35
69) Use the information below to answer the following question.
Assume a stock price of $42; a risk-free rate of 3.5 percent per year, compounded continuously;
a six-month maturity; and a standard deviation of 64 percent per year. If a six-month call with an
exercise price of $45 is priced at $6.66, what is the price of the six-month $45 put?
A) $8.57
B) $7.93
C) $8.88
D) $9.07
E) $8.74
37
70) Use the information below to answer the following question.
You own a lot in Key West, Florida, that you are considering selling. Similar lots have recently
sold for $1.2 million. Over the past five years, the price of land in the area has varied with a
standard deviation of 19 percent. A potential buyer wants an option to buy the land in the next 9
months for $1,310,000. The risk-free rate of interest is 7 percent per year, compounded
continuously. How much should you charge for the option? Round your answer to the nearest
$100.
A) $62,000
B) $68,900
C) $63,700
D) $62,500
E) $60,400
39
71) Use the information below to answer the following question.
Assume a stock price of $88; risk-free rate of 4 percent per year, compounded continuously; time
to maturity of five months; standard deviation of 48 percent per year; and a put and call exercise
price of $85. What is the delta of the put option?
A) −.6850
B) −.3742
C) −.3158
D) −.0525
E) −.4685
72) A call option matures in six months. The underlying stock price is $37 and the stock’s return
has a standard deviation of 27 percent per year. The annual risk-free rate is 3.4 percent,
compounded continuously. The exercise price is $0. What is the price of the call option?
A) $39.65
B) $32.14
C) $36.37
D) $32.23
E) $37.00
73) The delta of a call option on a firm’s assets is .624. How much will a project valued at
$48,000 increase the value of equity?
A) $18,048
B) $45,336
C) $29,952
D) $76,923
E) $32,189
74) The delta of a call option on a firm’s assets is .408. By how much will a $220,000 project
increase the value of equity?
A) $89,760
B) $71,622
C) $309,760
D) $130,240
E) $539,216
75) The current market value of the assets of AMN Co. is $47 million, with a standard deviation
of 21 percent per year. The firm has zero-coupon bonds outstanding with a total face value of
$35 million. These bonds mature in two years. The risk-free rate is 3.6 percent per year,
compounded continuously. What is the value of d1 as it applies to the Black-Scholes option
pricing model?
A) 1.32471
B) 1.48002
C) 1.60067
D) 1.38357
E) .89006
43
76) Use the information below to answer the following question.
Upside Down has a zero coupon bond issue outstanding with a $10,000 face value that matures
in one year. The current market value of the firm’s assets is $12,400 while the standard deviation
of the returns on those assets is 22 percent annually. The annual risk-free rate is 4.6 percent,
compounded continuously. What is the market value of the firm’s debt based on the Black-
Scholes model?
A) $8,415
B) $8,900
C) $9,413
D) $8,962
E) $9,311
45
77) Use the information below to answer the following question.
S&C Co. has a zero coupon bond issue outstanding with a face value of $20,000 that matures in
one year. The current market value of the firm’s assets is $23,000. The standard deviation of the
return on the firm’s assets is 52 percent per year, and the annual risk-free rate is 6 percent per
year, compounded continuously. What is the firm’s continuously compounded cost of debt?
A) 11.24 percent
B) 20.32 percent
C) 16.48 percent
D) 18.69 percent
E) 17.09 percent
47
78) Use the information below to answer the following question.
Alpha is considering a purely financial merger with Beta. Alpha currently has a market value of
$14 million, an asset return standard deviation of 55 percent, and pure discount debt of $6
million that matures in four years. Beta has a market value of $6 million, an asset return standard
deviation of 60 percent, and pure discount debt of $2 million that matures in four years. The risk
free rate, continuously compounded, is 3.5 percent. The combined equity value of the two
separate firms is $14,180,806. By what amount will the combined equity value change if the
merger occurs and the asset return standard deviation of the merged firm is 45 percent?
A) −$548,285
B) −$314,007
C) $0
D) $99,087
E) $286,403