E09 G11 Sally Jameson Case
E09-G11
Mridul Arora, Florent Bernard, Jacqueline Kwok, Pu Wang
E09-G11
Sally Jameson Case
1. How much is the option compensation package worth
With the 5-year T-Bill yield, we can calculate the rf rate, compounded continuously, input for the BlackScholes model. e5r = 1 + (5-year T-Bill yield) e5r = 1.0602 r = 0.0117
Exercise price
X
35
Given by case text
Current stock price
Volatility of stock returns
Time to maturity
S ơ Ƭ
18.75
43%
5
r
6.02%
1.17%
Given by case text
Approximation given by Exhibit 3
Given by case text, assumed that Sally will not leave the company within 5 years
Annualized 5-year T-Bill rate
Simple interest rate
Continuously compounded interest rate
Using a Black-Scholes excel template, we know that each option is worth $3.867, meaning that the 3000 options is worth $11,607.
Template - Black-Scholes Option Value
Input Data
Stock Price now (P)
Exercise Price of Option (EX)
Number of periods to Exercise in years (t)
Compounded Risk-Free Interest Rate (rf)
Standard Deviation (annualized ơ)
18.75
35
5
1.17%
43.00%
Output Data
Present Value of Exercise Price (PV(EX)) ơ *t^.5 d1 d2
Delta N(d1) Normal Cumulative Density Function
Bank Loan N(d2)*PV(EX)
33.0129
0.9615
-0.1076
-1.0691
0.4572
4.7047
Value of Call
Value of Put
3.8670
18.1299
E09-G11
Mridul Arora, Florent Bernard, Jacqueline Kwok, Pu Wang
Ignoring tax considerations, Sally Jameson can sell her options package for more than twice of her cash compensation of $5000. If she does so as soon as she receives the options, and that the stock price remains at 18.75, she should go for the options package.
2. Factors impacting Sally’s options valuation
In terms of the option valuation, we believe that volatility is the number that can be adjusted in this case, and we made the big assumption that the volatility is 43% according to the graph given in exhibit 3.
Moreover, we have found that Sally will be indifferent towards the cash bonus versus options if the volatility is 29-30%, which
Mridul Arora, Florent Bernard, Jacqueline Kwok, Pu Wang
E09-G11
Sally Jameson Case
1. How much is the option compensation package worth
With the 5-year T-Bill yield, we can calculate the rf rate, compounded continuously, input for the BlackScholes model. e5r = 1 + (5-year T-Bill yield) e5r = 1.0602 r = 0.0117
Exercise price
X
35
Given by case text
Current stock price
Volatility of stock returns
Time to maturity
S ơ Ƭ
18.75
43%
5
r
6.02%
1.17%
Given by case text
Approximation given by Exhibit 3
Given by case text, assumed that Sally will not leave the company within 5 years
Annualized 5-year T-Bill rate
Simple interest rate
Continuously compounded interest rate
Using a Black-Scholes excel template, we know that each option is worth $3.867, meaning that the 3000 options is worth $11,607.
Template - Black-Scholes Option Value
Input Data
Stock Price now (P)
Exercise Price of Option (EX)
Number of periods to Exercise in years (t)
Compounded Risk-Free Interest Rate (rf)
Standard Deviation (annualized ơ)
18.75
35
5
1.17%
43.00%
Output Data
Present Value of Exercise Price (PV(EX)) ơ *t^.5 d1 d2
Delta N(d1) Normal Cumulative Density Function
Bank Loan N(d2)*PV(EX)
33.0129
0.9615
-0.1076
-1.0691
0.4572
4.7047
Value of Call
Value of Put
3.8670
18.1299
E09-G11
Mridul Arora, Florent Bernard, Jacqueline Kwok, Pu Wang
Ignoring tax considerations, Sally Jameson can sell her options package for more than twice of her cash compensation of $5000. If she does so as soon as she receives the options, and that the stock price remains at 18.75, she should go for the options package.
2. Factors impacting Sally’s options valuation
In terms of the option valuation, we believe that volatility is the number that can be adjusted in this case, and we made the big assumption that the volatility is 43% according to the graph given in exhibit 3.
Moreover, we have found that Sally will be indifferent towards the cash bonus versus options if the volatility is 29-30%, which