Please complete using the Black-Scholes Model showing all
calculations. I have attempted to complete this several times and
have been unable to find an answer which matches the one found in
Chegg textbook solutions. Thank you in advance!
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 restaturant 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 $40 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 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 first 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 $27.15 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 been traded for only 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. Because 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 3.8 percent, and a 10-year Treasury note has a yield of
4.4 percent.
You’re trying to value your options. What minimum value would
you assign? What is the maximum value you would assign?