Deck 25: Option Valuation

Question 1

Under European put-call parity, the present value of the strike price is equivalent to the present value of:

A) the current value of the stock minus the call premium.
B) the market value of the stock plus the put premium.
C) a U.S. Treasury coupon bond with a face value equal to the strike price.
D) a U.S. Treasury bill with a face value equal to the strike price.
E) any risk-free security with a face value equal to the strike price and a coupon rate equal to the risk-free rate of return.

Answer 1

a U.S. Treasury bill with a face value equal to the strike price.

Question 2

In the Black-Scholes option pricing model, the symbol "σ" is used to represent the standard deviation of the:

A) option premium on a call with a specified exercise price.
B) rate of return on the underlying asset.
C) volatility of the risk-free rate of return.
D) rate of return on a risk-free asset.
E) option premium on a put with a specified exercise price.

Answer 2

rate of return on the underlying asset.

Question 3

Which one of the following statements is correct?

A) The price of an American put is equal to the stock price minus the exercise price.
B) The value of a European call is greater than the value of a comparable American call.
C) The value of a put is equal to one minus the value of an equivalent call.
D) The value of a put minus the value of a comparable call is equal to the value of the stock minus the exercise price.
E) The value of an American put will equal or exceed the value of a comparable European put.

Answer 3

The value of an American put will equal or exceed the value of a comparable European put.

Question 4

In the put-call parity formula, the present value of the exercise price is computed using the:

A) nominal market rate.
B) real market rate.
C) real inflation rate.
D) nominal inflation rate.
E) risk-free rate.

Question 5

Assume all stocks are non-dividend paying. Given this assumption, which one of these statements is correct regarding stock options?

A) European put options are more valuable than comparable American put options.
B) Exercising a well-into-the-money American put option is generally not a good idea.
C) It is never optimal to exercise an American call option early.
D) You should wait to exercise a put option if the stock price falls to zero.
E) You are better off exercising an in-the-money call option than selling it.

Question 6

Which one of these is most equivalent to e− ᴿᵗ?

A) −2.71828ᴿᵗ
B) −1/2.71828ᴿᵗ
C) 1/2.71828ᴿᵗ
D) 1 − 2.71828ᴿᵗ
E) 1/2.71828Rᵗ

Question 7

Travis owns a stock that is currently valued at $45.80 a share. He is concerned that the stock price may decline so he just purchased a put option on the stock with an exercise price of $45. Which one of the following terms applies to this strategy?

A) Put-call parity
B) Covered call
C) Protective put
D) Straddle
E) Strangle

Question 8

In the Black-Scholes option pricing formula, N(d₁) is the probability that a standardized, normally distributed random variable is:

A) less than or equal to N(d₂).
B) less than 1.
C) equal to 1.
D) equal to d₁.
E) less than or equal to d₁.

Question 9

Which one of the following can be used to replicate a protective put strategy?

A) Riskless investment and stock purchase
B) Stock purchase and call option
C) Call option and riskless investment
D) Riskless investment and writing a put
E) Call option, stock purchase, and riskless investment

Question 10

According to put-call parity, the present value of the exercise price is equal to the:

A) stock price plus the call premium minus the put premium.
B) call premium plus the put premium minus the stock price.
C) stock price minus the put premium minus the call premium.
D) put premium plus the call premium minus the stock price.
E) stock price plus the put premium minus the call premium.

Question 11

All of the following affect the value of a call option except the:

A) strike price.
B) stock price.
C) standard deviation of the returns on a risk-free asset.
D) continuously compounded risk-free rate.
E) time to maturity.

Question 12

Assume the standard deviation of the returns on ABC stock increases. This change will ________ the value of the call options and ________ the value of the put options on ABC stock.

A) increase; decrease
B) increase; increase
C) decrease; decrease
D) decrease; increase
E) not effect; not effect

Question 13

Assume the risk-free rate increases by one percent. Which one of the following measures the effect this change will have on the value of a firm's stock options?

A) Theta
B) Vega
C) Delta
D) Rho
E) Gamma

Question 14

Which one of the following defines the relationship between the value of an option and the option's time to expiration?

A) Theta
B) Vega
C) Rho
D) Delta
E) Gamma

Question 15

When computing the value of a call option using the Black-Scholes option pricing model, d₂ is calculated as:

A) σt .⁵ − 1.
B) 1 − σt .⁵.
C) d₁ − σt .⁵.
D) 1 + σt .⁵.
E) d₁ + σt .⁵.

Question 16

Which one of the following cannot be either used by or calculated by the Black-Scholes option pricing model?

A) Risk-free rate of return
B) Premium on an American call option
C) Time to maturity greater than one year
D) Underlying asset value
E) An exercise price equal to the face value of a firm's debt

Question 17

Which one of the following statements related to options is correct?

A) American stock options can be exercised but not resold.
B) A European call is either equal to or less valuable than a comparable American call.
C) European puts can be resold but can never be exercised.
D) European options can be exercised on any dividend payment date.
E) American options are valued using the Black-Scholes option pricing model.

Question 18

Which one of the following provides the option of selling a stock at a specified price on a stated date even if the market price of the stock declines to zero?

A) American call
B) European call
C) American put
D) European put
E) Either an American or European put

Question 19

To compute the value of a put using the Black-Scholes option pricing model, you:

A) assume the equivalent call is worthless and then apply the put-call parity formula.
B) have to compute the value of the put as if it is a call and then apply the put-call parity formula.
C) subtract the value of an equivalent call from 1.0.
D) subtract the value of an equivalent call from the market price of the stock.
E) multiply the value of an equivalent call by e−ʳᵗ.

Question 20

The primary purpose of a protective put is to:

A) ensure a maximum purchase price in the future.
B) offset an equivalent call option.
C) limit the downside risk of asset ownership.
D) lock in a risk-free rate of return on a financial asset.
E) increase the upside potential return on an investment.

Question 21

The value of an option is equal to the:

A) intrinsic value minus the time premium.
B) time premium plus the intrinsic value.
C) implied standard deviation plus the intrinsic value.
D) summation of the intrinsic value, the time premium, and the implied standard deviation.
E) summation of delta, theta, vega, and rho.

Question 22

The value of a call option delta is best defined as a value that is:

A) between zero and one.
B) less than zero.
C) greater than zero.
D) greater than or equal to zero.
E) less than or equal to zero.

Question 23

Paying off a firm's debt is comparable to ________ on the assets of the firm.

A) purchasing a put option
B) purchasing a call option
C) exercising an in-the-money put option
D) exercising an in-the-money call option
E) writing a put option

Question 24

The implied standard deviation used in the Black-Scholes option pricing model is:

A) based on historical performance.
B) a prediction of the volatility of the return on the underlying asset over the life of the option.
C) a measure of the time decay of an option.
D) an estimate of the future value of an option given a strike price e.
E) a measure of the historical intrinsic value of an option.

Question 25

Which one of the following statements is correct?

A) The value of a call option decreases as the time to expiration increases.
B) A decrease in the risk-free rate decreases the value of a put option.
C) Increasing the risk-free rate decreases the value of a call option.
D) The value of a put option increases when the standard deviation of the returns on the underlying stock increase.
E) Increasing the strike price decreases the value of a put option.

Question 26

A firm has assets of $16.4 million and 2-year, zero-coupon, risky bonds with a total face value of $7.4 million. The bonds have a total current market value of $7.1 million. The shareholders of this firm can change these risky bonds into risk-free bonds by purchasing a ________ option with a 2-year life and a strike price of ________ million.

A) call; $7.1
B) call; $7.4
C) put; $16.4
D) put; $7.1
E) put; $7.4

Question 27

The estimate of the future volatility of the returns on the underlying asset that is computed using the Black-Scholes option pricing model is referred to as the:

A) residual error.
B) implied mean return.
C) derived case volatility.
D) forecast rho.
E) implied standard deviation.

Question 28

Purely financial mergers:

A) are beneficial to stockholders.
B) are beneficial to both stockholders and bondholders.
C) are detrimental to stockholders.
D) add value to both the total assets and the total equity of a firm.
E) reduce both the total assets and the total equity of a firm.

Question 29

The value of the risky debt of a firm is equal to the value of:

A) a call option plus the value of a risk-free bond.
B) a risk-free bond plus a put option.
C) the equity of the firm minus a put.
D) the equity of the firm plus a call option.
E) a risk-free bond minus a put option.

Question 30

Which one of the five factors included in the Black-Scholes option pricing model cannot be directly observed?

A) Risk-free rate
B) Strike price
C) Standard deviation
D) Stock price
E) Life of the option

Question 31

Which one of the following statements related to the implied standard deviation (ISD) is correct?

A) The ISD is an estimate of the historical standard deviation of the underlying security.
B) ISD is equal to (1 − d₁).
C) The ISD estimates the volatility of an option's price over the option's lifespan.
D) The value of ISD is dependent upon both the risk-free rate and the time to option expiration.
E) ISD confirms the observable volatility of the return on the underlying security.

Question 32

The shareholders of a firm will benefit the most from a positive net present value project when the delta of the call option on the firm's assets is:

A) equal to one.
B) between zero and one.
C) equal to zero.
D) between zero and minus one.
E) equal to minus one.

Question 33

Assume the risk-free rate increases. This change will ________ the value of call options and ________ the value of put options on shares of stock.

A) increase; decrease
B) increase; increase
C) decrease; decrease
D) decrease; increase
E) not affect; not affect

Question 34

If the price of the underlying stock decreases, then the value of the call options ________ and the value of the put options ________.

A) decrease; decrease
B) decrease; increase
C) increase; decrease
D) increase; increase
E) increase; remain unchanged

Question 35

Theta measures an option's:

A) intrinsic value.
B) volatility.
C) rate of time decay.
D) sensitivity to changes in the value of the underlying asset.
E) sensitivity to changes in the risk-free rate.

Question 36

Which one of the following statements is correct?

A) Increasing the time to maturity may not increase the value of a European put.
B) An increase in time decreases the value of a call option.
C) Exercising an American option is always more valuable than selling the option.
D) Call options tend to be less sensitive to the passage of time than are put options.
E) Vega measures the sensitivity of an option's value to the passage of time.

Question 37

Selling a call option is generally more valuable than exercising the option because of the option's:

A) riskless value.
B) intrinsic value.
C) standard deviation.
D) exercise price.
E) time premium.

Question 38

A decrease in which of the following will increase the value of a put option on a stock?

A) Strike price and standard deviation of the returns on the underlying stock
B) Stock price and risk-free rate
C) Time to expiration and strike price
D) Risk-free rate and standard deviation of the returns on the underlying stock
E) Time to expiration and stock price

Question 39

Given a small change in the value of the underlying stock, the change in an option's price is approximately equal to the change in stock value:

A) divided by delta.
B) divided by (1 − Delta).
C) divided by (1 + Delta).
D) multiplied by (1 − Delta).
E) multiplied by delta.

Question 40

For the equity of a firm to be considered a call option on the firm's assets, the firm must:

A) be in default.
B) be leveraged.
C) pay dividends.
D) have a negative cash flow from operations.
E) have a negative cash flow from assets.

Question 41

A put option that expires in eight months with an exercise price of $55 sells for $7.34. The stock is currently priced at $52, 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?

A) $5.67
B) $5.47
C) $5.34
D) $4.71
E) $4.92

Question 42

Today, you purchased 300 shares of Lazy Z stock for $49.80 per share. You also bought three 1-year, $50 put options on Lazy Z stock at a cost of $.55 per share. What is the maximum total amount you can lose over the next year on these purchases?

A) −$15,105
B) −$11,050
C) −$160
D) −$105
E) $0

Question 43

Webster United stock is priced at $35.79 per share. The 6-month $35 call options are priced at $1.40 and the risk-free rate is 3.2 percent, compounded continuously. What is the per share value of the 6-month put option?

A) $.15
B) $.05
C) $0
D) $.20
E) $.25

Question 44

What is the value of a 6-month put with a strike price of $27.50 if the stock price is $22.60, the 6-month $27.50 call is priced at $1.46, and the risk-free rate is 3.5 percent, compounded continuously?

A) $4.71
B) $5.43
C) $5.24
D) $5.88
E) $6.62

Question 45

Which one of the following statements is correct?

A) Mergers benefit shareholders but not creditors.
B) Positive NPV projects will automatically benefit both creditors and shareholders.
C) There may be conflicts between the interests of bondholders and shareholders.
D) Creditors prefer negative NPV projects while shareholders prefer positive NPV projects.
E) Mergers rarely affect bondholders.

Question 46

Grocery Express stock is selling for $22 a share. A three-month, $20 call on this stock is priced at $2.85. Risk-free assets are currently returning .2 percent per month. What is the price of a three-month put on Grocery Express stock with a strike price of $20?

A) $.37
B) $.73
C) $.87
D) $1.10
E) $1.18

Question 47

Todd invested $12,000 in an account today at 4.5 percent, compounded continuously. What will this investment be worth in 15 years?

A) $26,203
B) $25,845
C) $24,287
D) $25,941
E) $23,568

Question 48

The stock of EHI has a current market value of $21.50 a share. The 3-month call with a strike price of $20 is selling for $2.07 while the 3-month put with a strike price of $20 is priced at $.41. What is the continuously compounded risk-free rate of return?

A) 2.9 percent
B) 3.0 percent
C) 4.1 percent
D) 3.7  percent
E) 3.2 percent

Question 49

The one-year call on TLM stock with a strike price of $65 is priced at $2.20 while the one-year put with a strike price of $65 is priced at $11.18. The annual risk-free rate is 3.8 percent, compounded continuously. What is the current price of TLM stock?

A) $53.60
B) $48.90
C) $56.70
D) $50.10
E) $47.65

Question 50

You need $15,400 in three years. How much do you need to deposit today to fund this need if you can earn 5 percent per year, compounded continuously? Assume this is the only deposit you make.

A) $13,506
B) $13,049
C) $14,179
D) $13,255
E) $12,916

Question 51

A stock is selling for $62 per share. A call option with an exercise price of $65 sells for $3.85 and expires in three 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?

A) $6.74
B) $6.23
C) $6.67
D) $6.40
E) $6.95

Question 52

A purely financial merger:

A) increases the risk that the merged firm will default on its debt obligations.
B) has no effect on the risk level of the firm's debt.
C) reduces the value of the option to go bankrupt.
D) has no effect on the equity value of a firm.
E) reduces the risk level of the firm thereby increasing the value of the firm's equity.

Question 53

Day's End stock is selling for $43 a share. The 6-month call with a strike price of $45 is priced at $.30. Risk-free assets are currently returning 4.1 percent per year, compounded continuously. What is the price of a 6-month put with a strike price of $45?

A) $1.39
B) $1.46
C) $1.28
D) $1.51
E) $1.32

Question 54

WT Foods stock is selling for $38 a share. The 6-month $40 call on this stock is selling for $2.01 while the 6-month $40 put is priced at $3.60. What is the continuously compounded risk-free rate of return?

A) 2.7 percent
B) 2.4 percent
C) 1.8 percent
D) 1.5 percent
E) 2.1 percent

Question 55

A call option with an exercise price of $25 and 9 months to expiration has a price of $4.92. The stock is currently priced at $26.90, and the risk-free rate is 4.1 percent per year, compounded continuously. What is the price of a put option with the same exercise price and expiration date?

A) $3.89
B) $1.57
C) $1.24
D) $2.69
E) $2.26

Question 56

J&N stock has a current market price of $51.97 a share and the annual risk-free rate is 4.2 percent, compounded continuously. The 1-year call on this stock with a strike price of $55 is priced at $2.30. What is the price of the one-year put with a strike price of $55?

A) $3.07
B) $2.86
C) $3.22
D) $2.94
E) $2.99

Question 57

Today, Ted purchased 500 shares of ABC stock at a price of $42.20 per share. He also purchased five put option contracts on ABC at a price of $.10 per share, an exercise price of $40 and a 1-year term. What is the maximum loss Ted can realize on his investments over the next year?

A) −$1,105
B) −$1,050
C) −$1,115
D) −$1,150
E) $0

Question 58

You invest $2,500 today at 5.5 percent, compounded continuously. How much will this investment be worth 12 years from now?

A) $3,728
B) $4,837
C) $4,311
D) $3,422
E) $3,791

Question 59

This morning, Kate put a European protective put strategy in place when the cost of ABC stock was $29.15 per share and the 1-year $30 ABC put was priced at $1.05 per share. How much profit per share will she earn from this strategy if the stock is worth $28 a share on the put expiration date?

A) $7.80
B) −$1.05
C) −$.20
D) $8.85
E) $1.25

Question 60

If the risk-free rate is 6.5 percent compounded annually, what is the continuously compounded risk-free rate equal to?

A) 1/ln1.065
B) 6.10%
C) ln1.065
D) 6.24%
E) e¹.⁰⁶⁵ − 1

Question 61

A stock is priced at $52.90 a share, the 3-month $45 call is priced at $9.31 a share, and the risk-free rate is 4.5 percent, compounded continuously. What is the value of the 3-month put with a strike price of $45?

A) $.57
B) $.63
C) $.91
D) $1.36
E) $1.54

Question 62

A stock is currently selling for $34 a share. The risk-free rate is 3.1 percent and the standard deviation is 33 percent. What is the value of d₁ of a 3-month call option with a strike price of $35?

A) −.01872
B) −.04621
C) −.05047
D) −.02950
E) −.20356

Question 63

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

Question 64

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

Question 65

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

Question 66

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

Question 67

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

Question 68

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

Question 69

Assume a stock price of $21.80, an exercise price of $20, three months to expiration, a risk-free rate of 3.40 percent, standard deviation of 46 percent, and a d₁ value of .52664. What is the value of d₂ as it is used in the Black-Scholes option pricing model?

A) .31218
B) .31225
C) .29664
D) .29535
E) .31340

Question 70

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

Question 71

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

Question 72

Assume a stock price of $16.80, risk-free rate of 2.7 percent, standard deviation of 59 percent, N(d₁) value of .93116, and an N(d₂) value of .85708. What is the value of a 6-month call with a strike price of $10 given the Black-Scholes option pricing model?

A) $7.62
B) $7.19
C) $8.06
D) $7.85
E) $6.97

Question 73

A stock is currently priced at $38. A call option with an expiration of one year has an exercise price of $40. The risk-free rate is 4.2 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?

A) $2.47
B) $34.80
C) $38.00
D) $5.63
E) $40.00

Question 74

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) 0.89006

Question 75

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

Question 76

A stock is currently selling for $39 a share. The risk-free rate is 2.5 percent and the standard deviation is 26 percent. What is the value of d₁ of a 9-month call option with a strike price of $40?

A) −.01506
B) 0.08341
C) 0.07746
D) 0.06420
E) −.06752

Question 77

Assume a stock price of $34.80, an exercise price of $35, nine months to expiration, risk-free rate of 2.40 percent, standard deviation of 57 percent, and a d₁ value of .27167. What is the value of d₂ as it is used in the Black-Scholes option pricing model?

A) −.22196
B) −.18657
C) −.18241
D) −.27427
E) −.22238

Question 78

Assume a stock price of $31.18, risk-free rate of 3.6 percent, standard deviation of 44 percent, N(d₁) value of .62789, and an N(d₂) value of .54232. What is the value of a 3-month call option with a strike price of $30 given the Black-Scholes option pricing model?

A) $3.38
B) $3.99
C) $3.68
D) $1.76
E) $3.45