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Online Tutorial #6: How Do You Calculate The Cost of Employee Stock Options?

We discuss the impact of Employee Stock Options (ESOs) in the Appendix to Chapter 5, entitled "Employee Stock Options and Expectations Investing." Stock options can materially affect shareholder value, and thus our Price-Implied Expectations analysis.

In this tutorial, we give further detail and provide data sources for the analysis of Microsoft's ESOs. In particular, we drill down on two primary ways in which ESOs can affect the expectations investing process:

1. Outstanding stock options. Already issued and currently outstanding ESOs represent an economic liability from the perspective of shareholders. Thus, you must subtract outstanding ESOs, like debt, from corporate value to derive shareholder value.

2. Future option grants. Options to be granted in the future represent an economic cost that you must subtract from future cash flows.

We walk through both calculations below. Readers who want to calculate the cost of ESO for this Microsoft case study may also wish to download the accompanying spreadsheet. Please note that certain numbers in this tutorial may differ slightly from the book, as we have incorporated some additional steps in this more detailed analysis. For example, in this exercise, we adjust for the fact that ESOs are really a "warrant." In the book, we simply referred to this in a footnote.

Readers who want to analyze the cost of Gateway's ESOs may wish to download this spreadsheet.

Finally, readers interested in exploring this subject further may be interested in a lengthy CSFB Equity Research Report on ESOs -- entitled "A Piece of the Action" -- that can be downloaded by clicking here.

Step 1: Valuing Outstanding Stock Options

We can value the economic liability that outstanding stock options using information dislosed in a company's Annual Report. Here, we walk through this calculation, using Microsoft as a case study.

The first step is to value the ESOs using the Black-Scholes option pricing method. Microsoft gives us detailed information on options in five groups—each with its own range of exercise prices. To calculate the Black-Scholes value, we must combine this information with our estimates of the following six parameters for each group:

1. Stock price: Microsoft closed at $80.00 on June 30, 2000. Enter the stock price in cell C29 of the "Inputs" worksheet and the date in cell C28.

2. "Weighted average characteristics of outstanding stock options." The annual report and 10-K SEC filing give this information for each group of outstanding options. To find these data, we can consult the Microsoft Investor Relations web site and look on page 13 of the Financial Review section in the fiscal 2000 annual report. Specifically, look at the table under the text "For various price ranges, weighted average characteristics of outstanding stock options at June 30, 2000 were as follows." In the spreadsheet, transcribe this data into the cells ranging from B4 to G10. In addition to the number of options granted and the weighted average exercise price, it is also necessary to note the "expected life of the options." Microsoft reports this data point as “Remaining life (in years)” for each group of outstanding options. We use this number to value the company’s ESOs. Note that we are using the option's contractual life, not its expected life. If we used an average expected life of 6 or 7 years, which accomodates the likelihood of early exercise, the value of each option is approximately 10 to 20% lower.

3. Risk-free rate. The appropriate risk-free rate is the rate associated with the risk-free zero-coupon security with the same maturity as the option. For example, to use a Bloomberg terminal to obtain the yield of a zero-coupon Treasury Bill expiring in a year, type “B mm ” and hit the button. (Note that “mm” stands for the month of the T-bill’s expiration.) In practice, using the rate of return on five-year government treasury bonds will come close to this number. Sources for the ten-year treasury bond include:

  • CBS Marketwatch. Even unregistered users can use CBS MarketWatch's free bond quotes by clicking here.
  • New York Times. Any user can see the "10yr. Tres. Yield" on the front page of the New York Time's web site by clicking here. To get further details on the five-year government treasury bond, you can register free of charge.
  • Wall Street Journal. Paid subscribers to the WSJ's online service can find quotes for key interest rate measures.

Another common practice is to use the risk-free rate assumed by the company. While this may be an acceptable shortcut, the value of ESOs may change if rates fluctuate or if the company picks a inappropriate risk-free rate. You can find the company's assumed risk-free rates in the last paragraph of page 13 of the Financial Review section in the fiscal 2000 annual report. Transcribe this number into cell C30 of the "Inputs" worksheet.

4. Volatility. This parameter refers to the expected volatility—technically, the standard deviation—of the underlying stock. This number should be entered into cell C31 of the "Inputs" worksheet.

Companies disclose their own estimate of volatility, which can serve as the starting point for this analysis. However, as with risk-free rates, companies have an incentive to choose a lower volatility level, so using a company’s estimate may result in understating the value of outstanding options. This data point can also be found in the last paragraph of page 13 of the Financial Review section in the fiscal 2000 annual report.

5. Dividend yield (q). This equals next year’s expected dividend per share divided by the share price. Note that this assumes that the company has a constant dividend yield over the option’s life. Alternatively, this assumption can be relaxed by assuming the dividend yield is zero and lowering the stock price by the present value of future dividend payments expected during the life of the option. We can find the dividend for any stock at many sources including Yahoo and CBS Marketwatch. Enter the dividend in dollars into cell C32 of the "Inputs" worksheet.

Using these inputs, we can calculate the value of each group of Microsoft’s employee stock options.

To illustrate this methodology, the remainder of this tutorial on outstanding ESOs develops the Microsoft ESO case study described in the appendix to Chapter 5, focusing on valuing a group of Microsoft’s fiscal 2000 ESOs with an exercise price ranging from $83.29 and $119.13.

There are four main steps:

1. Black-Scholes valuation. Microsoft’s 2000 Annual Report shows that the company had approximately 166 million of these ESOs outstanding. The company also discloses the inputs it uses to calculate the Black-Scholes value of its annual option grants. For the purposes of this exercise, we have valued Microsoft’s outstanding ESOs using these same estimates (see Table 1).

Table 1

Characteristics of Microsoft’s ESOs with Exercise Prices between $83.29 and $119.13, Fiscal 2000

Range of Exercise Prices Weighted Average Exercise Price Stock Price 6/30/00 Time to Expiration Risk Free Rate Volatility Dividend Yield Value of Call Option
$83.29 - 119.13 $ 89.91 80.00 8.6 6.2% 33.0% 0.0% $ 41.41

Source: SEC filings and analysis.

The Black-Scholes formula tells us that a call option with these characteristics has a value of $41.41. At first glance, it seems we should multiply this value times the number of outstanding options and have our answer. However, we must make a number of additional and potentially major adjustments:

2. Employees leaving before their options vest. Most firms use ESOs as a tool to retain valuable employees. Thus, options are typically structured so that an employee who leaves the firm has to forfeit any unvested options. While losing a valuable employee does not help a company, shareholders do benefit in part from the resulting option forfeiture. To value this effect, we estimate how long each option group has before it becomes fully vested. Then, using our estimate of how frequently employees leave the firm, we estimate how many of the ESOs in a particular group will exist at expiration date. We then multiply this number—the expected number of options at expiration date—by the company’s estimate of each option’s Black-Scholes value to get a preliminary estimate of those ESOs’ value.

We applied this technique to our case study of Microsoft’s ESOs with exercise prices between $83.29 and $119.13. These ESOs have an expected life of 8.6 years. Our next step is to estimate the vesting period of the typical Microsoft option.

Microsoft’s 2000 Annual Report states that:

Options granted during and after 1995 generally vest over four and one-half years and expire seven years from the date of grant, while certain options vest over seven and one-half years and expire after ten years.

Choosing a point estimate here will be somewhat subjective, as the company gives us a range of between 4 ½ to 7 years for the vesting schedule of its ESOs. We would lean toward the lower end of the range at five years since the text implies that the majority of the options are of the kind that vest in 4 ½ years. Using this estimate, and assuming that most options expire in 10 years, only an option that has less than 5 years to expiration will be fully vested. Thus, we can infer that these options with a 8.6 year contractual life have 3.6 years before they will be fully vested.

In the spreadsheet, then, enter the assumed option vesting period into cell C27 of the "Inputs" worksheet.

The next step is to estimate the number of options that Microsoft employees forfeit annually. Fortunately, Microsoft discloses the number of options outstanding, along with annual option grants, cancellations, and exercises. We can see this information on page 13 of the Financial Review section in the fiscal 2000 annual report in the first table on that page. Enter this information into the "Inputs" worksheet in the cells ranging from C17 to D22.

Using this information, we can divide the number of options cancelled annually by the average of the options outstanding during the year to calculate what we call the “option forfeiture rate” (see Table 2).

Table 2
Estimate of Microsoft’s Annual “Option Forfeiture Rate”

 

Year

Average Number of Options During Year

Annual Cancellations

Option Churn Rate

June-95

 

 

 

June-96

                       932

28

3.0%

June-97

                       954

36

3.8%

June-98

                       925

25

2.7%

June-99

                       830

30

3.6%

June-00

                       799

40

5.0%

 

 

 

 

 

 

Average

3.6%

Source: Company SEC filings.
Note: "Average Number of Options During Year" equals the average of beginning and ending outstanding options for a particular year.

 

We can see that Microsoft employees typically forfeit between 2.7% and 5.0% of total outstanding options annually. Taking a simple average of this tight range, we arrive at a estimate of approximately 3.6% for Microsoft’s annual option churn. In the absence of an “option reload”—in which management cancels all options with exercise prices above a certain price and replaces them with options with a lower exercise price—we can use this number as a proxy for the percentage of options cancelled annually.

We can then use this estimate to infer how many of these options will actually exist when they become fully vested. To do this, we use the following formula:


Applying this formula to our group of options, we see that Vested Options Expected = 166 million x (100 - 3.6%) raised to the power of 3.6 years, or 146 million. With a Black-Scholes value of $41.41 per option, we estimate that the group has an expected pretax “option equivalent” value of $6.0 billion. Thus, the estimated option forfeiture rate reduces the value of the group by approximately 12%.

3. Dilutive effect of employee stock options. In Footnote 11 of Chapter 5, we note that "Technically, employee stock options are not options--they're warrants." Here, we provide further details on how to make this adjustment.

Specifically, an ESO will always be worth slightly less than its “option equivalent”—a regular option with similar characteristics. This is because an ESO forces the company to issue a dilutive share, which lowers the value of each existing common share. In contrast, a regular option is "written" on existing shares, so when a regular option is exercised, the company does not issue any dilutive additional shares.

Option experts have derived a formula to calculate this effect:


We can use the “warrant conversion factor” to calculate precisely how much each ESO is worth. First, however, we need to estimate the dilution that occurs when employees exercise the options in each tranche of ESOs. For this group of options, we need to calculate how many shares will exist when employees exercise all vested options with lower exercise prices (see Table 3).

Table 3
Dilution from Exercise of Vested Options

Range of Exercise Prices

Value of Call Option Equivalent

Number Of Outstanding Warrants

Number of Years Before Options Vest

Estimated Number of Options at Vesting Period End

Number of Basic Shares

Warrant Conversion Factor [1/(1+q)]

$0.56 - $5.97

$ 75.99

133

-

133

5,283

97.5%

$5.98 - $13.62

$ 70.96

104

-

104

5,416

98.1%

$13.63 - $29.8

$ 68.09

135

-

135

5,520

97.6%

$29.81 - $43.62

$ 56.37

96

-

96

5,655

98.3%

$43.63 - $83.28

$ 46.52

198

2.3

182

5,751

96.9%

$83.29 - $119.13

$ 41.41

166.0

3.6

145

5,933

97.6%

Source: Company SEC filings and analysis.

If employees exercise all ESOs with lower exercise prices, 5.933 billion shares will be outstanding. Since there are 145 million ESOs expected to be fully vested, we can use these two numbers to infer the “warrant conversion factor” and value how much the ESOs will actually be worth. Using the equation above, the warrant conversion factor is 1 divided by the quantity (1 + (145 million/5.933 billion)), or 97.6%. Each ESO is worth only 97.6% of the calculated Black-Scholes value of $41.41, or $40.42. Thus, the unadjusted value of this warrant group is 145 million ESOs times $40.42, or approximately $5.9 billion (see Table 4).

Range of Exercise Prices

Value of Call Option Equivalent

Estimated Number of Options at Vesting Period End

Warrant Conversion Factor [1/(1+q)]

Fair Market Value Of Each Warrant

Expected Pre-Tax ESO Value

$83.29 - $119.13

$41.41

145

97.60%

$40.42

$5,869

Source: Company SEC filings and analysis.

4. Tax deductibility of an ESO’s intrinsic value at exercise date. Finally, we must take into account the benefit that the company will reap from tax savings. The IRS allows companies to deduct the intrinsic value of any option from pretax income during the year in which the employee exercises it. This lowers the cost of the option to the company by the calculated Black-Scholes value times the marginal tax rate. Thus, to calculate the expected after-tax value of Microsoft’s options, we multiply the expected pretax ESO value by the quantity one minus 35%. This reduces the value of this group from $5.9 billion to $3.8 billion.

If we repeat this exercise for all six groups of Microsoft’s ESOs, we come up with a total pretax value of approximately $45.5 billion and a total after-tax value of approximately $29.5 billion.

Step 2: Valuing Future Stock Option Grants

The disclosures mandated by Statement of Financial Accounting Standards (SFAS) 123 also allow us calculate the value of historical annual stock option grants. Here, we detail the specific steps needed to perform this analysis. Continuing our Microsoft case study, we apply our methodology to value Microsoft’s annual stock option grants.

1. Black-Scholes valuation. SFAS 123 requires that every company calculate the Black-Scholes per-option value of its annual stock option grants. It also requires disclosure of the inputs into the Black-Scholes formula. For example, page 13 of Microsoft’s 2000 Annual Report states that its 2000 annual stock option grant had a Black-Scholes per-option value of $36.67.

As with outstanding options, we can use disclosed information together with several assumptions to calculate the Black-Scholes value of option grants. Because we are going along with Microsoft’s assumptions here, we can accept the company’s valuation of its annual stock option grants.

2. Employees leaving before their options vest. We estimated that Microsoft employees tend to forfeit about 3.6% of outstanding options annually. Applying this churn rate to the number of ESOs granted annually, we can estimate how many options we expect will actually exist when they become fully vested. Using our estimate of a five-year vesting period and 10-year option life, we follow the same method as outlined previously to arrive at the following estimates:

Table 5

Microsoft’s Estimated Number of ESOs Expected at Vesting Period End, 1997-2000
in millions

 

Year

Number of Options Granted

Estimate of Annual Employee Churn

Vesting Period of Granted Options

Estimated Number of Options at Vesting Period End

1997

110

3.6%

5

91

1998

69

3.6%

5

57

1999

78

3.6%

5

65

2000

304

3.6%

5

252

Source: SEC filings.

 

3. Dilutive effect of employee stock options. Next, we estimate the dilutive effects of the annual ESO option grants, following the same procedure as outlined previously. To do this, we must calculate the “warrant conversion factor” formula:


The only major change is that we must estimate the number of shares that will exist when employees exercise a particular year’s ESOs. For example, looking at the 2000 ESO grants, we must assume that all outstanding options will be exercised before the employees exercise the ESOs freshly granted in 2000. After employees exercise all 795 million of the outstanding ESOs expected to be vested and exercised, the expected share count will rise from the basic share count of 5.283 billion to 6.115 billion. With 252 million options from the 2000 grant expected to be vested, we can calculate the warrant conversion factor of 96.0%.

With a Black-Scholes calculated “option equivalent” value of $36.67 for ESOs granted in 2000, this translates into an expected pretax ESO value of $36.67 times 96.0%, or $35.20 per ESO.

4. Tax deductibility of an ESO’s intrinsic value at exercise date. Finally, we adjust this value for the tax deductibility of the ESO’s intrinsic value at exercise. This lowers the cost of the option to the company by the amount of the marginal tax rate. At a tax rate of 35%, this translates into a value of $35.20 times 65%, or $22.88. With 252 million options expected to be vested, we can value the after-tax value expected economic value of the 2000 option grant at 252 million times $22.88, or $5.8 billion.

Repeating this exercise for past years, we arrive at the following estimates for the value of the grants from 1996 to 2000:

Table 6

Microsoft’s Expected After-Tax Economic Value Imparted to Employees, 1996-2000

in millions

Year Weighted Average Black-Scholes Value Warrant Conversion Factor [1/(1+q)] Expected Pretax Economic Value Imparted to Employees Marginal Tax Rate Expected After-Tax Economic Value Imparted to Employees

1996

$8.86

96.0%

$806

35%

$524

1997

$11.72

96.0%

$1,028

35%

$668

1998

$23.62

96.0%

$1,300

35%

$845

1999

$20.90

96.0%

$1,300

35%

$845

2000

$36.67

96.0%

$8,891

35%

$5,779

Source: SEC filings and analysis.

Note: These calculations assume that Microsoft’s warrant conversion factor from 1996 to 1999 equals the 2000 level.

After estimating the historical cost of annual ESO grants, we can then attempt to place a value on future annual ESO grants. This estimate depends on many factors, such as changes in business fundamentals, trend analysis, and the scalability of a company’s business model.

To estimate Microsoft’s future annual ESO grants, we first analyzed the company’s historical option cost as a percent of revenues—including both revenues and changes in deferred revenues. Over the last five fiscal years, this percentage was fairly stable between 4.0% and 5.7%--with the exception of 2000, a significant outlier owing to Microsoft's volatile stock price.

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