firm increases by 0,30. (This figure relates to the present value of the future cash flows caused by the higher incentive). 4. Some analysts prefer another way to adjust the DCF-value calculated for SOP: they account for dilution by dividing the equity value by a number of shares adjusted for the effect of outstanding options. Does this correctly reflect the value impact of a SOP? First, you may only think about such an adjustment when the firm is serving the options by issuing new shares to the managers. Under a buyback program or under a SAR program with cash settlement there will be no dilution. Let us start with looking at options granted in the past: Adding the number of shares tied to SOP granted in the past to the current number of shares outstanding does not reflect the value impact of the options outstanding. That becomes clear by looking at out-of the-money options: clearly, it is wrong to add the shares tied to this options to the number of shares outstanding as under current conditions they will not be exercised. A better (but still wrong) version only relates to the number of in the money-options to the number of shares; still, 8

it does not fully capture the value impact of SOP granted in the past because it ignores the fact that managers will be paying in the strike price of the option. Both methods implicitly assume that the firm will give away the underlying stock for free. So a more sophisticated method to adjust for dilution is to calculate the future cash inflow (as sum over the strike prices of all in the money options), add it to the current value of equity and adjust for the number of shares. Still this method does not fully reflect the value impact of SOP as it assumes that the value of the options outstanding (and thus the value of the contingent liability for the firm) is equal to the intrinsic value of the options and thus ignores the option s time value. So as a result none of the adjustments for dilution is fully capturing the value impact of SOP options granted in the past. If there is a need for a per share calculation of the fair value, the better way to account for SOP is to calculate the fair value per share based on the current ( undiluted ) number of shares and to calculate the current per share fair value of the SOP and deduct it. For future grants of SOP the case is even more against any dilution adjustment: you should calculate the value of the equity to the current shareholders; giving options to the managers in my view can best be incorporated by referring to the fair value of the options at their grant date and deducting this amount from the future cash flows to the current owners. As a result there is no need to adjust the number of shares for dilution. 9