Question

You have taken a management position in Ocean Cuisines plc that just went public last year. The company’s restaurants specialize in seafood dishes. A concern you had was that the restaurant business is risky. During your interview process, one of the benefits you heard was employee stock option. Upon signing your employment contract, you obtained options with a strike price of £65 for 10,000 shares of company stock. As is fairly common, your stock options have a three-year vesting period and a 10-year expiration, meaning that you cannot exercise the options for a period of three years and you lose them if you leave before they vest. So your employee stock options are European for the first three years and American afterward. You cannot sell the option nor can you enter into any sort of hedging. Ocean Cuisines is currently trading at £40 per share, a slight increase from the initial offering price last year. You estimated that the annual average standard deviation for restaurant company stock is 20 percent. Since Ocean Cuisines is a new restaurant chain you decide to use a 25percent standard deviation in your calculations. You expect no dividends will be paid for the next 10 years. A three-year Treasury note currently has a yield of 3.4% and a 10 year Treasury note has a yield of 6%. 1. Suppose that in three years, the company’s stock is trading at £55. At that time, should you keep the options or exercise immediately? What are some of the important determinants in making such a decision? 2. You are trying to value your option. What minimum value would you assign? What is the maximum value you would assign?

Answer 1

Solution:

Strike Price of the Option = 65

After three years Stock Price = 55

1. Since the stock price is lower than options strike price, so it would not yield any gain upon exercising the option when the vesting period is over that is after 3 years.

We should keep the option as it may result in positive gains in future.

Factor that we consider while exercising the option is strike price and current market price of the stock.

As these are not favourable after 3 years time when the vesting period is over so we should keep the option.

2. Valuing the option can be done with the help of Black Scholes Option pricing model as the data given is sufficient to calculate the price of the call option:

Current trading price of the stock = 40

Exercise Price = 65

Time duration = 3 years and 10 years(Employee can exercise option since the end of 3 years time till 10 years before the option expires)

Historical Volatility = 25%

Risk Free Rate = 3.4% for 3 years time duration and 6% for 10 years time duration.

Dividend Yield = 0%

Formula for calculation of Call option value using Black Scholes Model is

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By using the above formula we get two values for the Employee Stock Option at the beginning of 4th year and at the end of 10th year.

Call Option Price C = 2.134 (Using the Black Scholes Formula for 3 years duration(1095 days) and 3.4% risk free rate)

Call Option Price C = 13.9087 (Using the Black Scholes Formula for 10 years duration(3650 days) and 6% risk free rate)

Minimum is at the beginning of 4th year when the option can be excercised. (Due to less time value)

Maximim is at the end of 10 years after which option will expire.( Due to more time value )