Sally Case Study Havard Business
1. If we ignore tax considerations and assume that Sally is free to sell options at any time after her joins Telstar, which compensation package is worth more? If tax consideration is ignored and assume that Ms. Jameson is free to sell options at any time after her joins Telstar.
First scenario If Ms. Jameson chooses stock options, she will hold until maturity date. Cash compensation at the end of the 5th year[1] = $5,000(1+6.02%)^5 = $6,697.44 To equal $6,697.44, the stock price must increase to at least $37.23[2] at the end of the 5th year. The stock price has to be higher than $35 in order to be exercised and make a gain, otherwise she will leave it expire worthlessly. However, from Exhibit 2, Telstar stock price has increased higher than $35 only once and 10-year average stock price is $21.17. Therefore, the chance that the value of option is greater than the cash compensation is very rare. The options will even worth nothing to Ms. Jameson if the stock price is below $35 at the maturity date. If Sally holds options until maturity, she should choose cash compensation.
Second scenario Because, Ms. Jameson is free to sell options at any time after her joins Telstar, she may sell her option immediately after receiving (at the time that the value of option is greatest) We price the value of stock option by using Black and Schole’s Model and compare it with cash compensation of $5,000. [pic]
[pic] and [pic]
S0 = 18.75 K = 35 T = 5 (refer in case) rf = 6.02% (use 5 year T-bond yield, which match with time to maturity of the option)
For volatility, we calculate both historical volatility and implied volatility.
(1) Historical volatility : calculate from historical stock returns for 10 years.
V = 0.3687 or 36.87%
V comes from: The return of stocks = ln(stock priceT/stock priceT-1 Standard deviation of stock return = 0.023 per day, Convert to per annum = [pic]
First scenario If Ms. Jameson chooses stock options, she will hold until maturity date. Cash compensation at the end of the 5th year[1] = $5,000(1+6.02%)^5 = $6,697.44 To equal $6,697.44, the stock price must increase to at least $37.23[2] at the end of the 5th year. The stock price has to be higher than $35 in order to be exercised and make a gain, otherwise she will leave it expire worthlessly. However, from Exhibit 2, Telstar stock price has increased higher than $35 only once and 10-year average stock price is $21.17. Therefore, the chance that the value of option is greater than the cash compensation is very rare. The options will even worth nothing to Ms. Jameson if the stock price is below $35 at the maturity date. If Sally holds options until maturity, she should choose cash compensation.
Second scenario Because, Ms. Jameson is free to sell options at any time after her joins Telstar, she may sell her option immediately after receiving (at the time that the value of option is greatest) We price the value of stock option by using Black and Schole’s Model and compare it with cash compensation of $5,000. [pic]
[pic] and [pic]
S0 = 18.75 K = 35 T = 5 (refer in case) rf = 6.02% (use 5 year T-bond yield, which match with time to maturity of the option)
For volatility, we calculate both historical volatility and implied volatility.
(1) Historical volatility : calculate from historical stock returns for 10 years.
V = 0.3687 or 36.87%
V comes from: The return of stocks = ln(stock priceT/stock priceT-1 Standard deviation of stock return = 0.023 per day, Convert to per annum = [pic]