1. Valuing Derivatives Sally Jameson: Valuing Stock Options in a Compensation Package By: Ravindra Pandhey, VU EF Finance I Course
2017 October 3

2. Content Introduction to Case Study Given Facts Analysis
Choice I for Sally
Choice II for Sally
Important Considerations
Other Strategy in Case of Choice II
Recommendation
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3. Introduction to Case Study
Sally Jameson a 2nd Year MBA student at Harvard Business School in May 1992 got a desired job offer from a multinational telecommunications company Telstar. Salary offer described by MBA recruiter of the company –
Salary of Dollars non-negotiable.
Signing bonus of 5000 Dollars or Stock Options, only one option is allowed.
This is the first time company offering Stock Options to MBA students.
3000 Stock Options will be granted which can be exercised only after successful completion of 5 years with the company then power to exercise will give 1 35 dollars only.
Confusion state for Sally due to not much information being provided by recruiter and she has to decide in one day either Cash or Stock Options.
Recruiter gave the current price of company is dollars and no dividend payout policy and in future also no hope for dividends.
Sally needs help.
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4. Given Facts
Sally tried to extract some information from a journal WSJ and this is the only limited information for the case on the basis of which we need to analyze. Given Facts are –
Current May month 1992 and 3 months strike price option premiums.
Long Term strike price option premiums with expiry of two years.
Stock Price history of Telstar company from 1982 to 1992.
Volatility history of Telstar company stock from 1982 to 1992.
Annualized Treasury Bill Interest Rates as of May 1992.
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5. First Fact
Listed Telstar Options Quotations as of Close of Market - May 27, 1992
Expiration Date (1992)
Strike Price
June 20
July 18
October 17
17.5 Dollars
1.4375
1.875
2.5
20 Dollars
0.1875
0.5
1.31
22.50 Dollars
NT*
0.125
0.5625
*NT - Not Traded, it is liquidity problem in Options Trading
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6. Second Fact Long Term Call Options Expiration Date Strike Price
Option Price
January 22, 1994
12.50 Dollars
7.75
17.50 Dollars
4.62
20 Dollars
3.75
As we can see these options are having expiry of two years from the year 1992
12.50 and Strike Prices are In-The-Money Call Options (ITM)
20 Strike Price is Out-Of-The-Money Call Option (OTM)
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7. Third Fact Stock Price History of Telstar Company from 1982 to1992
Highest Price 35 ( ), 15 touched (1988), Average Price around 20
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8. Fourth Fact Volatility History of Telstar Company from 1982 to1992
Highly Volatile between 1988 to 1992 in the range of 80% - 30%
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9. Fifth Fact Treasury Security Yields as of May 27, 1992 TIME
INTEREST RATES
1 Month
3.70%
2 Months
3.72%
3 Months
3.69%
6 Months
3.81%
1 Year
4.02%
2 Years
5.25%
5 Years
6.02%
7 Years
7.08%
10 Years
7.41%
30 Years
7.89%
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10. Analysis
Sally has a choice to choose either cash signing bonus of 5000 dollars or Stock Options but these options with a condition to stay 5 years in a company.
Choice I: Accepting cash 5000 Dollars
Utilize cash for personal use after capital gains tax rate of 28%
Invest Cash for 5 years with an Interest Rate of 6.02% on Treasury Bonds
Choice II: Accepting Stock Options quantity 3000 and wait for 5 years to exercise and convert into 35 dollars for 1 share.
At the end of 5 years Expected Future Stock Price
Expected growth of company
Use of Hedging strategies in Call Options
Recommendation: It is based on analysis of both choices and then choosing the most suitable option for Sally.
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11. Choice I
If Sally chooses cash signing bonus of 5000 dollars and wants to utilize that cash immediately, then she will receive -
5000 * 28% Tax = 1400
5000 – 1400 = 3600 (Ready Money for Sally as Cash in Hand)
If she wants to invest 5000 dollars for 5 years in the Treasury Bonds with an Interest Rate of 6.02% then she will receive after 5 years –
Future Value = Invested Amount * {(1+Rate of Interest)Time }
5000 * {( )5}
at the end of 5 years
Same can be done by clicking on the below link of calculator online –
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12. Choice I
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13. Choice I
If Sally would have opted Stock Options then what is the value of her options money in comparison to Cash Bonus.
Calculation of Options Price with respect to Current Market Price with the help of Black Sholes Model (BSM). Inputs for BSM -
Current Underlying Price (18.75 Dollars)
Options Strike Price (35 Dollars)
Time until Expiration (5 Years)
Implied Volatility (30% from Fourth Fact)
Risk-free Interest Rates ( 6.02% from Fifth Fact)
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14. Choice I
Black Sholes pricing is very complex so click on the below link for options price
Result will be – Black Sholes Calculator
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15. CASH Choice I STOCK OPTIONS
Now the value of 3000 Stock Options at the current price the Option Price as per BSM is –
Option Price = 2.92 Dollars
3000 * 2.92 = 8760 Dollars (without tax rate & transaction rate)
Originally Cash Compensation was 3600 after 28% Tax but Stock Options Compensation value is much higher than Cash but biggest condition for Sally is she cant sell Stock Options until 5 years.
Choice I suggests in the event of urgent utilization ‘Cash Compensation’ is a better option.
Right Wrong
CASH
STOCK OPTIONS
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16. Choice II
If Sally wants to stay with the company for 5 years and opts 3000 stock options then what would be the scenario after 5 years. These are European Style Options because she can not sell before expiration period. She will exercise the option only when the company stock price will cross 35 dollars which is the highest price and just touched only once (as per stock price history).
What should be the fair value she needs the stock price should reach to?
=> 5000 * ( )5 =
3000 (Fair Price – 35) =
37.23 Dollars
In order to have the same profit as that of cash compensation, the stock price must rise up to dollars then only stock options would be worth exercising.
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17. Choice II
To reach up to dollars the company needs how much growth ? The company has no dividend history so we cant apply any growth model but we can calculate the expected Compound Annual Growth Rate (CAGR). CAGR = (37.23/18.75) (1/5) - 1 CAGR = 1.14 – 1 = *100 = 14.70% Company has to grow almost by 15% every year to reach the price up to which is a very difficult task as seen the stock price history. Choice II is also exhibiting difficulties in reaching price to dollars.
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18. Important Considerations
Stock Options do look lucrative but the pricing calculation is not easy because all indications show probability but not certainty.
Options Liquidity – Liquidity is a very important factor in options trading because it helps in understanding how much people are keen in options strike price. As we have seen in “First Fact” the Strike Price for 2 years expiry there were no trades at all. As the current stock price increases the future strike prices open in the market for trading.
Tax Rates – As we have seen Capital Gains Tax Rate was 28% even on cash compensation and even on Stock Options when it will get converted into stocks then if Sally sells stock immediately after exercise options then tax rate will get applied. She has to keep stock for 1 year after exercising to avoid tax.
European Style Options are those options which can be exercised only at expiry like Sally has lock in period of 5 years so these options are European.
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19. Other Strategy in Case of Choice II
If Sally has a good understanding of Options Trading then despite of risky Stock Options she can apply Options Hedging Strategies every year to avoid the opportunity loss.
Options Strategy - Selling/Writing Out-Of-The-Money (OTM) Call Options
Every year there are strike prices open above the current market price like in the “First Fact” there was OTM Strike Price of so she can sell the option and pocket the premium. If current market price doesn’t reach to that same Strike Price whose Option premium which already sold then it would be profit at expiry.
If current market reaches to that OTM strike price then it would be loss but eventually underlying stock price is increasing.
While selecting higher OTM strike prices Implied Volatility (IV) gives good indication of bullish or bearish sentiment of market. If IV is high then sentiment is bearish which is always good for Writing OTM Call Options.
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20. Other Strategy in Case of Choice II
Writing OTM Call Option
From the second fact we take Jan Strike Price 20 Dollars OTM
20 Dollars (Strike Price) => 3.75 (Option Premium)
3000 * 3.75 = 11250
If Sally write the OTM Call then premium collection is Now there will be two scenarios for covering position -
Scenario 1
If stock price till expiry date Jan 22, 1994 does not reach to 20 then all profit of 11250
Scenario 2
If stock price crossed 20 then loss starts from the level of 20 till the closing price * 3000.
Margin Money is needed to write OTM Call Options because it is considered as short position without underlying stock. Even if Sally wants to cover short position then LIQUIDITY in that strike price has to be there in any given point of time.
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21. Recommendation
CASH
After analyzing both the choices based on limited facts available, the best would be CHOICE 1 for Sally that is choosing Cash Compensation
because -
Cash component has much more promising worth than stock options and important fact is she cant sell stock options immediately after joining.
We had seen from stock price history 35 just touched once so imagine to reach 37 in order to get good profit more than cash component is almost a very vague possibility.
The volatility in stock is huge which creates ripples in mind and hesitation to choose stock options.
Post tax Cash compensation is 3600 and post tax Stock Options worth would be 6307 in case of immediate selling then ( =2707) so in order to get 2707 more waiting period of 5 years is a very risky venture and totally uncertain but opting Cash component gives 3600 which is very much profitable and certain. Rather she can invest Cash for 5 years and earn handsome 6697.
Hedging Options is very tedious task which also involves lot of risk and big margin money with heavy transaction costs.
2017 October 3
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