Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
9th Edition
ISBN: 9781259277214
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Bradford D Jordan Professor
Publisher: McGraw-Hill Education
bartleby

Videos

Question
Book Icon
Chapter 10, Problem 28QP

a)

Summary Introduction

To determine: The probability of earning more than 10 percent on long-term corporate bonds.

Introduction:

The Normal distribution curve is a bell-shaped curve formed based on the frequency distribution of the observations The mean or average of the observations and their standard deviation define the normal distribution curve.

Standard deviation refers to the variation in the actual observations from the average.

Z-Score helps to know how many numbers of standard deviations is the raw score or outcome away from the average or mean.

a)

Expert Solution
Check Mark

Answer to Problem 28QP

The probability of earning more than 10 percent on long-term corporate bonds is 33.41 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return greater than 10 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  1

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  2

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  3

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  4

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  5

The probability of 0.665882 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.665882. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.334118 or 33.4118 percent(10.665882).

Summary Introduction

To determine: The probability of earning less than 0 percent on long-term corporate bonds

Expert Solution
Check Mark

Answer to Problem 28QP

The probability of earning less than 0 percent on long-term corporate bonds is 0.223058 or 0.223058 percent

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  6

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  7

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  8

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  9

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  10

The probability of 0.223058 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.223058 or 0.223058 percent.

b)

Summary Introduction

To determine: The probability of earning more than 10 percent on Treasury bills

b)

Expert Solution
Check Mark

Answer to Problem 28QP

The probability of earning more than 10 percent on Treasury bills is 0.018006785 or 1.80 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having a return greater than 10 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  11

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  12

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  13

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having more than 10 percent returns. Hence, “X” equals 10 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  14

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  15

The probability of 0.981993215 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10 percent return. The area to the right of Z is the probability of getting a return of 10 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.981993215. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10 percent return or more is 0.018006785 or 1.80 percent(10.981993215).

Summary Introduction

To determine: The probability of earning less than 0 percent on Treasury bills.

Expert Solution
Check Mark

Answer to Problem 28QP

The probability of earning less than 0 percent on Treasury bills is 0.129442113 or 12.94 percent.

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return less than 0 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  16

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  17

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  18

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (0 percent) return or less. Hence, “X” equals (0 percent). The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  19

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  20

The probability of 0.129442113 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (0 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning less than 0 percent is 0.129442113 or 12.94 percent.

c)

Summary Introduction

To determine: The probability of earning (4.18 percent) on long-term corporate bonds.

c)

Expert Solution
Check Mark

Answer to Problem 28QP

The probability of earning (4.18 percent) on long-term corporate bonds is 0.1039 or 10.39 percent.

Explanation of Solution

Given information:

Assume that the returns of long-term corporate bonds have a normal distribution. The average return or mean of long-term corporate bonds is 6.4 percent, and the standard deviation is 8.4 percent (Refer to Figure 10.10 in the textbook).

Determine the probability of having (4.18 percent) on long-term government bonds:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  21

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  22

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  23

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having (4.18 percent) return or less. Hence, “X” equals (4.18 percent). The mean or average return is 6.4 percent. The standard deviation is 8.4 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  24

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  25

The probability of 0.103921 represents the area to the left of Z. The area to the left of Z refers to the probability of getting (4.18 percent) return or less because the left-hand side of the normal distribution curve indicates negative returns. Hence, the probability of earning (4.18 percent) is 0.1039 or 10.39 percent.

Summary Introduction

To determine: The probability of earning 10.56 percent on Treasury bills.

Expert Solution
Check Mark

Answer to Problem 28QP

The probability of earning 10.56 percent on Treasury bills is 0.011380598 or 1.14 percent

Explanation of Solution

Given information:

Assume that the returns of Treasury bills have a normal distribution. The average return or mean of Treasury bills is 3.5 percent, and the standard deviation is 3.1 percent (Refer to Figure 10.10 in the text).

Determine the probability of having a return of 10.56 percent on Treasury bills:

Follow the common steps from Step 1 to Step 3 given below. Then, proceed with the Step 4.

The common steps to be followed to use the “NORM.DIST” function in Excel:

Step 1:

Open an Excel worksheet.

Step 2:

Place the cursor in cell A1.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  26

Step 3:

Select the “Formulas” tab, and go to “More functions” in the ribbon. Under “More functions”, select “Statistical”. Under the drop-down menu of “Statistical”, select “NORM.DIST” function.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  27

After clicking the “NORM.DIST” function, a popup window named “Function arguments” appears.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  28

Step 4:

Enter the values. “X” represents the raw score or outcome. Here, it is necessary to test the probability of having 10.56 percent returns. Hence, “X” equals 10.56 percent. The mean or average return is 3.5 percent. The standard deviation is 3.1 percent. The cumulative distribution function provides the probability of the area to the left of Z. Hence, enter “TRUE” in the “Cumulative” column.

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  29

Press “OK” after providing the inputs. The probability of the area to the left of Z is as follows:

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate), Chapter 10, Problem 28QP , additional homework tip  30

The probability of 0.988619402 represents the area to the left of Z. The area to the left of Z is the probability of getting less than 10.56 percent return. The area to the right of Z is the probability of getting a return of 10.56 percent or more.

The total area represented by the normal distribution curve has a probability of “1”. The area to the left of Z has a probability of 0.988619402. Hence, the probability of the area to the right of Z is “1” minus the probability of the area to the left of Z. Hence, the probability of getting 10.56 percent return or more is 0.011380598 or 1.14 percent(10.988619402).

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
1. Give one new distribution channels for Virtual Assistance (freelance business) that is not commonly used.   - show a chart/diagram to illustrate the flow of the distribution channels.   - explain the rationale behind it. (e.g., increased market reach, improved customer experience, cost-efficiency).   - connect the given distribution channel to the marketing mix: (How does it align with the overall marketing strategy? Consider product, price, promotion, and place.).    - define the target audience: (Age, gender, location, interests, etc.).    - lastly, identify potential participants: (Wholesalers, retailers, online platforms, etc.)
An individual is planning for retirement and aims to withdraw $100,000 at the beginning of each year, starting from the first year of retirement, for an expected retirement period of 20 years. To fund this retirement plan, he intends to make 20 equal annual deposits at the end of each year during his working years. Assume a simple annual interest rate of 20% during his working years and a simple annual interest rate of 5% during retirement. What should his annual deposit amount be to achieve his desired retirement withdrawals? Please write down the steps of your calculation and explain result economic meaning.
Assume an investor buys a share of stock for $18 at t=0 and at the end of the next year (t=1), he buys 12 shares with a unit price of $9 per share. At the end of Year 2 (t=2), the investor sells all shares for $40 per share. At the end of each year in the holding period, the stock paid a $5.00 per share dividend. What is the annual time-weighted rate of return? Please write down the steps of your calculation and explain result economic meaning.

Chapter 10 Solutions

Essentials of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)

Ch. 10.3 - Prob. 10.3BCQCh. 10.3 - Prob. 10.3CCQCh. 10.3 - What is the first lesson from capital market...Ch. 10.4 - In words, how do we calculate a variance? A...Ch. 10.4 - Prob. 10.4BCQCh. 10.4 - Prob. 10.4CCQCh. 10.4 - What is the second lesson from capital market...Ch. 10.5 - Prob. 10.5ACQCh. 10.5 - Prob. 10.5BCQCh. 10.6 - What is an efficient market?Ch. 10.6 - Prob. 10.6BCQCh. 10 - Section 10.1Say you buy a share of stock for 50....Ch. 10 - Prob. 10.3CCh. 10 - Prob. 10.4CCh. 10 - Prob. 10.5CCh. 10 - Prob. 10.6CCh. 10 - Prob. 1CTCRCh. 10 - Prob. 2CTCRCh. 10 - Risk and Return. We have seen that over long...Ch. 10 - Market Efficiency Implications. Explain why a...Ch. 10 - Prob. 5CTCRCh. 10 - Prob. 6CTCRCh. 10 - Prob. 7CTCRCh. 10 - Prob. 8CTCRCh. 10 - Efficient Markets Hypothesis. There are several...Ch. 10 - Prob. 10CTCRCh. 10 - Prob. 1QPCh. 10 - Prob. 2QPCh. 10 - Prob. 3QPCh. 10 - Prob. 4QPCh. 10 - Nominal versus Real Returns. What was the...Ch. 10 - Bond Returns. What is the historical real return...Ch. 10 - Prob. 7QPCh. 10 - Prob. 8QPCh. 10 - Prob. 9QPCh. 10 - Calculating Real Returns and Risk Premiums. For...Ch. 10 - Prob. 11QPCh. 10 - Prob. 12QPCh. 10 - Calculating Returns. You purchased a zero-coupon...Ch. 10 - Prob. 14QPCh. 10 - Prob. 15QPCh. 10 - Calculating Real Returns. Refer to Table 10.1....Ch. 10 - Return Distributions. Refer back to Figure 10.10....Ch. 10 - Prob. 18QPCh. 10 - Prob. 19QPCh. 10 - Arithmetic and Geometric Returns. A stock has had...Ch. 10 - Prob. 21QPCh. 10 - Prob. 22QPCh. 10 - Prob. 23QPCh. 10 - Prob. 24QPCh. 10 - Prob. 25QPCh. 10 - Prob. 26QPCh. 10 - Prob. 27QPCh. 10 - Prob. 28QPCh. 10 - Prob. 1CCCh. 10 - Prob. 2CCCh. 10 - Prob. 3CCCh. 10 - Prob. 4CCCh. 10 - Prob. 5CC
Knowledge Booster
Background pattern image
Finance
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Intermediate Financial Management (MindTap Course...
Finance
ISBN:9781337395083
Author:Eugene F. Brigham, Phillip R. Daves
Publisher:Cengage Learning
Text book image
Entrepreneurial Finance
Finance
ISBN:9781337635653
Author:Leach
Publisher:Cengage
Text book image
Financial Management: Theory & Practice
Finance
ISBN:9781337909730
Author:Brigham
Publisher:Cengage
Text book image
Personal Finance
Finance
ISBN:9781337669214
Author:GARMAN
Publisher:Cengage
Journalizing Bonds Payable/Amortization of a Premium; Author: TLC Tutoring;https://www.youtube.com/watch?v=5gEpAFFnIE8;License: Standard YouTube License, CC-BY
Investing Basics: Bonds; Author: TD Ameritrade;https://www.youtube.com/watch?v=IuyejHOGCro;License: Standard YouTube License, CC-BY