# Sara’s Options Harvard Case Solution & Analysis

Sara's Options

1. Use the Black Schole's options pricing Model to value the annual options grant from ClearLake.

The options granted to Sara were designed in a way that approximately half of the options vested within three years and the remaining half of the options vested in the final two years. However, the options expired after five years. The Black Schole's Model will be applied to find out two values; one at the end of three years, and the other at the end of five years.

She will be getting only half of the options at the end of third year, so the number of stocks will be divided by two in order to calculate the value of the option. The risk free rate for the three year T Bond will be 6.42%. With the stock price of 137, exercise price of 129 and Volatility of 48%, the Value of call option will be \$56.22. With 1920 stocks, the total value of the options will be \$107,939.

If she stays in the company for five years, that has a probability of only 40%, then she can exercise all the option by the fifth year. That is also the time when the options will expire. The risk free rate for the five year T-Bond will be 6.33%. With the stock price of \$137, exercise price of 129 and Volatility of 48%, the Value of call option will be \$71.25. With 3840 stocks, the total value of the options will be \$273,612.

How might the value of this option grant change with?

• A 10% increase in the stock price?

If the stock price increases with 10%, then the new share price will be \$150.7. With all other variables being same, at the option expiry of 5 years, the value of call option will increase to \$82.55. Hence, the total value of the options will be \$316,983.

• A 10% percentage point increase in volatility?

If the volatility of the stock increases by 10%, with all other variables being same as the base case of 5 year expiration of option, then the standard deviation will increase to 52.8% from previous 48%. The value of call option will increase to 75.17% as compared to previous \$71.25. The total value of the options will become \$288,663.

• A one year reduction in the “time to expiration” of the options?

If the time to expiration reduces from 5 years to 4 years, with all other variables same as the base case, then the value of call option will reduce to \$64.27. Hence, the total value of the option will reduce to \$246,795.

Explain intuitively why options values change in the ways indicated by your analysis.

The value of the option changes by changing any variable in the Black Schole's Model. If the stock price increases, then it will be beneficial for the call option owner, since more people will be willing to exercise the option. The difference between the stock price and the exercise price will be higher by leading to a higher benefit.

Similarly, higher volatility means higher risk. To compensate the higher risk, the return is also higher according to the trade-off between risk and return. However, if the options expire early, then this is bad for the holder because he will have less time before the option gets expired.

1. How might the market value of Sara’s ClearLake options help Sara understand the value of her ClearLake compensation options?  Will her private value options generally be higher or lower than the value determined by the Black Schole's Model?  Why?

If Sara is to value the options offered to her by the ClearLake in the market, the value she will receive will be lower then what has been determined through the Black Schole's Model. The reason for such a phenomenon will be the fact that each option traded in the market will have specific terms which are institutionalized by the trade. These exchange traded options are also known as “listed options”. Therefore, in order to make the option valuable, then the commitment against the option has to be fulfilled.

In the case of Sara’s options, she has to stay with the company for a minimum of 3 years otherwise she cannot exercise the options. If the option offered to Sara is itself traded on the market, then it will have lower value due to the fact that it is tailor made for her. If Sara completes the 3 years’ vesting period in the company so she will get the power to exercise these options at that point then she can get a more realistic and comparable value from the market.

What factors, considered in the Black Schole's Model, affect the value of ClearLake’s options to Sara?

2.The assumptions that are embed within calculations of the Black Schole's Model are as follows, .......................

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