Sally Jameson Valuing Stock Options in a Compensation Package
Sally Jameson: Valuing Stock Options in a Compensation Package
By Group 10
1. If we ignore tax consideration and assume that Sally Jameson is free to sell her options at any time after she joins Telstar, which compensation package is worth more?
First scenario, if Sally chooses stock options and hold until maturity date. Ignoring the taxation and other constraints, the future value of cash compensation at the end of the 5th year will be 5000 * (1 + 0.0602) ^ 5 = 6697.44. We can easily form the equation 3000 * (P – 35) = 6697.44, where P is the future stock price of Telstar, so the stock price must increase to at least 37.23 at the end of 5th year to get the same amount of the cash compensation and if the stock price where to stay below 35, Sally’ option would be worth nothing. The stock, which pays no dividend and is not expected to pay one in the foreseeable future, is trading at 18.75. It seems significant difference between the exercise price and the spot price. As shown in Exhibit 2, Telstar stock price has increased higher than $35 only once and 10-year average stock price is around 20. Therefore, the chance that the value of option is greater than the cash compensation is very rare.
Second scenario, assume Sally is free to sell options at any time after her joining Telstar, she may sell her option immediately after receiving. Then we try to price the value of stock option by using Black - Scholes Model.
We know that the stock is currently trading at $18.75 and the exercise price is $35. We take the 5 year T-bill rate 6.02% as the risk free rate. From the Exhibit 2, we can calculate the volatility of Telstar stock return is around 27.65%. Plug them into the formula, the call option price will be 2.53. At this amount, Sally’s options would be presently worth 2.53 * 3000 = 7590. She is better off taking the option.
2. How should we factor in the complications ignored in question 1? How would they affect the value of the option to Ms. Jameson? What should
By Group 10
1. If we ignore tax consideration and assume that Sally Jameson is free to sell her options at any time after she joins Telstar, which compensation package is worth more?
First scenario, if Sally chooses stock options and hold until maturity date. Ignoring the taxation and other constraints, the future value of cash compensation at the end of the 5th year will be 5000 * (1 + 0.0602) ^ 5 = 6697.44. We can easily form the equation 3000 * (P – 35) = 6697.44, where P is the future stock price of Telstar, so the stock price must increase to at least 37.23 at the end of 5th year to get the same amount of the cash compensation and if the stock price where to stay below 35, Sally’ option would be worth nothing. The stock, which pays no dividend and is not expected to pay one in the foreseeable future, is trading at 18.75. It seems significant difference between the exercise price and the spot price. As shown in Exhibit 2, Telstar stock price has increased higher than $35 only once and 10-year average stock price is around 20. Therefore, the chance that the value of option is greater than the cash compensation is very rare.
Second scenario, assume Sally is free to sell options at any time after her joining Telstar, she may sell her option immediately after receiving. Then we try to price the value of stock option by using Black - Scholes Model.
We know that the stock is currently trading at $18.75 and the exercise price is $35. We take the 5 year T-bill rate 6.02% as the risk free rate. From the Exhibit 2, we can calculate the volatility of Telstar stock return is around 27.65%. Plug them into the formula, the call option price will be 2.53. At this amount, Sally’s options would be presently worth 2.53 * 3000 = 7590. She is better off taking the option.
2. How should we factor in the complications ignored in question 1? How would they affect the value of the option to Ms. Jameson? What should