As a newly minted MBA, you\'ve taken a management position with Exotic Cuisines,
ID: 2753574 • Letter: A
Question
As a newly minted MBA, you've taken a management position with Exotic Cuisines, Inc., a restaurant chain that just went public last year. The company's restaurants specialize in exotic main dishes, using ingredients such as alligator, buffalo, and ostrich. A concern you had going in was that the restaurant business is very risky. However, after some due diligence, you discovered a common misperception about the restaurant industry. It is widely thought that 90 percent of new restaurants close within three years; however, recent evidence suggests the failure rate is closer to 60 percent over three years. So, it is a risky business, although not as risky as you originally thought.
During your interview process, one of the benefits mentioned was employee stock options. Upon signing your employment contract, you received options with a strike price of $75 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. After the three-year vesting period, you can exercise the options at any time. Thus, the employee stock options are European (and subject to forfeit) for the rst three years and American afterward. Of course, you cannot sell the options, nor can you enter into any sort of hedging agreement. If you leave the company after the options vest, you must exercise within 90 days or forfeit.
Exotic Cuisines stock is currently trading at $38.47 per share, a slight increase from the initial offering price last year. There are no market traded options on the company's stock. Because the company has only been traded for about a year, you are reluctant to use the historical returns to estimate the standard deviation of the stock's return. However, you have estimated that the average annual standard deviation for restaurant company stocks is about 55 percent. Since Exotic Cuisines is a newer restaurant chain, you decide to use a 60 percent standard deviation in your calculations. The company is relatively young, and you expect that all earnings will be reinvested back into the company for the near future. Therefore, you expect no dividends will be paid for at least the next 10 years. A three-year Treasury note currently has a yield of 5.4 percent, and a 10-year Treasury note has a yield of 6.1 percent.
1.You're trying to value your options. What minimum value would you assign? What is the maximum value you would assign?
2.Suppose that, in three years, the company's stock is trading at $60. At that time, should you keep the options or exercise them immediately? What are some of the important determinants in making such a decision?
3.Your options, like most employee stock options, are not transferable or tradeable. Does this have a significant effect on the value of the options? Why?
4.Why do you suppose employee stock options usually have a vesting provision? Why must they be exercised shortly after you depart the company even after they vest?
5.A controversial practice with employee stock options is repricing. What happens is that a company experiences a stock price decrease, which leaves employee stock options far out of the money or “underwater.” In such cases, many companies have “repriced” or “restruck” the options, meaning that the company leaves the original terms of the option intact, but lowers the strike price. Proponents of repricing argue that since the option is very unlikely to end in the money because of the stock price decline, the motivational force is lost. Opponents argue that repricing is in essence a reward for failure. How do you evaluate this argument? How does the possibility of repricing affect the value of an employee stock option at the time it is granted?
6.As we have seen, much of the volatility in a company's stock price is due to systematic or marketwide risks. Such risks are beyond the control of a company and its employees. What are the implications for employee stock options? In light of your answer, can you recommend an improvement over traditional employee stock options?
Explanation / Answer
Answer (1)
Given ESOP offered is a European call option for the first three years and an American call option from third to tenth year. As the employee is joining now. We may need to check what will be the value of call option at the beginning of vesting period.
Strike Price K = $ 75
Time period T = 3 years
Current Stock Price S = $ 38.47
Standard deviation sigma = 60% or 0.60
Dividends y = 0
T-Bill rate for 3 years r = 5.4%
Value of Call c = S * N(d1) – K * e^-r*T * N(d2)
Where d1 = (1/(sigma*Square root(T)) *[ln (S/K) + (r-y+sigma^2/2)*T]
And d2 = d1 – sigma * square root (T)
Substituting the values from above
d1 = (1/(0.60*square root (3))) * [ ln (38.47/75) + (0.054 – 0 + 0.60^2/2) * 3]
=(1/(0.60 * 1.7320508)) * [ln (0.51293333) + (0.054 + 0.36/2)*3]
= (1/1.0392304845) * [-0.289939077 + (0.054 +0.18)*3]
= 0.9622504486 * [-0.289939077 + 0.702]
= 0.9622504486 * 0.412060923
= 0.396505808 or 0.39651 (rounded off)
d2 = 0.39651 – 0.60 * Square root (3)
= 0.39651 – 0.6 * 1.7320508
= 0.39651 – 1.0392304845
= --0.6427204845 or 0.64272 (rounded off)
Value of Call c = 38.47 * 0.39651 – 75 * e^(-0.054 * 3) * (-0.64272)
C = 15.2537397 – 75 * 2.71828^-0.162 * (-0.64272)
C = 15.2537397 – 75 * 0.8504413 * (-0.64272)
C = 15.2537397 – (-40.99467229)
C = 56.24841199 or $ 56.25 (rounded off)
The above value is upper bound.
The lower bound for the ESOP = Max[(s-K)/(1+r)^t, 0]
= Max[(38.47-75)/(1.054)^3, 0]
= Max [-36.53/1.170905464, 0]
= Max [-31.20, 0]
= 0
Answer (2)
Suppose the share of the company is trading at $ 60 then the expected loss on exercise of ESOP would be
Loss in exercise of ESOP = 10000 * (60-75) = 10000*-15 = -150,000
Hence it is not profitable to exercise ESOP.
Answer (3)
As ESOPs are not tradable or transferable, the value of call arrived above is only notional value. In effect the ESOPs are worthless till the vesting date. That is in the first three years. Between 3rd and 10th year however, the employee can exercise ESOP and sell the stock in local market if the same is profitable.
Answer (4)
ESOPs are generally given as a bonus for continued association with the corporate and the long association with the company. Long association can be established based on a certain period of association with the company which could be a continued employment with the company for a minimum of 3 years before the employee is eligible for ESOPs and the same are vested for the employee. Similarly, if the employee is leaving the company after vesting, he/she needs to exercise immediately or within a short time as the ESOP are given for continued and long association with the company, a condition which is no more available once the employee leaves the company.
Answer (5)
Effect of repricing
As per the Binomial model the stock price has two states at the time of vesting after three years, it can either go up or go down. Let us assume that p is the probability that the stock price can go up which means that (1-p) is the probability the stock price can go down. We calculate the Binomial price and then estimate the value of call which is (Binomial Price - Strike Price).
We use the following formulas for estimating the probability (p), up movement (u) and down movement (d) factors
u = e^(sigma^(square root.(Time to maturity/time at which calculation is made)
u = 2.71828^ (0.60^(Square root (3/3))
u = 2.71828^ (0.60^1) = 2.71828^0.60 as 0.60^1 = 0.60
u = 1.822118
d = e^-(sigma^(square root.(Time to maturity/time at which calculation is made)
d = 2.71828^ -(0.60^(Square root (3/3))
d = 2.71828^ -(0.60^1) = 2.71828^-0.60
d = 0.548812
p = (e^(r*t/n) –d) / (u – d)
p = (2.71828^(0.054*3/3) - 0.548812) / (1.822118 -0.548812)
p = (2.71828^0.054 – 0.548812) / 1.273306
p = (1.055485 – 0.548812) / 1.273306
p =0.506673/1.273306 = 0.397919
(1-p) = 1-0.397919 = 0.602081
Binomial Price = p * S*u + (1-p) * S*d
= 0.397919 * 38.47 * 1.822118 + 0.602081 * 38.47 * 0.548812
= 27.89288 + 12.711614
= $ 40.604494 or $ 40.60
If the ESOP is expected to be repriced at $ 40.60 at the time of vesting the value of ESOP would be
Value of Call c = 38.47 * 0.39651 – 40.60 * e^(-0.054 * 3) * (-0.64272)
C = 15.2537397 – 40.60 * 2.71828^-0.162 * (-0.64272)
C = 15.2537397 – 40.60 * 0.8504413 * (-0.64272)
C = 15.2537397 – (-22.191783)
C = 37.445522 or $ 37.45 (rounded off)
Thus a repricing of the strike price of ESOP from $ 75 to $ 40.60 would reduce the call option from $ 56.25 to $ 37.45
Answer (6)
As the risk of price flucutations are beyond the control of both the company as well as employee, the ESOP may become un-exercisable or unviable if there is a substantial fall in the stock price of the company at the time or vesting. Similarly if there is substantial increase in the stock price compared to the exercise price, then the employees get benefitted but the company may lose out.
A better way could be to issue the ESOP at a certain discount to the stock price at the date of vesting instead of fixing an exercise price upfront. This way the employee can be assured of a minimum return whatever happens with the price on the date of vesting of ESOPs.
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