Sally Jameson: Valuing Stock Options in a Compensation Package (Abridged) Group Satie: Ai Nakajima, Chen-Wei Tang, Mithun Sridharan, Sarah Wright, Daniel de la Cuesta 23th May 2012
If we ignore tax considerations and assume that Sally Jameson is free to sell her options at any time after she joins Telstar, which w hich compensation package is worth more?
We can calculate the value of the stock options today using the Black-Scholes Model. If the value of the 3000 Sally´s stock options is greater than $5000 and she has the possibility to sell the options, then she should go for the stock options instead of the cash. To calculate the value of the stock s tock options today we have to find the volatility volati lity of the stock. In this case we are going to calculate the “historical implied volatility”, which refers to the implied volatility observed from historical prices of the stock. We have the historical price of the stock for the last 10 years so we calculate the gains for each value compared with the t he previous one (P1/PO) and we convert them to the logarithmic scale (LN(P1/P0)). After that, we calculate the standard deviation of the time serie and we multiply it by SQRT(252) to get the annualized volatility. The final value for the volatility is 0.3689. Now we have all the data to calculate c alculate the current fair value of the stock options offered to Sally: Option Price Exercise price
P X
Current Stock Price Risk-Free Rate Maturity of the call Volatility
S r T Delta
d1 d2
C0 (BlackScholes)
23 35 18.75 4.07% 5 0.368958192
0.369407882 -0.988822938
7.468518841
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The total value of the stock options offered to sally is: #Stock Options Value of the options
3000 22405.55652
The fair value of the stock options is higher than the cash ($5000) so, she should go for the stock options. Anyway, seems that there is not a market for these options in the conditions offered to Sally (Exercise price = $35 and longterm maturity of the call 5 years). If we look at Exhibit 2, the Telstar long-term Call Options traded have a maturity of 2 years and a maximum strike price of $20.00. Given the trading trend observed, we think that she is not going to be able to sell her stock options in the market. Hence, she should select the cash as compensation package. How should we factor in the complications ignored in the above question? How would they affect the value of the option to Ms. Jameson? What should Ms. Jameson do? Why?
Now we are assuming Sally can´t sell the options until 5 years. Also, if she leaves the company before 5 years she will lose the options. In addition, the capital gains of the stock options in 5 years (if we can sell them) have to be higher than $6754.49. This money is the return that you get if you invest the money ($5000) in zero-coupon US Treasury Yields at 6.20%. (Sp * 3000) – (35 * 3000) = 6754 Sp = $37.25 The price of the stock in five years should be $37.25 to make the stock options a better compensation package than cash. Looking at the historical data provided in the Excel spreadsheet, the stock price was above $35 only once in the last ten years (10/9/1989) and never has been above $37.25. So, it is very unlikely that the stock price will be above this number. Sally should go for the cash as a compensation package instead of the stock options. On the other hand, Sally could be very confident of her possibilities as a manager and if she thinks that can increase the value of the company to $37.25 per share she should go for the stock options.
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Does granting stock options cost companies anything? If so, who pays? What incentives do executive stock option plans create for their recipients? How might firms create more effective or more efficient incentives?
The stock options granted to employees can be considered as a cost. The cost of these stock options should be the economic value of the options if they were to trade in the market. The Black-Scholes formulae give us this fair value of the stock options. This cost doesn´t have to be declared in the income statement of the company although the cost can be disclosed in the notes to the financial statements. This improves the transparency of the company with its shareholders. Who pays? Nobody pays for this stock options, it is not a cash outflow for the company. For executives, stock options help resolve the agency problem. By dispatching a part of the compensation as stock with agreed upon goals, such as company value /EPS/Stock price, executives could be motivated to work harder for the benefit of the shareholders. When a company grows, it is in a better position to pay dividends, which broadcasts a positive message in the market. When messages are favorably received by the market, the stock trades at higher prices, thereby enhancing the probability of the stock price reaching or exceeding the strike price. This is the condition expected of the executives, so stock options motivate senior executives to work & add value to the company & its shareholders. By projecting the industrial growth and the growth of comparable firms in the industry, firms could, with a certain degree of confidence, make a strategic growth projection. This projection, when agreed upon by the stakeholders, is representative of the actual growth prospects that could be expected. So, managing expectations of stock price & objectively fixing the expected price is a good means to create effective incentives.
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