Binomial model* Over the coming year, Ragwort’s stock price will halve to $50 from its current level of $100 or it will rise to $200. The one-year interest rate is 10%. a. What is the delta of a one-year call option on Ragwort stock with an exercise price of $100? b. Use the replicating-portfolio method to value this call. c. In a risk-neutral world, what is the probability that Ragwort stock will rise in price? d. Use the risk-neutral method to check your valuation of the Ragwort option. e. If someone told you that in reality there is a 60% chance that Ragwort’s stock price will rise to $200, would you change your view about the value of the option? Explain.

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Answer 1

Textbook Question

Chapter 21, Problem 1PS

Binomial model* Over the coming year, Ragwort’s stock price will halve to $50 from its current level of $100 or it will rise to $200. The one-year interest rate is 10%.

a. What is the delta of a one-year call option on Ragwort stock with an exercise price of $100?
b. Use the replicating-portfolio method to value this call.
c. In a risk-neutral world, what is the probability that Ragwort stock will rise in price?
d. Use the risk-neutral method to check your valuation of the Ragwort option.
e. If someone told you that in reality there is a 60% chance that Ragwort’s stock price will rise to $200, would you change your view about the value of the option? Explain.

a.

Expert Solution

Summary Introduction

To compute: The delta of one year call option on R stock with a strike price of $100.

Explanation of Solution

The formula to calculate delta is:

Delta=Spread of possible option pricespread of possible share price

The calculation of delta is as follows:

Delta=($100−0$200−50)=.6667

b.

Expert Solution

Summary Introduction

To discuss: Apply the replicating portfolio technique to value this call.

Explanation of Solution

The replicating portfolio technique of valuing call is as follows.

PRIN.OF CORPORATE FINANCE, Chapter 21, Problem 1PS

c.

Expert Solution

Summary Introduction

To discuss: The probability of increasing stock R price in a risk neutral world.

Explanation of Solution

The probability of increasing stock R calculated as follows:

Expected value of calloption=(Probability of rise×call option value in rise)+[(1−Probability of rise)×Call option value in fall]

The computation as follows:

Expected value of call option=(p× 1.00) + (1 –p)(–.50) =.10p=.40

Foot note: The probability is calculated on the basis of expected return.

d.

Expert Solution

Summary Introduction

To compute: The value of stock R using the risk neutral method.

Explanation of Solution

The option value is calculated using the following formula:

Value of call=Expected future value1+Interest rate=.401.10=0.3636 OR $36.36

Hence, the value of call is $36.36

e.

Expert Solution

Summary Introduction

To discuss: Whether person X change his option regarding the value of option.

Explanation of Solution

Person X does not change his opinion regarding the value of option. The chance of price increase is most likely higher than the risk- neutral probability, but it does not aid to value the option.

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A company currently pays a dividend of $3.6 per share (D0 = $3.6). It is estimated that the company's dividend will grow at a rate of 19% per year for the next 2 years, and then at a constant rate of 6% thereafter. The company's stock has a beta of 1.4, the risk-free rate is 8.5%, and the market risk premium is 4.5%. What is your estimate of the stock's current price? Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 2

Textbook Question

Chapter 21, Problem 1PS

Binomial model* Over the coming year, Ragwort’s stock price will halve to $50 from its current level of $100 or it will rise to $200. The one-year interest rate is 10%.

a. What is the delta of a one-year call option on Ragwort stock with an exercise price of $100?
b. Use the replicating-portfolio method to value this call.
c. In a risk-neutral world, what is the probability that Ragwort stock will rise in price?
d. Use the risk-neutral method to check your valuation of the Ragwort option.
e. If someone told you that in reality there is a 60% chance that Ragwort’s stock price will rise to $200, would you change your view about the value of the option? Explain.

a.

Expert Solution

Summary Introduction

To compute: The delta of one year call option on R stock with a strike price of $100.

Explanation of Solution

The formula to calculate delta is:

Delta=Spread of possible option pricespread of possible share price

The calculation of delta is as follows:

Delta=($100−0$200−50)=.6667

b.

Expert Solution

Summary Introduction

To discuss: Apply the replicating portfolio technique to value this call.

Explanation of Solution

The replicating portfolio technique of valuing call is as follows.

PRIN.OF CORPORATE FINANCE, Chapter 21, Problem 1PS

c.

Expert Solution

Summary Introduction

To discuss: The probability of increasing stock R price in a risk neutral world.

Explanation of Solution

The probability of increasing stock R calculated as follows:

Expected value of calloption=(Probability of rise×call option value in rise)+[(1−Probability of rise)×Call option value in fall]

The computation as follows:

Expected value of call option=(p× 1.00) + (1 –p)(–.50) =.10p=.40

Foot note: The probability is calculated on the basis of expected return.

d.

Expert Solution

Summary Introduction

To compute: The value of stock R using the risk neutral method.

Explanation of Solution

The option value is calculated using the following formula:

Value of call=Expected future value1+Interest rate=.401.10=0.3636 OR $36.36

Hence, the value of call is $36.36

e.

Expert Solution

Summary Introduction

To discuss: Whether person X change his option regarding the value of option.

Explanation of Solution

Person X does not change his opinion regarding the value of option. The chance of price increase is most likely higher than the risk- neutral probability, but it does not aid to value the option.

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Answer 3

Textbook Question

Chapter 21, Problem 1PS

Binomial model* Over the coming year, Ragwort’s stock price will halve to $50 from its current level of $100 or it will rise to $200. The one-year interest rate is 10%.

a. What is the delta of a one-year call option on Ragwort stock with an exercise price of $100?
b. Use the replicating-portfolio method to value this call.
c. In a risk-neutral world, what is the probability that Ragwort stock will rise in price?
d. Use the risk-neutral method to check your valuation of the Ragwort option.
e. If someone told you that in reality there is a 60% chance that Ragwort’s stock price will rise to $200, would you change your view about the value of the option? Explain.

a.

Expert Solution

Summary Introduction

To compute: The delta of one year call option on R stock with a strike price of $100.

Explanation of Solution

The formula to calculate delta is:

Delta=Spread of possible option pricespread of possible share price

The calculation of delta is as follows:

Delta=($100−0$200−50)=.6667

b.

Expert Solution

Summary Introduction

To discuss: Apply the replicating portfolio technique to value this call.

Explanation of Solution

The replicating portfolio technique of valuing call is as follows.

PRIN.OF CORPORATE FINANCE, Chapter 21, Problem 1PS

c.

Expert Solution

Summary Introduction

To discuss: The probability of increasing stock R price in a risk neutral world.

Explanation of Solution

The probability of increasing stock R calculated as follows:

Expected value of calloption=(Probability of rise×call option value in rise)+[(1−Probability of rise)×Call option value in fall]

The computation as follows:

Expected value of call option=(p× 1.00) + (1 –p)(–.50) =.10p=.40

Foot note: The probability is calculated on the basis of expected return.

d.

Expert Solution

Summary Introduction

To compute: The value of stock R using the risk neutral method.

Explanation of Solution

The option value is calculated using the following formula:

Value of call=Expected future value1+Interest rate=.401.10=0.3636 OR $36.36

Hence, the value of call is $36.36

e.

Expert Solution

Summary Introduction

To discuss: Whether person X change his option regarding the value of option.

Explanation of Solution

Person X does not change his opinion regarding the value of option. The chance of price increase is most likely higher than the risk- neutral probability, but it does not aid to value the option.

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Answer 4

Textbook Question

Chapter 21, Problem 1PS

Binomial model* Over the coming year, Ragwort’s stock price will halve to $50 from its current level of $100 or it will rise to $200. The one-year interest rate is 10%.

a. What is the delta of a one-year call option on Ragwort stock with an exercise price of $100?
b. Use the replicating-portfolio method to value this call.
c. In a risk-neutral world, what is the probability that Ragwort stock will rise in price?
d. Use the risk-neutral method to check your valuation of the Ragwort option.
e. If someone told you that in reality there is a 60% chance that Ragwort’s stock price will rise to $200, would you change your view about the value of the option? Explain.

a.

Expert Solution

Summary Introduction

To compute: The delta of one year call option on R stock with a strike price of $100.

Explanation of Solution

The formula to calculate delta is:

Delta=Spread of possible option pricespread of possible share price

The calculation of delta is as follows:

Delta=($100−0$200−50)=.6667

b.

Expert Solution

Summary Introduction

To discuss: Apply the replicating portfolio technique to value this call.

Explanation of Solution

The replicating portfolio technique of valuing call is as follows.

PRIN.OF CORPORATE FINANCE, Chapter 21, Problem 1PS

c.

Expert Solution

Summary Introduction

To discuss: The probability of increasing stock R price in a risk neutral world.

Explanation of Solution

The probability of increasing stock R calculated as follows:

Expected value of calloption=(Probability of rise×call option value in rise)+[(1−Probability of rise)×Call option value in fall]

The computation as follows:

Expected value of call option=(p× 1.00) + (1 –p)(–.50) =.10p=.40

Foot note: The probability is calculated on the basis of expected return.

d.

Expert Solution

Summary Introduction

To compute: The value of stock R using the risk neutral method.

Explanation of Solution

The option value is calculated using the following formula:

Value of call=Expected future value1+Interest rate=.401.10=0.3636 OR $36.36

Hence, the value of call is $36.36

e.

Expert Solution

Summary Introduction

To discuss: Whether person X change his option regarding the value of option.

Explanation of Solution

Person X does not change his opinion regarding the value of option. The chance of price increase is most likely higher than the risk- neutral probability, but it does not aid to value the option.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

Summary Introduction

To compute: The delta of one year call option on R stock with a strike price of $100.

Explanation of Solution

The formula to calculate delta is:

Delta=Spread of possible option pricespread of possible share price

The calculation of delta is as follows:

Delta=($100−0$200−50)=.6667

b.

Expert Solution

Summary Introduction

To discuss: Apply the replicating portfolio technique to value this call.

Explanation of Solution

The replicating portfolio technique of valuing call is as follows.

PRIN.OF CORPORATE FINANCE, Chapter 21, Problem 1PS

c.

Expert Solution

Summary Introduction

To discuss: The probability of increasing stock R price in a risk neutral world.

Explanation of Solution

The probability of increasing stock R calculated as follows:

Expected value of calloption=(Probability of rise×call option value in rise)+[(1−Probability of rise)×Call option value in fall]

The computation as follows:

Expected value of call option=(p× 1.00) + (1 –p)(–.50) =.10p=.40

Foot note: The probability is calculated on the basis of expected return.

d.

Expert Solution

Summary Introduction

To compute: The value of stock R using the risk neutral method.

Explanation of Solution

The option value is calculated using the following formula:

Value of call=Expected future value1+Interest rate=.401.10=0.3636 OR $36.36

Hence, the value of call is $36.36

e.

Expert Solution

Summary Introduction

To discuss: Whether person X change his option regarding the value of option.

Explanation of Solution

Person X does not change his opinion regarding the value of option. The chance of price increase is most likely higher than the risk- neutral probability, but it does not aid to value the option.

Answer 8

a.

Expert Solution

Summary Introduction

To compute: The delta of one year call option on R stock with a strike price of $100.

Explanation of Solution

The formula to calculate delta is:

Delta=Spread of possible option pricespread of possible share price

The calculation of delta is as follows:

Delta=($100−0$200−50)=.6667

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Summary Introduction

To compute: The delta of one year call option on R stock with a strike price of $100.

Answer 13

Explanation of Solution

The formula to calculate delta is:

Delta=Spread of possible option pricespread of possible share price

The calculation of delta is as follows:

Delta=($100−0$200−50)=.6667

Answer 14

b.

Expert Solution

Summary Introduction

To discuss: Apply the replicating portfolio technique to value this call.

Explanation of Solution

The replicating portfolio technique of valuing call is as follows.

PRIN.OF CORPORATE FINANCE, Chapter 21, Problem 1PS

Answer 15

b.

Expert Solution

Answer 16

b.

Expert Solution

Answer 17

Expert Solution

Answer 18

Summary Introduction

To discuss: Apply the replicating portfolio technique to value this call.

Answer 19

Explanation of Solution

The replicating portfolio technique of valuing call is as follows.

PRIN.OF CORPORATE FINANCE, Chapter 21, Problem 1PS

Answer 20

c.

Expert Solution

Summary Introduction

To discuss: The probability of increasing stock R price in a risk neutral world.

Explanation of Solution

The probability of increasing stock R calculated as follows:

Expected value of calloption=(Probability of rise×call option value in rise)+[(1−Probability of rise)×Call option value in fall]

The computation as follows:

Expected value of call option=(p× 1.00) + (1 –p)(–.50) =.10p=.40

Foot note: The probability is calculated on the basis of expected return.

Answer 21

c.

Expert Solution

Answer 22

c.

Expert Solution

Answer 23

Expert Solution

Answer 24

Summary Introduction

To discuss: The probability of increasing stock R price in a risk neutral world.

Answer 25

Explanation of Solution

The probability of increasing stock R calculated as follows:

Expected value of calloption=(Probability of rise×call option value in rise)+[(1−Probability of rise)×Call option value in fall]

The computation as follows:

Expected value of call option=(p× 1.00) + (1 –p)(–.50) =.10p=.40

Foot note: The probability is calculated on the basis of expected return.

Answer 26

d.

Expert Solution

Summary Introduction

To compute: The value of stock R using the risk neutral method.

Explanation of Solution

The option value is calculated using the following formula:

Value of call=Expected future value1+Interest rate=.401.10=0.3636 OR $36.36

Hence, the value of call is $36.36

Answer 27

d.

Expert Solution

Answer 28

d.

Expert Solution

Answer 29

Expert Solution

Answer 30

Summary Introduction

To compute: The value of stock R using the risk neutral method.

Answer 31

Explanation of Solution

The option value is calculated using the following formula:

Value of call=Expected future value1+Interest rate=.401.10=0.3636 OR $36.36

Hence, the value of call is $36.36

Answer 32

e.

Expert Solution

Summary Introduction

To discuss: Whether person X change his option regarding the value of option.

Explanation of Solution

Person X does not change his opinion regarding the value of option. The chance of price increase is most likely higher than the risk- neutral probability, but it does not aid to value the option.

Answer 33

e.

Expert Solution

Answer 34

e.

Expert Solution

Answer 35

Expert Solution

Answer 36

Summary Introduction

To discuss: Whether person X change his option regarding the value of option.

Answer 37

Explanation of Solution

Person X does not change his opinion regarding the value of option. The chance of price increase is most likely higher than the risk- neutral probability, but it does not aid to value the option.