43.
|
Pure financial mergers:
Refer to section 25.5
|
AACSB: Analytic
Blooms: Remember Difficulty: 1 Easy Learning Objective: 25-05 How option valuation can result in some surprising conclusions regarding mergers and capital budgeting decisions. Section: 25.5 Topic: Options and mergers |
44.
|
A purely financial merger:
Refer to section 25.5
|
AACSB: Analytic
Blooms: Remember Difficulty: 1 Easy Learning Objective: 25-05 How option valuation can result in some surprising conclusions regarding mergers and capital budgeting decisions. Section: 25.5 Topic: Options and mergers |
45.
|
Which one of the following statements is correct?
Refer to section 25.5
|
AACSB: Analytic
Blooms: Understand Difficulty: 1 Easy Learning Objective: 25-05 How option valuation can result in some surprising conclusions regarding mergers and capital budgeting decisions. Section: 25.5 Topic: Options and capital budgeting |
46.
|
This morning, Krystal purchased shares of Global Markets stock at a cost of $39.40 per share. She simultaneously purchased puts on Global Markets stock at a cost of $1.50 per share and a strike price of $40 per share. The put expires in one year. How much profit will she earn per share on these transactions if the stock is worth $38 a share one year from now?
Profit = $40 - $39.40 - $1.50 = -$0.90
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Protective put strategy |
47.
|
Today, you purchased 100 shares of Lazy Z stock at a market price of $47 per share. You also bought a one year, $45 put option on Lazy Z stock at a cost of $0.15 per share. What is the maximum total amount you can lose on these purchases?
Maximum loss = 100 ($45 - $47 - $0.15) = -$215
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Protective put strategy |
48.
|
Today, you are buying a one-year call on Piper Sons stock with a strike price of $27.50 per share and a one-year risk-free asset which pays 4 percent interest. The cost of the call is $1.40 per share and the amount invested in the risk-free asset is $26.57. How much total profit will you earn on these purchases if the stock has a market price of $29 one year from now?
Profit = ($26.57 × 1.04) - $26.57 + ($29 - $27.50) - $1.40 = $1.16
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Risk-free asset plus call |
49.
|
Today, you are buying a one-year call on one share of Webster United stock with a strike price of $40 per share and a one-year risk-free asset that pays 4 percent interest. The cost of the call is $1.85 per share and the amount invested in the risk-free asset is $38.46. What is the most you can lose on these purchases over the next year?
Maximum loss = ($38.46 × 1.04) - $38.46 + $0 - $1.85 = -$0.31
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Risk-free asset plus call |
50.
|
A.K. Scott's stock is selling for $37 a share. A 3-month call on this stock with a strike price of $35 is priced at $3.40. Risk-free assets are currently returning 0.18 percent per month. What is the price of a 3-month put on this stock with a strike price of $35?
P = ($35/1.00183) + $3.40 - $37 = $1.71
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Put-call parity |
51.
|
Cell Tower stock has a current market price of $62 a share. The one-year call on Cell Tower stock with a strike price of $65 is priced at $7.16 while the one-year put with a strike price of $65 is priced at $7.69. What is the risk-free rate of return?
$65/(1 + r) = -$7.16 + $62 + $7.69; r = 3.95 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Put-call parity |
52.
|
Grocery Express stock is selling for $22 a share. A 3-month, $20 call on this stock is priced at $2.85. Risk-free assets are currently returning 0.2 percent per month. What is the price of a 3-month put on Grocery Express stock with a strike price of $20?
P = ($20/1.0023) + $2.85 - $22 = $0.73
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Put-call parity |
53.
|
J&N, Inc. stock has a current market price of $46 a share. The one-year call on this stock with a strike price of $55 is priced at $0.05 while the one-year put with a strike price of $55 is priced at $8.24. What is the risk-free rate of return?
$55/(1 + r) = -$0.05 + $46 + $8.24; r = 1.49 percent
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Put-call parity |
54.
|
You invest $4,500 today at 6.5 percent, compounded continuously. How much will this investment be worth 8 years from now?
FV = $4,500 × 2.718280.065 × 8 = $7,569
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Continuous compounding |
55.
|
Todd invested $8,500 in an account today at 7.5 percent compounded continuously. How much will he have in his account if he leaves his money invested for 5 years?
FV = $8,500 × 2.718280.075 × 5 = $12,367
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Continuous compounding |
56.
|
Wesleyville Markets stock is selling for $36 a share. The 9-month $40 call on this stock is selling for $2.23 while the 9-month $40 put is priced at $5.63. What is the continuously compounded risk-free rate of return?
($40 × e-R × 0.75) = -$2.23 + $36 + $5.63
$40 e-0.75R = $39.40 ln(e-0.75R) = ln0.985 -0.75R = -0.0151 R = 2.02 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Continuously compounded rate |
57.
|
The stock of Edwards Homes, Inc. has a current market value of $23 a share. The 3-month call with a strike price of $20 is selling for $3.80 while the 3-month put with a strike price of $20 is priced at $0.54. What is the continuously compounded risk-free rate of return?
($20 × e-R × 0.25) = -$3.80 + $23 + $0.54
$20 e-0.25R = $19.74 ln(e-0.25R) = ln 0.987 -0.25R = -0.013085 R = 5.23 percent |
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Continuously compounded rate |
58.
|
What is the value of d2 given the following information on a stock?
d2 = 0.63355 - [0.58 × (0.751/2)] = 0.1313
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.2 Topic: Black-Scholes |
59.
|
Given the following information, what is the value of d2 as it is used in the Black-Scholes option pricing model?
d2 = -0.65829 - [0.55 × (0.751/2)] = -1.1346
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.2 Topic: Black-Scholes |
60.
|
What is the value of a 3-month call option with a strike price of $25 given the Black-Scholes option pricing model and the following information?
C = ($29.30 × 0.74699) - ($25 × 2.71828-0.04 × 0.25 × 0.66642) = $5.39
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.2 Topic: Black-Scholes |
61.
|
What is the value of a 6-month call with a strike price of $25 given the Black-Scholes option pricing model and the following information?
C = ($17.20 × 0.26016) - ($25 × 2.71828-0.0375 × 0.5 × 0.14456) = $0.93
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.2 Topic: Black-Scholes |
62.
|
What is the value of a 6-month put with a strike price of $27.25 given the Black-Scholes option pricing model and the following information?
P = ($27.25 × 2.71828-0.035 × 0.5) + $1.46106 - $22.60 = $5.64
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.2 Topic: Black-Scholes |
63.
|
What is the value of a 3-month put with a strike price of $45 given the Black-Scholes option pricing model and the following information?
P = ($45 × 2.71828-0.045 × .25) + $9.31 - $52.90 = $0.91
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.2 Topic: Black-Scholes |
64.
|
A stock is currently selling for $56 a share. The risk-free rate is 3 percent and the standard deviation is 18 percent. What is the value of d1 of a 9-month call option with a strike price of $57.50?
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.2 Topic: Call option delta |
65.
|
A stock is currently selling for $36 a share. The risk-free rate is 3.8 percent and the standard deviation is 27 percent. What is the value of d1 of a 9-month call option with a strike price of $40?
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.2 Topic: Call option delta |
66.
|
The delta of a call option on a firm's assets is 0.767. This means that a $75,000 project will increase the value of equity by:
Increase in equity value = $75,000 × 0.767 = $57,525
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-04 How the Black-Scholes model can be used to value the debt and equity of a firm. Section: 25.4 Topic: Market value of equity |
67.
|
The delta of a call option on a firm's assets is 0.727. This means that a $195,000 project will increase the value of equity by:
Increase in equity value = $195,000 × 0.727 = $141,765
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-04 How the Black-Scholes model can be used to value the debt and equity of a firm. Section: 25.4 Topic: Market value of equity |
68.
|
The current market value of the assets of Smethwell, Inc. is $54 million, with a standard deviation of 16 percent per year. The firm has zero-coupon bonds outstanding with a total face value of $40 million. These bonds mature in 2 years. The risk-free rate is 4 percent per year compounded continuously. What is the value of d1?
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium Learning Objective: 25-04 How the Black-Scholes model can be used to value the debt and equity of a firm. Section: 25.4 Topic: Market value of equity |
69.
|
The current market value of the assets of Cristopherson Supply is $46.5 million. The market value of the equity is $28.7 million. The risk-free rate is 4.75 percent and the outstanding debt matures in 4 years. What is the market value of the firm's debt?
Market value of debt = $46.5m - $28.7m = $17.8m
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-04 How the Black-Scholes model can be used to value the debt and equity of a firm. Section: 25.4 Topic: Market value of debt |
70.
|
The current market value of the assets of Nano Tek is $19.5 million. The market value of the equity is $7.5 million. The risk-free rate is 4.5 percent and the outstanding debt matures in 5 years. What is the market value of the firm's debt?
Market value of debt = $19.5m - $7.5m = $12m
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy Learning Objective: 25-04 How the Black-Scholes model can be used to value the debt and equity of a firm. Section: 25.4 Topic: Market value of debt |
71.
|
You need $12,000 in 6 years. How much will you need to deposit today if you can earn 11 percent per year, compounded continuously? Assume this is the only deposit you make.
PV = $12,000 × e-0.11(6) = $6,202.22
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 25-2 Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Continuous compounding |
72.
|
A stock is selling for $60 per share. A call option with an exercise price of $65 sells for $3.31 and expires in 4 months. The risk-free rate of interest is 2.8 percent per year, compounded continuously. What is the price of a put option with the same exercise price and expiration date?
$60 + P = $65e-(0.028)(1/3) + $3.31; P = $7.21
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 25-3 Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Put-call parity |
73.
|
A put option that expires in eight months with an exercise price of $57 sells for $3.85. The stock is currently priced at $59, and the risk-free rate is 3.1 percent per year, compounded continuously. What is the price of a call option with the same exercise price and expiration date?
$59 + $3.85 = $57 e-(0.031)(2/3) + C; C = $7.02
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 25-4 Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Put-call parity |
74.
| What is the price of a put option given the following information?
d1 = [ln ($78/$81) + (0.04 + 0.642/2) × 0.5]/[0.64 × (0.51/2)] = 0.1871
d2 = 0.1871 - [0.64 × (0.51/2)] = -0.2655 N(d1) = 0.5742 N(d2) = 0.3953 C = $78(0.5742) - ($81e-0.04(0.5)) (0.3953) = $13.40 P = $81e-0.04(0.5) + $13.40 - $78 = $14.80 |
AACSB: Analytic
Blooms: Analyze Difficulty: 1 Easy EOC: 25-9 Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.2 Topic: Black-Scholes |
75.
| What is the delta of a put option given the following information?
d1 = [ln ($90/$85) + (0.07 + 0.52/2) × (10/12)]/[0.5 × (10/12)1/2] = 0.4812
N(d1) = 0.685 Put delta = 0.685 - 1 = -0.315 |
AACSB: Analytic
Blooms: Analyze Difficulty: 1 Easy EOC: 25-10 Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.3 Topic: Option delta |
76.
| You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1.2 million. Over the past five years, the price of land in the area has increased 10 percent per year, with an annual standard deviation of 19 percent. A buyer has recently approached you and 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 $1,000.)
d1 = [ln ($1,200,000/$1,310,000) + (0.07 + 0.192/2) × (0.75)]/[0.19 × (0.751/2)] = -0.13168497
d2 = -0.077157 - [0.19 × (0.751/2)] = -0.2962298 N(d1) = 0.4476 N(d2) = 0.3835 C = $1,200,000(0.4476) - ($1,310,000e-0.07(0.75)) (0.3835) = $60,415.96 ≈ $60,000 |
AACSB: Analytic
Blooms: Analyze Difficulty: 1 Easy EOC: 25-11 Learning Objective: 25-04 How the Black-Scholes model can be used to value the debt and equity of a firm. Section: 25.4 Topic: Black-Scholes and asset value |
77.
| A call option with an exercise price of $31 and 6 months to expiration has a price of $3.77. The stock is currently priced at $17.99, and the risk-free rate is 3 percent per year, compounded continuously. What is the price of a put option with the same exercise price and expiration date?
$17.99 + P = $31e-0.03(0.5) + $3.77; P = $16.32
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 25-14 Learning Objective: 25-01 The relationship between stock prices; call prices; and put prices using put-call parity. Section: 25.1 Topic: Put-call parity |
78.
| A call option matures in nine months. The underlying stock price is $90, and the stock's return has a standard deviation of 19 percent per year. The risk-free rate is 3 percent per year, compounded continuously. The exercise price is $0. What is the price of the call option?
If the exercise price is equal to zero, the call price will equal the stock price, which is $90.
|
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium EOC: 25-15 Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.2 Topic: Black-Scholes |
79.
| A stock is currently priced at $45. A call option with an expiration of one year has an exercise price of $60. The risk-free rate is 14 percent per year, compounded continuously, and the standard deviation of the stock's return is infinitely large. What is the price of the call option?
If the standard deviation is infinite, d1 goes to positive infinity so N(d1) goes to 1, and d2 goes to negative infinity so N(d2) goes to 0. In this case, the call price is equal to the stock price, which is $45.
|
AACSB: Analytic
Blooms: Apply Difficulty: 1 Easy EOC: 25-17 Learning Objective: 25-02 The famous Black-Scholes option pricing model and its uses. Section: 25.2 Topic: Black-Scholes |
80.
| Sunburn Sunscreen 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 $10,600. The standard deviation of the return on the firm's assets is 32 percent per year, and the annual risk-free rate is 7 percent per year, compounded continuously. What is the market value of the firm's debt based on the Black-Scholes model? (Round your answer to the nearest $100.)
d1 = [ln ($10,600/$10,000) + (0.07 + 0.322/2) × 1]/[0.32 × (11/2)] = 0.560840
d2 = 0. 560840- [0.32 × (11/2)] = 0.240840 N(d1) = 0.7125 N(d2) = 0.5952 Equity = $10,600(0.7125) - ($10,000e-0.07(1)) (0.5952) = $2,003.76 Debt = $10,600 - $2,003.76 = $8,596.24 ≈ $8,600 |
AACSB: Analytic
Blooms: Analyze Difficulty: 2 Medium EOC: 25-18 Learning Objective: 25-04 How the Black-Scholes model can be used to value the debt and equity of a firm. Section: 25.4 Topic: Equity as an option |
81.
| Frostbite Thermal Wear 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 market value of the firm's equity based on the Black-Scholes model? (Round your answer to the nearest $100.)
d1 = [ln ($23,000/$20,000) + (0.06 + 0.522/2) × 1]/[0.52 × (11/2)] = 0.6442
d2 = 0.6442 - [0.52 × (11/2)] = 0.1242 N(d1) = 0.7403 N(d2) = 0.5494 Equity = $23,000(0.7403) - ($20,000e-0.06(1)) (0.5494) = $6,677.86 ≈ $6,700 |
AACSB: Analytic
Blooms: Analyze Difficulty: 1 Easy EOC: 25-20 Learning Objective: 25-04 How the Black-Scholes model can be used to value the debt and equity of a firm. Section: 25.4 Topic: Equity as an option |
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