Chapter 18, Problem 4P

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250

Chapter
Section

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250
Textbook Problem

# Intermediate Problems 4-5BLACK-SCHOLES MODEL Assume that you have been given the following information on Fire Industries: Current stock price = $16 Exercise price of option =$16 Time until expiration of option = 6 months Risk-free rate = 8% Variance of stock price = 0.12 d1 =0.28577 d2 = 0.04082 N(d1) = 0.61247 N(d2) = 051628   Using the Black-Scholes Option Pricing Model, what is the value of the option?

Summary Introduction

To determine: The value of the option.

Introduction:

Option is a contract to purchase a financial asset from one party and sell it to another party on an agreed price for a future date. There are two types of options, which are as follows:

• Call option
• Put option
Explanation

Given information:

F Company’s stock price is $16, exercise price of option is$16, and time until expiration of option is 6 months. The risk-free rate is 8 percent and variance of stock price is 0.12. The value of d1 is 0.28577 and d2 is 0.04082. The value of N(d1) is 0.61247 and value of N(d2) is 0.51628.

The formula to value of option using the Black-Scholes option pricing model is as follows:

V=P[N(d1)] Xe-rRFt[N(d2)]

Where,

V refers to the value of option

P refers to the current price of stock

N(d1) refers to the probability where a deviation is less than d1.

X refers to the exercise price of option

N(d2) refers to the probability that the Stock price is greater than strike price

rRF refers to the risk-free rate

t refers to the number of periods

Compute the value of option:

Note: The value of “e” is 2.718281828

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