28) I. M. Not. Greedy has been granted options on 50,000 shares. The stock is currently trading
at $17 a share and the options are at the money. The volatility of the stock returns averages 16
percent. The options mature in 2 years and the risk-free rate is 3.45 percent. N(d1) is .662055
and N(d2) is .576052. Given this information, what is the value of a call option on one share of
this stock?
A) $2.11
B) $1.70
C) $1.89
D) $2.28
E) $2.21
29) Alpha stock is currently trading at $34.50 a share and the 6-month call options are at the
money. The stock returns have a standard deviation of 21 percent and the risk-free rate is 4.21
percent. What is the price of the call option per share given that N(d1) is .585508 and N(d2) is
.526913?
A) $1.07
B) $2.79
C) $1.38
D) $2.40
E) $1.64
30) A stock has a market price of $25 and a standard deviation of returns of 24 percent. The $25
call option matures in 4 months and the risk-free rate is 2.89 percent. N(d1) is .555198 and N(d2)
is .500096. What is the value of the call option per share of stock?
A) $1.71
B) $1.86
C) $1.50
D) $1.62
E) $2.16
31) Jeff is analyzing an expansion project for a new business and has developed this input for a
Black-Scholes model. Stock price = $7,365,000, exercise price = $12,400,000, time period = 3
years, standard deviation = 14.5 percent, and the continuously compounded interest rate = 4.2
percent. What is the value of d1 as it is used in the model?
A) .1945
B) .5487
C) −1.4102
D) .4593
E) −1.4470
32) Katrina is analyzing an expansion project for a new business and has developed this input for
a Black-Scholes model. Stock price = $4,186,300, exercise price = $7,250,000, time period = 4
years, standard deviation = 13.8 percent, and the continuously compounded interest rate = 3.84
percent. What is the value of d2 as it is used in the model?
A) .01338
B) 1.2784
C) 1.2953
D) −1.5713
E) −1.0293
33) Ernst is trying to evaluate some options for a firm. However, he can’t remember how to
compute e−Rt. Can you help him? If the rate is 4.38 percent and the time period is 6 months,
what is the value of e−Rt?
A) .9087
B) .8087
C) .9952
D) .8476
E) .9783
34) What are the values of u, the up state multiplier, and d, the down state multiplier, if there are
monthly intervals and the standard deviation is .38?
A) 1.1159; .8961
B) .0317; 1.0327
C) .0317; .9683
D) .2193; .7807
E) 1.1159; −.1159
35) The price of oil is currently at $24 but you expect it to either increase by 18 percent or
decrease by 7 percent over the next 6 months. The 6-month risk-free rate of interest is 1.98
percent. What is the probability that the price will increase?
A) 32.47 percent
B) 36.03 percent
C) 38.06 percent
D) 35.92 percent
E) 37.94 percent
36) One of Modular Products (MP) customers would like to obtain a 6-month option to purchase
500,000 tables for $119 each. These tables currently sell for $110 each. Assume u equals 1.0994
and d equals .9096. What price should MP charge for this option if the annual risk-free rate is 3.2
percent? Round your answer to the nearest $100.
A) $338,400
B) $421,900
C) $598,100
D) $479,900
E) $533,600
37) A SunSet Co. customer would like to obtain a 3-month option to purchase additional units of
a product for $77 each. This product currently sells for $76 each. Assume u equals 1.1502 and d
= .8694. Approximately what price per unit should SunSet charge for this option if the annual
risk-free rate is 2.8 percent?
A) $4.79
B) $5.98
C) $6.17
D) $6.02
E) $5.07
38) Jennifer has just been granted at-the-money company options on 300,000 shares. These
options expire in 5 years and are exercisable after 3 years. The options are valued at $1.2 million.
It is normal for her to receive annual option grants such as this. She also receives a current salary
of $550,000. Why might Jennifer prefer to receive a straight annual salary of $1.5 million rather
than this salary and option combination?
39) A CEO is being granted 1,000,000 at-the-money options. The current stock price is $45, the
continuously compounded risk-free rate is 5 percent, and the variance on the stock’s return is .04.
The options expire in 5 years. What is the value of the options contract? If the CEO had
negotiated a larger salary and only 10,000 options, what would be the value of that options
contract?
40) Why would a company pay an executive in options as opposed to salary?
41) You want to become a very successful entrepreneur. Your desire is to operate a business
from a single location without becoming so large you lose personal touch with all the firm’s
employees and the day-to-day operations. Before determining what type of business you want to
open, you have decided to compile a list of options that would add value to whatever business
you select. Identify options that you would include in this list.
42) Why is straight NPV analysis flawed as compared to models that include option pricing in
the analysis?
43) In what instances is the binomial option pricing model superior to the Black-Scholes option
pricing model?