Principles of Corporate Finance
Principles of Corporate Finance
13th Edition
ISBN: 9781260465099
Author: BREALEY, Richard
Publisher: MCGRAW-HILL HIGHER EDUCATION
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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%.

  1. a. What is the delta of a one-year call option on Ragwort stock with an exercise price of $100?
  2. b. Use the replicating-portfolio method to value this call.
  3. c. In a risk-neutral world, what is the probability that Ragwort stock will rise in price?
  4. d. Use the risk-neutral method to check your valuation of the Ragwort option.
  5. 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
Check Mark
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=($1000$20050)=.6667

b.

Expert Solution
Check Mark
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.

Principles of Corporate Finance, Chapter 21, Problem 1PS

c.

Expert Solution
Check Mark
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)+[(1Probability 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
Check Mark
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
Check Mark
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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