CHAPTER 9
Time Value of Money
Future value
Present value
Annuities
Rates of return
Amortization
9-‹#›
1
Time lines
Show the timing of cash flows.
Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period.
CF0
CF1
CF3
CF2
0
1
2
3
I%
9-‹#›
2
Drawing time lines
100
100
100
0
1
2
3
I%
3 year $100 ordinary annuity
100
0
1
2
I%
$100 lump sum due in 2 years
9-‹#›
3
Future Value of Money
If you deposit $1,000 today at 10%, how much will you have after 15 years?
Interest($) = Principal ∙ Interest Rate(%)
Simple Interest
The original principal stays the same.
There is no interest on interest. The interest is only on the original principal.
Compound Interest
The principal changes through time.
There is “interest on interest”. The interest is on the new principal.
9-‹#›
9-‹#›
9-‹#›
Simple Interest
Interest($) = Principal($) ∙ Interest Rate(%) = V0 ∙ I
V1 = V0 + Interest = V0 + V0 ∙ I = V0(1 + I)
V2 = V1 + Interest = V1 + V0 ∙ I = V0(1 + I) + V0 ∙ I
= V0(1 + I + I) = V0(1 + 2I)
V3 = V2 + Interest = V2 + V0 ∙ I = V0(1 + 2I) + V0 ∙ I
= V0(1 + 2I + I) = V0(1 + 3I)
.
.
Vn = V0(1 + nI)
FVn = PV(1 + nI)
9-‹#›
Compound Interest
Interest ($) = Principal ($) ∙ Interest Rate (%) = V ∙ I
V1 = V0 + Interest = V0 + V0 ∙ I = V0(1 + I)
V2 = V1 + Interest = V1 + V1 ∙ I = V1(1 + I)
V3 = V2 + Interest = V2 + V2 ∙ I = V2(1 + I)
V2 = V1(1 + I) = V0(1 + I)(1 + I) = V0(1 + I)2
V3 = V2(1 + I) = V0(1 + I)2(1 + I) = V0(1 + I)3
Vn = V0 (1 + I)n
FVn = PV(1 + I)n = PV∙FVIF
V2 = V1 + Interest = V1 + (V0 + Interest) ∙ I
9-‹#›
Example
What is the future value of $20 invested for 2 years at 10%?
Simple: FV = PV(1+nI)
= 20(1+2I) = 20(1+0.2) = $24
Compound: FV = PV(1+I)n
= 20(1+I)2 = 20(1+0.1)2 = $24.2
What is the future value of $20 invested for 100 years at 10%?
Simple: FV = 20(1+ ) =
Compound : FV = 20(1.1)100 = 275,612.25
9-‹#›
The Power of Compounding
The Value of Manhattan
In 1626, the land was bought from American Indians at $24.
In 2018, value = $24(1+I)392
9-‹#›
Solving for FV:
The formula method
Solve the general FV equation:
FVN = PV∙(1 + I)N = PV ∙ FVIF
FV15 = PV∙(1 + I)15 = $1,000∙(1.10)15 = $4,177.25
= $1,000∙4.177 = $4,177
(Table A)
9-‹#›
Present Value of Money
If you want to have $4,177.25 after 15 years, how much do you have to deposit today at 10%?
9-‹#›
PV = ?
4,177.25
Present Value of Money
Finding the PV of a cash flow or series of cash flows is called discounting (the reverse of compounding).
0
1
2 …
15
10%
9-‹#›
13
Solving for PV:
The formula method
Solve the general FV equat.
The time value of money is the concept that money available at the present time is worth more than the identical sum in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. Time Value of Money is also sometimes referred to as present discounted value.
The time value of money is the concept that money available at the present time is worth more than the identical sum in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. Time Value of Money is also sometimes referred to as present discounted value.
Time lines
Future value / Present value of lump sum
FV / PV of annuity
Perpetuities
Uneven CF stream
Compounding periods
Nominal / Effective / Periodic rates
Amortization
CFA LEVEL 1- Time Value of Money_compressed (1).pdfAlison Tutors
This document focuses on End of Chapter questions and commonly asked questions under Quantitative methods (Time Value of Money ) . The mainly asked questions include :
-calculation and interpretation of Future Value and Present Value of a single sum of money , an ordinary annuity, annuity due, a perpetuity (PV only) and a series of unequal cash flows.
-demonstration of the use of timelines in modeling and solving time value of money
This is a very interesting topic!
CHAPTER 3Understanding Regulations, Accreditation Criteria, and .docxtiffanyd4
CHAPTER 3
Understanding Regulations, Accreditation Criteria, and Other Standards ofPractice
NAEYC Administrator Competencies Addressed in This Chapter:
Management Knowledge and Skills
2. Legal and Fiscal Management
· Knowledge and application of the advantages and disadvantages of different legal structures
· Knowledge of different codes and regulations as they relate to the delivery of early childhood program services
· Knowledge of child custody, child abuse, special education, confidentiality, anti-discrimination, insurance liability, contract, and laborlaws pertaining to program management
5. Program Operations and Facilities Management
· Knowledge and application of policies and procedures that meet state/local regulations and professional standards pertaining to thehealth and safety of young children
7. Marketing and public relations
· Skill in developing a business plan and effective promotional literature, handbooks, newsletters, and press releases
Early Childhood Knowledge and Skills
5. Children with Special Needs
· Knowledge of licensing standards, state and federal laws (e.g., ADA, IDEA) as they relate to services and accommodations for childrenwith special needs
10. Professionalism
· Knowledge of laws, regulations, and policies that impact professional conduct with children and families
· Knowledge of center accreditation criteria
Learning Outcomes
After studying this chapter, you will be able to:
1. Describe the purpose of regulations that apply to programs of early care and education and list several topics they address.
2. Identify several ways accreditation standards are different from child care regulations.
3. State the purpose of Quality Rating and Improvement Systems (QRIS).
4. List some ways qualifications for administrators and teachers are different for licensure, for accreditation, and in QRIS systems.
5. Identify laws that apply to the childcare workplace, such as those that govern the program’s financial management and employees’well-being.
Marie’s Experience
Marie has been successful over the years in keeping her center in compliance with all licensing regulations. She is proud of her teachers andconfident that the center consistently goes above and beyond licensing provisions designed simply to keep children healthy and safe. She knowsthat the center provides high-quality care to the children it serves, but has never pursued accreditation or participated in her state’s optionalQuality Rating and Improvement System (QRIS) because of the time and effort it would require. Her families have confidence in her program anddo not seem to need this additional assurance that it provides high-quality services day in and day out.
Large numbers of families rely on out-of-home care for their infants, toddlers, preschoolers, and school-age children during the workday. In2011, there were 312,254 licensed child care facilities with a capacity to serve almost 10.2 million children. About 34% of these facilitieswere child care center.
Chapter 3 Human RightsINTERNATIONAL HUMAN RIGHTS–BASED ORGANIZ.docxtiffanyd4
Chapter 3 Human Rights
INTERNATIONAL HUMAN RIGHTS–BASED ORGANIZATIONS LIKE THE UN COMMISSION ON HUMAN RIGHTS HAVE MADE MONITORING HUMAN RIGHTS A GLOBAL ISSUE. The United Nations is headquartered in New York City.
Learning Objectives
1. 3.1Review the expansion of and the commitment to the human rights agenda
2. 3.2Evaluate the milestones that led to the current concerns around human rights
3. 3.3Evaluate some of the philosophical controversies over human rights
4. 3.4Recognize global, regional, national, and local institutions and rules designed to protect human rights across the globe
5. 3.5Report the efforts made globally in bringing violators of human rights to justice
6. 3.6Relate the need for stricter laws to protect women’s human rights across the globe.
7. 3.7Recognize the need to protect the human rights of the disabled
8. 3.8Distinguish between the Western and the Islamic beliefs on individual and community rights
9. 3.9Review the balancing act that needs to be played while fighting terrorism and protecting human rights
10. 3.10Report the controversy around issuing death penalty as punishment
When Muammar Qaddafi used military force to suppress people demonstrating in Libya for a transition to democracy, there was a general consensus that there was a global responsibility to protect civilians. However, when Bashar Assad used fighter jets, tanks, barrel bombs, chemical weapons, and a wide range of brutal methods, including torture, to crush the popular uprising against his rule in Syria, the world did not respond forcefully to protect civilians. The basic reason given for allowing Syria to descend into brutality and chaos was that it was difficult to separate Syrians favoring human rights from those who embraced terrorism. Although cultural values differ significantly from one society to another, our common humanity has equipped us with many shared ideas about how human beings should treat each other. Aspects of globalization, especially communications and migration, reinforce perceptions of a common humanity. In general, there is global agreement that human beings, simply because we exist, are entitled to at least three types of rights. First is civil rights, which include personal liberties such as freedom of speech, religion, and thought; the right to own property; and the right to equal treatment under the law. Second is political rights, including the right to vote, to voice political opinions, and to participate in the political process. Third is social rights, including the right to be secure from violence and other physical danger, the right to a decent standard of living, and the right to health care and education. Societies differ in terms of which rights they emphasize. Four types of human rights claims that dominate global politics are
1. The abuse of individual rights by governments
2. Demands for autonomy or independence by various groups
3. Demands for equality and privacy by groups with unconventional lifestyles
4. Cla.
More Related Content
Similar to CHAPTER 9Time Value of MoneyFuture valuePresent valueAnn.docx
Time lines
Future value / Present value of lump sum
FV / PV of annuity
Perpetuities
Uneven CF stream
Compounding periods
Nominal / Effective / Periodic rates
Amortization
CFA LEVEL 1- Time Value of Money_compressed (1).pdfAlison Tutors
This document focuses on End of Chapter questions and commonly asked questions under Quantitative methods (Time Value of Money ) . The mainly asked questions include :
-calculation and interpretation of Future Value and Present Value of a single sum of money , an ordinary annuity, annuity due, a perpetuity (PV only) and a series of unequal cash flows.
-demonstration of the use of timelines in modeling and solving time value of money
This is a very interesting topic!
CHAPTER 3Understanding Regulations, Accreditation Criteria, and .docxtiffanyd4
CHAPTER 3
Understanding Regulations, Accreditation Criteria, and Other Standards ofPractice
NAEYC Administrator Competencies Addressed in This Chapter:
Management Knowledge and Skills
2. Legal and Fiscal Management
· Knowledge and application of the advantages and disadvantages of different legal structures
· Knowledge of different codes and regulations as they relate to the delivery of early childhood program services
· Knowledge of child custody, child abuse, special education, confidentiality, anti-discrimination, insurance liability, contract, and laborlaws pertaining to program management
5. Program Operations and Facilities Management
· Knowledge and application of policies and procedures that meet state/local regulations and professional standards pertaining to thehealth and safety of young children
7. Marketing and public relations
· Skill in developing a business plan and effective promotional literature, handbooks, newsletters, and press releases
Early Childhood Knowledge and Skills
5. Children with Special Needs
· Knowledge of licensing standards, state and federal laws (e.g., ADA, IDEA) as they relate to services and accommodations for childrenwith special needs
10. Professionalism
· Knowledge of laws, regulations, and policies that impact professional conduct with children and families
· Knowledge of center accreditation criteria
Learning Outcomes
After studying this chapter, you will be able to:
1. Describe the purpose of regulations that apply to programs of early care and education and list several topics they address.
2. Identify several ways accreditation standards are different from child care regulations.
3. State the purpose of Quality Rating and Improvement Systems (QRIS).
4. List some ways qualifications for administrators and teachers are different for licensure, for accreditation, and in QRIS systems.
5. Identify laws that apply to the childcare workplace, such as those that govern the program’s financial management and employees’well-being.
Marie’s Experience
Marie has been successful over the years in keeping her center in compliance with all licensing regulations. She is proud of her teachers andconfident that the center consistently goes above and beyond licensing provisions designed simply to keep children healthy and safe. She knowsthat the center provides high-quality care to the children it serves, but has never pursued accreditation or participated in her state’s optionalQuality Rating and Improvement System (QRIS) because of the time and effort it would require. Her families have confidence in her program anddo not seem to need this additional assurance that it provides high-quality services day in and day out.
Large numbers of families rely on out-of-home care for their infants, toddlers, preschoolers, and school-age children during the workday. In2011, there were 312,254 licensed child care facilities with a capacity to serve almost 10.2 million children. About 34% of these facilitieswere child care center.
Chapter 3 Human RightsINTERNATIONAL HUMAN RIGHTS–BASED ORGANIZ.docxtiffanyd4
Chapter 3 Human Rights
INTERNATIONAL HUMAN RIGHTS–BASED ORGANIZATIONS LIKE THE UN COMMISSION ON HUMAN RIGHTS HAVE MADE MONITORING HUMAN RIGHTS A GLOBAL ISSUE. The United Nations is headquartered in New York City.
Learning Objectives
1. 3.1Review the expansion of and the commitment to the human rights agenda
2. 3.2Evaluate the milestones that led to the current concerns around human rights
3. 3.3Evaluate some of the philosophical controversies over human rights
4. 3.4Recognize global, regional, national, and local institutions and rules designed to protect human rights across the globe
5. 3.5Report the efforts made globally in bringing violators of human rights to justice
6. 3.6Relate the need for stricter laws to protect women’s human rights across the globe.
7. 3.7Recognize the need to protect the human rights of the disabled
8. 3.8Distinguish between the Western and the Islamic beliefs on individual and community rights
9. 3.9Review the balancing act that needs to be played while fighting terrorism and protecting human rights
10. 3.10Report the controversy around issuing death penalty as punishment
When Muammar Qaddafi used military force to suppress people demonstrating in Libya for a transition to democracy, there was a general consensus that there was a global responsibility to protect civilians. However, when Bashar Assad used fighter jets, tanks, barrel bombs, chemical weapons, and a wide range of brutal methods, including torture, to crush the popular uprising against his rule in Syria, the world did not respond forcefully to protect civilians. The basic reason given for allowing Syria to descend into brutality and chaos was that it was difficult to separate Syrians favoring human rights from those who embraced terrorism. Although cultural values differ significantly from one society to another, our common humanity has equipped us with many shared ideas about how human beings should treat each other. Aspects of globalization, especially communications and migration, reinforce perceptions of a common humanity. In general, there is global agreement that human beings, simply because we exist, are entitled to at least three types of rights. First is civil rights, which include personal liberties such as freedom of speech, religion, and thought; the right to own property; and the right to equal treatment under the law. Second is political rights, including the right to vote, to voice political opinions, and to participate in the political process. Third is social rights, including the right to be secure from violence and other physical danger, the right to a decent standard of living, and the right to health care and education. Societies differ in terms of which rights they emphasize. Four types of human rights claims that dominate global politics are
1. The abuse of individual rights by governments
2. Demands for autonomy or independence by various groups
3. Demands for equality and privacy by groups with unconventional lifestyles
4. Cla.
CHAPTER 13Contributing to the ProfessionNAEYC Administrator Co.docxtiffanyd4
CHAPTER 13
Contributing to the Profession
NAEYC Administrator Competencies Addressed in This Chapter:
Management Knowledge and Skills
1. Personal and Professional Self-Awareness
· The ability to evaluate ethical and moral dilemmas based on a professional code of ethics
8. Leadership and Advocacy
· Knowledge of the legislative process, social issues, and public policy affecting young children and their families
· The ability to advocate on behalf of young children, their families and the profession
Early Childhood Knowledge and Skills
1. Historical and Philosophical Foundations
· Knowledge of research methodologies
10. Professionalism
· Knowledge of different professional organizations, resources, and issues impacting the welfare of early childhood practitioners
· Ability to make professional judgments based on the NAEYC “Code of Ethical Conduct and Statement of Commitment”
· Ability to work as part of a professional team and supervise support staff or volunteers
Learning Outcomes
After studying this chapter, you will be able to:
1. Describe how the field of early childhood education has made progress achieving two of the eight criteria of professional status.
2. Identify the advocacy tools that early childhood advocates should have at their disposal.
3. Discuss opportunities that program administrators have to contribute to the field’s future.
Grace’s Experience
Grace had found that working with children came naturally, and she considered herself to be a gifted teacher after only a short time in theclassroom. She thought she would spend her entire career working directly with children. She is now somewhat surprised how much she isenjoying the new responsibilities that come with being a program director. She is gaining confidence that she can work effectively with allfamilies, even when faced with difficult conversations; and her skills as a supervisor, coach, and mentor are increasing as well. She is nowcomfortable as a leader in her own center and is considering volunteering to fill a leadership role in the local early childhood professionalorganization. That would give her opportunities to refine her leadership skills while contributing to the quality of care provided for childrenthroughout her community.
Early childhood administrators are leaders. They contribute to the profession by making the public aware of the field’s emergingprofessionalism, including its reliance on a code of ethics; engaging in informed advocacy; becoming involved in research to increase whatwe know about how children learn, grow, and develop; and coaching and mentoring novices, experienced practitioners, and emergingleaders.
13.1 PROMOTING PROFESSIONALIZATION1
Lilian Katz, one of the most influential voices in the field of early care and education, began discussions about the professionalism of thefield in the mid-1980s. Her work extended a foundation that had been laid by sociologists, philosophers, and other scholars and continuesto influence how early childhoo.
Chapter 2 The Law of EducationIntroductionThis chapter describ.docxtiffanyd4
Chapter 2 The Law of Education
Introduction
This chapter describes the various agencies and types of law that affect education. It also discusses the organization and functions of the various judicial bodies that have an impact on education. School leadership candidates are introduced to standards of review, significant federal civil rights laws, the contents of legal decisions, and a sample legal brief.
Focus Questions
1. How are federal courts organized, and what kind of decisions do they make?
2. What is law? How is law different from policy?
3. From what source does the authority of local boards of education emanate?
4. How can campus and district leaders remain current with changes in law and policy at the national and state level?
Key Terms
1.
2.
3.
4. En banc
5.
6.
7.
8.
9.
10.
11. Stare decisis
12.
13.
14.
15.
Case Study Confused Yet?
As far as Elise Daniels was concerned, the monthly meeting of the 20 River County middle school principals was the most informative and relaxing activity in her school year. Twice per year, the principals invited a guest to speak to the group. Elise was particularly interested in the fall special guest speaker, the attorney for the state school boards association. Elise had heard him speak several times, so she was aware of his deep knowledge of school law and emerging issues. As the attorney, spoke Elise found herself becoming more anxious. It was as if the attorney was speaking a foreign language. Tinker rules, due process, Title IX, Office of Civil Rights, and the state bullying law. Elise found herself thinking, “The Americans with Disabilities Act has been amended? How am I supposed to keep up with all of this?”
Leadership Perspectives
Middle School Principal Elise Daniels in the case study “Confused Yet?” is correct. School law can be confusing. Educators work in a highly regulated environment directly and indirectly impacted by a wide variety of local, state, and federal authorities. When P–12 educators refer to “the law,” they are often referring to state and/or federal statutes enacted by legislatures (). This understanding is correct. The U.S. Congress and 50 state legislatures are active in the law-making business. To make matters more difficult, the law is constantly changing and evolving as new situations arise. For example, 10 years ago few if any states had passed antibullying laws. By 2008, however, almost every state had some form of antibullying legislation on the books. Soon after, the phenomenon of cyberbullying emerged, and state legislators rushed to add cyberbullying and/or electronic bullying to their state education laws. One can only guess at what new real or perceived problem affecting public P–12 schools will be next.
P–12 educators also refer to school board policy as “law.” However, law and policy are not necessarily identical. , p. 4) defines policy as “one way through which a political system handles a public problem. It includes a government’s expressed inten.
CHAPTER 1 Legal Heritage and the Digital AgeStatue of Liberty,.docxtiffanyd4
CHAPTER 1 Legal Heritage and the Digital Age
Statue of Liberty, New York Harbor
The Statue of Liberty stands majestically in New York Harbor. During the American Revolution, France gave the colonial patriots substantial support in the form of money for equipment and supplies, officers and soldiers who fought in the war, and ships and sailors who fought on the seas. Without the assistance of France, it is unlikely that the American colonists would have won their independence from Britain. In 1886, the people of France gave the Statue of Liberty to the people of the United States in recognition of friendship that was established during the American Revolution. Since then, the Statue of Liberty has become a symbol of liberty and democracy throughout the world.
Learning Objectives
After studying this chapter, you should be able to:
1. Define law.
2. Describe the functions of law.
3. Explain the development of the U.S. legal system.
4. List and describe the sources of law in the United States.
5. Discuss the importance of the U.S. Supreme Court’s decision in Brown v. Board of Education.
Chapter Outline
1. Introduction to Legal Heritage and the Digital Age
2. What Is Law?
1. Landmark U.S. Supreme Court Case • Brown v. Board of Education
3. Schools of Jurisprudential Thought
1. CASE 1.1 • U.S. Supreme Court Case • POM Wonderful LLC v. Coca-Cola Company
2. Global Law • Command School of Jurisprudence of Cuba
4. History of American Law
1. Landmark Law • Adoption of English Common Law in the United States
2. Global Law • Civil Law System of France and Germany
5. Sources of Law in the United States
1. Contemporary Environment • How a Bill Becomes Law
2. Digital Law • Law of the Digital Age
6. Critical Legal Thinking
1. CASE 1.2 • U.S. Supreme Court Case • Shelby County, Texas v. Holder
“ Where there is no law, there is no freedom.”
—John Locke Second Treatise of Government, Sec. 57
Introduction to Legal Heritage and the Digital Age
In the words of Judge Learned Hand, “Without law we cannot live; only with it can we insure the future which by right is ours. The best of men’s hopes are enmeshed in its success.”1 Every society makes and enforces laws that govern the conduct of the individuals, businesses, and other organizations that function within it.
Although the law of the United States is based primarily on English common law, other legal systems, such as Spanish and French civil law, also influence it. The sources of law in this country are the U.S. Constitution, state constitutions, federal and state statutes, ordinances, administrative agency rules and regulations, executive orders, and judicial decisions by federal and state courts.
Human beings do not ever make laws; it is the accidents and catastrophes of all kinds happening in every conceivable way that make law for us.
Plato
Laws IV, 709
Businesses that are organized in the United States are subject to its laws. They are also subject to the laws of other countries in which they operate. Busin.
CHAPTER 1 BASIC CONCEPTS AND DEFINITIONS OF HUMAN SERVICESPAUL F.docxtiffanyd4
CHAPTER 1 BASIC CONCEPTS AND DEFINITIONS OF HUMAN SERVICES
PAUL F. CIMMINO
This chapter is dedicated to the development of basic definitions that describe and identify human services. However, any attempt to define human services in one sentence, or to use one description, is doomed to fail. According to Schmolling, Youkeles, and Burger, there is no generally accepted or “official” definition of human services (, p. 9). Human services is a multidisciplinary profession that reflects complex human interactions and a comprehensive social system. To understand human services, it is important to develop ideas that construct an organized perspective of the field. In this chapter, three general questions about human services are incorporated into the text. First, “What is it, and what isn’t it?” Second, “Who is helped and why?” Third, “How is help delivered and by whom?” These fundamental questions tend to exemplify the basic concepts and definitions in human services. This chapter proceeds to introduce important terms, definitions, subconcepts, and concentration areas in human services, which are expounded upon by a host of authors who have contributed their expertise to create this book.
The professional field of human services can be reduced to three basic concepts: intervention (needs and services); professionalism (applied practice and credentialing); and education (academic training and research). Each basic concept comprises important aspects of the human service field and identifies primary areas of the profession. The supporting background that nourishes intervention, professionalism, and education in human services is the history of the human service movement (Fullerton, ). The formal development of human services in society is located in the legislative, training, and service history of the field. This chapter attempts to offer a collective understanding of these important areas related to the professional development of human services. In this chapter, basic concepts and definitions converge to generate a comprehensive and theoretical notion of human services in forming an overview of the field. To further assist the reader in developing thoughts about the human service profession, and to avoid ambiguity in the field, a medley of contemporary definitions of human services is presented later in the chapter.
Finally, an important letter written by Dr. Harold McPheeters in 1992, which addresses the basic question of what comprises human services, is presented to close the chapter. McPheeters’s letter was sent in response to a manuscript written by me in 1991. The paper proposes an idealistic model that defines human services in terms of its purpose and professional responsibility in society. Later in the chapter, the central ideas are summarized, providing an orientation to the thoughtful feedback from Harold McPheeters. In my view, his written response conveys landmark perspectives in development of the emerging human service field. Thus, .
CHAPTER 20 Employment Law and Worker ProtectionWashington DC.docxtiffanyd4
CHAPTER 20 Employment Law and Worker Protection
Washington DC
Federal and state laws provide workers’ compensation and occupational safety laws to protect workers in the United States.
Learning Objectives
After studying this chapter, you should be able to:
1. Explain how state workers’ compensation programs work and describe the benefits available.
2. Describe employers’ duty to provide safe working conditions under the Occupational Safety and Health Act.
3. Describe the minimum wage and overtime pay rules of the Fair Labor Standards Act.
4. Describe the protections afforded by the Family and Medical Leave Act.
5. Describe unemployment insurance and Social Security.
Chapter Outline
1. Introduction to Employment Law and Worker Protection
2. Workers’ Compensation
1. Case 20.1 • Kelley v. Coca-Cola Enterprises, Inc.
3. Occupational Safety
1. Case 20.2 • R. Williams Construction Company v. Occupational Safety and Health Review Commission
4. Fair Labor Standards Act
1. Case 20.3 U.S. SUPREME COURT Case • IBP, Inc. v. Alvarez
5. Family and Medical Leave Act
6. Consolidated Omnibus Budget Reconciliation Act and Employee Retirement Income Security Act
7. Government Programs
“ It is difficult to imagine any grounds, other than our own personal economic predilections, for saying that the contract of employment is any the less an appropriate subject of legislation than are scores of others, in dealing with which this Court has held that legislatures may curtail individual freedom in the public interest.”
—Stone, Justice Dissenting opinion, Morehead v. New York (1936)
Introduction to Employment Law and Worker Protection
Generally, the employer–employee relationship is subject to the common law of contracts and agency law. This relationship is also highly regulated by federal and state governments that have enacted myriad laws that protect workers from unsafe working conditions, require employers to provide workers’ compensation to employers injured on the job, prohibit child labor, require minimum wages and overtime pay to be paid to workers, require employers to provide time off to employees with certain family and medical emergencies, and provide other employee protections and rights.
Poorly paid labor is inefficient labor, the world over.
Henry George
This chapter discusses employment law, workers’ compensation, occupational safety, pay and hour rules, and other laws affecting employment.
Workers’ Compensation
Many types of employment are dangerous, and many workers are injured on the job each year. Under common law, employees who were injured on the job could sue their employers for negligence. This time-consuming process placed the employee at odds with his or her employer. In addition, there was no guarantee that the employee would win the case. Ultimately, many injured workers—or the heirs of deceased workers—were left uncompensated.
Workers’ compensation acts were enacted by states in response to the unfairness of that result. These acts crea.
Chapter 1 Global Issues Challenges of GlobalizationA GROWING .docxtiffanyd4
Chapter 1 Global Issues: Challenges of Globalization
A GROWING WORLDWIDE CONNECTEDNESS IN THE AGE OF GLOBALIZATION HAS GIVEN CITIZENS MORE OF A VOICE TO EXPRESS THEIR DISSATISFACTION. In Brazil, Protestors calling for a wide range of reforms marched toward the soccer stadium where a match would be played between Brazil and Uruguay.
Learning Objectives
1. 1.1Identify important terms in international relations
2. 1.2Report the need to adopt an interdisciplinary approach in understanding the impact of new world events
3. 1.3Examine the formation of the modern states with respect to the thirty years’ war in 1618
4. 1.4Recall the challenges to the four types of sovereignty
5. 1.5Report that the European Union was created by redefining the sovereignty of its nations for lasting peace and security
6. 1.6Recall the influence exerted by the Catholic church, transnational companies, and other NGOs in dictating world events
7. 1.7Examine how globalization has brought about greater interdependence between states
8. 1.8Record the major causes of globalization
9. 1.9Review the most important forms of globalization
10. 1.10Recount the five waves of globalization
11. 1.11Recognize reasons as to why France and the US resist globalization
12. 1.12Examine the three dominant views of the extent to which globalization exists
Revolutions in technology, finance, transportation, and communications and different ways of thinking that characterize interdependence and globalization have eroded the power and significance of nation-states and profoundly altered international relations. Countries share power with nonstate actors that have proliferated as states have failed to deal effectively with major global problems.
Many governments have subcontracted several traditional responsibilities to private companies and have created public-private partnerships in some areas. This is exemplified by the hundreds of special economic zones in China, Dubai, and elsewhere. Contracting out traditional functions of government, combined with the centralization of massive amounts of data, facilitated Edward Snowden’s ability to leak what seems to be an almost unlimited amount of information on America’s spying activities.
The connections between states and citizens, a cornerstone of international relations, have been weakened partly by global communications and migration. Social media enable people around the world to challenge governments and to participate in global governance. The prevalence of mass protests globally demonstrates growing frustration with governments’ inability to meet the demands of the people, especially the global middle class.
The growth of multiple national identities, citizenships, and passports challenges traditional international relations. States that played dominant roles in international affairs must now deal with their declining power as global power is more diffused with the rise of China, India, Brazil, and other emerging market countries. States are i.
CHAPTER 23 Consumer ProtectionRestaurantFederal and state go.docxtiffanyd4
CHAPTER 23 Consumer Protection
Restaurant
Federal and state governments have enacted many statutes to protect consumers from unsafe food items.
Learning Objectives
After studying this chapter, you should be able to:
1. Describe government regulation of food and food additives.
2. Describe government regulation of drugs, cosmetics, and medicinal devices.
3. Identify and describe unfair and deceptive business practices.
4. Describe the United Nations Biosafety Protocol concerning genetically altered foods.
5. List and describe consumer financial protection laws.
Chapter Outline
1. Introduction to Consumer Protection
2. Food Safety
1. Case 23.1 • United States of America v. LaGrou Distribution Systems, Incorporated
3. Food, Drugs, and Cosmetics Safety
1. LANDMARK LAW • Food, Drug, and Cosmetic Act
2. ETHICS • Restaurants Required to Disclose Calories of Food Items
3. GLOBAL LAW • United Nations Biosafety Protocol for Genetically Altered Foods
4. Product and Automobile Safety
5. Medical and Health Care Protection
1. LANDMARK LAW • Health Care Reform Act of 2010
6. Unfair and Deceptive Practices
1. CONTEMPORARY ENVIRONMENT • Do-Not-Call Registry
7. Consumer Financial Protection
1. CONTEMPORARY ENVIRONMENT • Consumer Financial Protection Bureau
2. ETHICS • Credit CARD Act
3. BUSINESS ENVIRONMENT • Dodd-Frank Wall Street Reform and Consumer Protection Act
“ I should regret to find that the law was powerless to enforce the most elementary principles of commercial morality.”
—Lord Herschell Reddaway v. Banham (1896)
Introduction to Consumer Protection and Product Safety
Originally, sales transactions in this country were guided by the principle of caveat emptor(“let the buyer beware”). This led to abusive practices by businesses that sold adulterated food products and other unsafe products. In response, federal and state governments have enacted a variety of statutes that regulate the safety of food, drugs, cosmetics, toys, vehicles, and other products. In addition, governments have enacted consumer financial protection laws that protect consumer-debtors in credit transactions. These laws are collectively referred to as consumer protection laws .
consumer protection laws
Federal and state statutes and regulations that promote product safety and prohibit abusive, unfair, and deceptive business practices.
This chapter covers consumer protection and product safety laws.
Food Safety
The safety of food is an important concern in the United States and worldwide. In the United States, the U.S. Department of Agriculture (USDA) is the federal administrative agency that is responsible primarily for regulating meat, poultry, and other food products. The USDA conducts inspections of food-processing and storage facilities. The USDA can initiate legal proceedings against violators.
U.S. Department of Agriculture (USDA)
A federal administrative agency that is responsible for regulating the safety of meat, poultry, and other food products.
The following case involve.
Chapter 18 When looking further into the EU’s Energy Security and.docxtiffanyd4
Chapter 18
: When looking further into the EU’s Energy Security and ICT sustainable urban development, and government policy efforts:
Q2
– What are the five ICT enablers of energy efficiency identified by European strategic research Road map to ICT enabled Energy-Efficiency in Buildings and constructions, (REEB, 2010)?
identify and name those
five ICT enablers
,
provide a brief narrative for each enabler,
note:
Need 400 words. Need references
Please find the attached
.
CHAPTER 17 Investor Protection and E-Securities TransactionsNe.docxtiffanyd4
CHAPTER 17 Investor Protection and E-Securities Transactions
New York Stock Exchange
This is the home of the New York Stock Exchange (NYSE) in New York City. The NYSE, nicknamed the Big Board, is the premier stock exchange in the world. It lists the stocks and securities of approximately 3,000 of the world’s largest companies for trading. The origin of the NYSE dates to 1792, when several stockbrokers met under a buttonwood tree on Wall Street. The NYSE is located at 11 Wall Street, which has been designated a National Historic Landmark. The NYSE is now operated by NYSE Euronext, which was formed when the NYSE merged with the fully electronic stock exchange Euronext.
Learning Objectives
After studying this chapter, you should be able to:
1. Describe the procedure for going public and how securities are registered with the Securities and Exchange Commission (SEC).
2. Describe e-securities transactions and public offerings.
3. Describe the requirements for qualifying for private placement, intrastate, and small offering exemptions from registration.
4. Describe insider trading that violates Section 10(b) of the Securities Exchange Act of 1934.
5. Describe the changes made to securities law by the Jumpstart Our Business Startups (JOBS) Act and its effect on raising capital by small businesses.
Chapter Outline
1. Introduction to Investor Protection and E-Securities Transactions
2. Securities Law
1. LANDMARK LAW • Federal Securities Laws
3. Definition of Security
4. Initial Public Offering: Securities Act of 1933
1. BUSINESS ENVIRONMENT • Facebook’s Initial Public Offering
2. CONTEMPORARY ENVIRONMENT • Jumpstart Our Business Startups (JOBS) Act: Emerging Growth Company
5. E-Securities Transactions
1. DIGITAL LAW • Crowdfunding and Funding Portals
6. Exempt Securities
7. Exempt Transactions
8. Trading in Securities: Securities Exchange Act of 1934
9. Insider Trading
1. Case 17.1 • United States v. Bhagat
2. Case 17.2 • United States v. Kluger
3. ETHICS • Stop Trading on Congressional Knowledge Act
10. Short-Swing Profits
11. State “Blue-Sky” Laws
“The insiders here were not trading on an equal footing with the outside investors.”
—Judge Waterman Securities and Exchange Commission v. Texas Gulf Sulphur Company 401 F.2d 833, 1968 U.S. App. Lexis 5796 (1968)
Introduction to Investor Protection and E-Securities Transactions
Prior to the 1920s and 1930s, the securities markets in this country were not regulated by the federal government. Securities were issued and sold to investors with little, if any, disclosure. Fraud in these transactions was common. To respond to this lack of regulation, in the early 1930s Congress enacted federal securities statutes to regulate the securities markets, including the Securities Act of 1933 and the Securities Exchange Act of 1934. The federal securities statutes were designed to require disclosure of information to investors, provide for the regulation of securities issues and trading, and prevent fraud. Today, many .
Chapter 13 Law, Ethics, and Educational Leadership Making the Con.docxtiffanyd4
Chapter 13 Law, Ethics, and Educational Leadership: Making the Connection
Introduction
This chapter presents examples from the ISLLC standards of the relationship between law and ethics. The chapter also provides examples of how knowledge of law and the application of ethical principles to decision making helps guide school leaders through the sometimes treacherous waters of educational leadership.
Focus Questions
1. How may ethical considerations and legal knowledge guide school leader decision making?
2. Why is it important to consider a balance between these two sometimes competing concepts?
Case Study So Many Detentions, So Little Time
Jefferson Middle School (JMS) was the most racially and culturally diverse of the three middle schools in Riverboat School District, a relatively affluent bedroom community within commuter distance of Capital City. Unfortunately, the culture of Jefferson Middle School was not going well. Over the past 5 years, assistant superintendent Sharon Grey had seen JMS become a school divided by an underlying animosity along racial and socioeconomic lines. This animosity was characterized by numerous clashes between student groups, between teachers and students, between campus administrators and teachers, and between teachers and parents. Sharon finally concluded that JMS was a “mess.”
After much thought and a few sleepless nights, Sharon as part of her job description made the recommendation to the Riverboat school board to not reemploy Jeremy Smith as principal of JMS. Immediately after the board decision, Sharon organized a search committee of teachers, parents, and campus administrators and began the process of finding the right principal for JMS. The committee finally agreed on Charleston Jones. Charleston was a relatively inexperienced campus administrator but had impressed the committee with his instructional leadership knowledge, intelligence, and youthful energy. However, the job of stabilizing JMS was proving to be more of a challenge than anyone had anticipated.
Charleston had instituted a schoolwide discipline plan and had insisted that teachers and school administrators not deviate from the plan. However, he could sense that things were still not right. Animosity among student and parent groups remained just below the surface, ready to erupt at the slightest provocation. Clashes between teachers and students were still relatively frequent. Teachers still blamed one another, school administrators, and the school resource officer for a lack of order in the school. Change was not coming quickly to RMS, and Charleston understood that although school management had improved, several aspects of school culture were less than desirable. Student suspension rates remained high, and parental support was waning. As one of the assistant principals remarked after the umpteenth student referral, “So many detentions, so little time!”
Charleston felt the need to talk. He reached for the phone and made an appointment with.
Chapter 12 presented strategic planning and performance with Int.docxtiffanyd4
Chapter 12 presented strategic planning and performance with Intuit. Define Key Performance Indicators (KPI) and Key Risk Indicators (KRI)? How does an organization come up with these key indicators? Do you know of any top-down indicators? Do you know of any bottom-up indicators? Give some examples of both. In what way does identifying these indicators help an organization? Are there any other key indicators that would help an organization?
Requirements:
Initial posting by Wednesday
Reply to at least 2 other classmates by Sunday (Post a response on different days throughout the week)
Provide a minimum of 2 references on the initial post and one reference any response posts.
Proper APA Format (References & Citations)/No plagiarism
.
ChapterTool KitChapter 7102715Corporate Valuation and Stock Valu.docxtiffanyd4
ChapterTool KitChapter 710/27/15Corporate Valuation and Stock Valuation7-4 Valuing Common Stocks—Introducing the Free Cash Flow (FCF) Valuation ModelData for B&B Corporation (Millions)Constant free cash flow (FCF) =$10Weighted average cost of capital (WACC) =10%Short-term investments =$2Debt =$28Preferred stock =$4Number of shares of common stock =5The first step is to estimate the value of operations, which is the present value of all expected free cash flows. Because the FCF's are expected to be constant, this is a perpetuity. The present value of a perpetuity is the cash flow divided by the cost of capital:Value of operations (Vop) =FCF/WACCValue of operations (Vop) =$100.00millionB&B's total value is the sum of value of operations and the short-term investments: Value of operations$100+ ST investments$2Estimated total intrinsic value$102The next step is to estimate the intrinsic value of equity, which is the remaining total value after accounting for the claims of debtholders and preferred stockholders: Value of operations$100+ ST investments$2Estimated total intrinsic value$102− All debt$28− Preferred stock$4Estimated intrinsic value of equity$70The final step is to estimate the intrinsic common stock price per share, which is the estimated intrinsic value of equity divided by the number of shares of common stock: Value of operations$100+ ST investments$2Estimated total intrinsic value$102− All debt$28− Preferred stock$4Estimated intrinsic value of equity$70÷ Number of shares5Estimated intrinsic stock price =$14.00The figure below shows a summary of the previous calculations.Figure 7-2B&B Corporation's Sources of Value and Claims on Value (Millions of Dollars except Per Share Data)Inputs:Valuation AnalysisConstant free cash flow (FCF) =$10Value of operations$100Weighted average cost of capital (WACC) =10%+ ST investments$2Short-term investments =$2Estimated total intrinsic value$102Debt =$28− All debt$28Preferred stock =$4− Preferred stock$4Number of shares of common stock =5Estimated intrinsic value of equity$70÷ Number of shares5Estimated intrinsic stock price$14.00Data for Pie ChartsShort-term investments =$2Value of operations =$100Total =$102Debt =$28Preferred stock =$4Estimated equity value =$70Total =$1027-5 The Constant Growth Model: Valuation when Expected Free Cash Flow Grows at a Constant RateCase 1: The expected free cash flow at t=1 and the expected constant growth rate after t=1 are known.First expected free cash flow (FCF1) =$105Weighted average cost of capital (WACC) =9%Constant growth rate (gL) =5%When free cash flows are expected to grow at a constant rate, the value of operations is:Value of operations (Vop) =FCF1 / [WACC-gL]Value of operations (Vop) =$2,625Case 2: Constant growth is expected to begin immediately.Most recent free cash flow (FCF0) =$200Weighted average cost of capital (WACC) =12%Constant growth rate (gL) =7%When free cash flows are expected to grow at a constant rate, the value of operations is:.
CHAPTER 12Working with Families and CommunitiesNAEYC Administr.docxtiffanyd4
CHAPTER 12
Working with Families and Communities
NAEYC Administrator Competencies Addressed in This Chapter:
Management Knowledge and Skills
6. Family Support
· Knowledge and application of family systems and different parenting styles
· The ability to implement program practices that support families of diverse cultural, ethnic, linguistic, and socio-economic backgrounds
· The ability to support families as valued partners in the educational process
3. Staff Management and Human Relations
· The ability to relate to staff and board members of diverse racial, cultural, and ethnic backgrounds
7. Marketing and Public Relations
· The ability to promote linkages with local schools
9. Oral and Written Communication
· Knowledge of oral communication techniques, including establishing rapport, preparing the environment, active listening, and voicecontrol
· The ability to communicate ideas effectively in a formal presentation
Early Childhood Knowledge and Skills
6. Family and Community Relationships
· Knowledge of the diversity of family systems, traditional, non-traditional and alternative family structures, family life styles, and thedynamics of family life on the development of young children
· Knowledge of socio-cultural factors influencing contemporary families including the impact of language, religion, poverty, race,technology, and the media
· Knowledge of different community resources, assistance, and support available to children and families
· Knowledge of different strategies to promote reciprocal partnerships between home and center
· Ability to communicate effectively with parents through written and oral communication
· Ability to demonstrate awareness and appreciation of different cultural and familial practices and customs
· Knowledge of child rearing patterns in other countries
10. Professionalism
· Ability to make professional judgments based on the NAEYC “Code of Ethical Conduct and Statement of Commitment”
Learning Outcomes
After studying this chapter, you will be able to:
1. Explain three approaches that programs of early care and education might take to working with families.
2. Identify some of the benefits enjoyed by children, families, and programs when families are engaged with the programs serving theiryoung children.
3. Describe some effective strategies for building trusting relationships with all families.
4. Identify the stakeholder groups and the kinds of expertise that should be represented on programs’ advisory committees and boardsof directors.
Grace’s Experience
The program that Grace directs has been an important part of the neighborhood for more than 20 years. She knows she is benefiting from thegoodwill it has earned over the years. It is respected because of its tradition of high-quality outreach projects, such as the sing-along the childrenpresent at the senior center in the spring. The program’s tradition of community involvement has meant that local businesses have always beenwilling to help out when asked fo.
Chapter 10. Political Socialization The Making of a CitizenLear.docxtiffanyd4
Chapter 10. Political Socialization: The Making of a Citizen
Learning Objectives
· 1Describe the model citizen in democratic theory and explain the concept.
· 2Define socialization and explain the relevance of this concept in the study of politics.
· 3Explain how a disparate population of individuals and groups (families, clans, and tribes) can be forged into a cohesive society.
· 4Demonstrate how socialization affects political behavior and analyze what happens when socialization fails.
· 5Characterize the role of television and the Internet in influencing people’s political beliefs and behavior, and evaluate their impact on the quality of citizenship in contemporary society.
The year is 1932. The Soviet Union is suffering a severe shortage of food, and millions go hungry. Joseph Stalin, leader of the Communist Party and head of the Soviet government, has undertaken a vast reordering of Soviet agriculture that eliminates a whole class of landholders (the kulaks) and collectivizes all farmland. Henceforth, every farm and all farm products belong to the state. To deter theft of what is now considered state property, the Soviet government enacts a law prohibiting individual farmers from appropriating any grain for their own private use. Acting under this law, a young boy reports his father to the authorities for concealing grain. The father is shot for stealing state property. Soon after, the boy is killed by a group of peasants, led by his uncle, who are outraged that he would betray his own father. The government, taking a radically different view of the affair, extols the boy as a patriotic martyr.
Stalin considered the little boy in this story a model citizen, a hero. How citizenship is defined says a lot about a government and the philosophy or ideology that underpins it.
The Good Citizen
Stalin’s celebration of a child’s act of betrayal as heroic points to a distinction Aristotle originally made: The good citizen is defined by laws, regimes, and rulers, but the moral fiber (and universal characteristics) of a good person is fixed, and it transcends the expectations of any particular political regime.*
Good citizenship includes behaving in accordance with the rules, norms, and expectations of our own state and society. Thus, the actual requirements vary widely. A good citizen in Soviet Russia of the 1930s was a person whose first loyalty was to the Communist Party. The test of good citizenship in a totalitarian state is this: Are you willing to subordinate all personal convictions and even family loyalties to the dictates of political authority, and to follow the dictator’s whims no matter where they may lead? In marked contrast are the standards of citizenship in constitutional democracies, which prize and protect freedom of conscience and speech.
Where the requirements of the abstract good citizen—always defined by the state—come into conflict with the moral compass of actual citizens, and where the state seeks to obscure or obliterate t.
Chapters one and twoAnswer the questions in complete paragraphs .docxtiffanyd4
Chapters one and two
Answer the questions in complete paragraphs (at least 3), APA style (citations/references) and make sure to separate/number the answers
1. Explain the differences between Classic Autism and Asperger Disorder according to the DSM-V (Diagnostic Statistical Manual of the American Psychiatric Association).
2. How is ASD identified and diagnosed? Name and describe some of the measurement tools.
3. Describe the characteristics of ASD under each criterion: a) language deficits, b) social differences, c) behavior, and d) motor deficits.
4. List and describe the evidence-base practices for educating ASD children discussed in chapter 2.
5. Describe the differences between a focused intervention and comprehensive treatment models.
6. What are the components of effective instruction for students with ASD?
.
ChapterTool KitChapter 1212912Corporate Valuation and Financial .docxtiffanyd4
ChapterTool KitChapter 1212/9/12Corporate Valuation and Financial Planning12-2 Financial Planning at MicroDrive, Inc.The process used by MicroDrive to forecast the free cash flows from its operating plan is described in the sections below.Setting Up the Model to Forecast OperationsWe begin with MicroDrive's most recent financial statements and selected additional data.Figure 12-1 MicroDrive’s Most Recent Financial Statements (Millions, Except for Per Share Data)INCOME STATEMENTSBALANCE SHEETS20122013Assets20122013Net sales$ 4,760$ 5,000Cash$ 60$ 50COGS (excl. depr.)3,5603,800ST Investments40-Depreciation170200Accounts receivable380500Other operating expenses480500Inventories8201,000EBIT$ 550$ 500Total CA$ 1,300$ 1,550Interest expense100120Net PP&E1,7002,000Pre-tax earnings$ 450$ 380Total assets$ 3,000$ 3,550Taxes (40%)180152NI before pref. div.$ 270$ 228Liabilities and equityPreferred div.88Accounts payable$ 190$ 200Net income$ 262$ 220Accruals280300Notes payable130280Other DataTotal CL$ 600$ 780Common dividends$48$50Long-term bonds1,0001,200Addition to RE$214$170Total liabilities$ 1,600$ 1,980Tax rate40%40%Preferred stock100100Shares of common stock5050Common stock500500Earnings per share$5.24$4.40Retained earnings800970Dividends per share$0.96$1.00Total common equity$ 1,300$ 1,470Price per share$40.00$27.00Total liabs. & equity$ 3,000$ 3,550The figure below shows all the inputs required to project the financial statements for the scenario that has been selected with the Scenario Manager: Data, What-If Analysis, Scenario Manager. There are two scenarios. The first is named Status Quo because all operating ratios except the sales growth rate are assumed to remain unchanged. The initial sales growth rate was chosen by MicroDrive's managers based on the existing product lines. The growth rate declines over time until it eventually levels off at a sustainable rate. The other scenario is named Final because it is the set of inputs chosen by MicroDrive's management team.Section 1 shows the inputs required to estimate the items in an operating plan. For each of these inputs, Section 1 shows the industry averages, the actual values for the past two years for MicroDrive, and the forecasted values for the next five years. The managers assumed the inputs for future years (except the sales growth rate) would be equal to the inputs in the first projected year.MicroDrive's managers assume that sales will eventually level off at a sustaniable constant rate.Sections 2 and 3 show the data required to estimate the weighted average cost of capital. Section 4 shows the forecasted growth rate in dividends.Note: These inputs are linked throughout the model. If you want to change an input, do it here and not other places in the model.Figure 12-2MicroDrive's Forecast: Inputs for the Selected ScenarioStatus QuoIndustryMicroDriveMicroDriveInputsActualActualForecast1. Operating Ratios2013201220132014201520162017201.
Chapters 4-6 Preparing Written MessagesPrepari.docxtiffanyd4
Chapters 4-6: Preparing Written Messages
Preparing Written Messages
Lesson Outline
Seven Steps to Preparing Written Messages
Effective Sentences and Coherent Paragraphs
Revise to Grab Your Audience’s Attention
Improve Readability
Proofread and Revise
Seven Steps to Preparing
Written Messages
Seven Preparation Steps
Step 1: Consider Contextual Forces
Step 2: Determine Purpose, Channel, and Medium
Step 3: Envision Audience
Step 4: Adapt Message to Audience Needs and Concerns
Step 5: Organize the Message
Step 6: Prepare First Draft
Step 7: Revise, Edit, and Proofread
Effective Sentences and
Coherent Paragraphs
Step 6: Prepare the First Draft
Proceed Deductively or Inductively
Know Logical Sequence of Minor Points
Write rapidly with Intent to Rewrite
Use Active More Than Passive Voice
Craft Powerful Sentences
Rely on Active Voice—Subject Doer of Action
(Passive—Subject Receiver of Action Sentence Is Less Emphatic)
Passive Voice Uses
Conceal the Doer/Avoid Finger Pointing
Doer Is Unknown
Place More Emphasis on What Was Done
(Receiver of Action)
5
Emphasize Important Ideas
Techniques
Sentence Structure—place important ideas in simple sentences/place in independent clauses (emphasis)
Repetition—repeat a word in a sentence
Labeling Words—use words that signal important
Position—position it first or last in a clause, sentence, paragraph, or presentation
Space and Format—use extraordinary amount of space for important items or use headings
Develop Coherent Paragraphs
Develop Deductive/Inductive Paragraphs Consistently
Link Ideas to Achieve Coherence
Keep Paragraphs Unified
Vary Sentence and Paragraph Length
Position Topic Sentences and
Link Ideas
Deductive—topic sentence precedes details
Inductive—topic sentence follows details
Link Ideas to Achieve Coherence (Cohesion)
Repeat Word from Preceding Sentence
Use a Pronoun for a Noun in Preceding Sentence
Use Connecting Words (e.g., Conjunctive Adverbs)
Link Paragraphs by Using Transition Words
Use Transition Sentences before Headings,
But Not Subheadings
Paragraph Unity
Keep Paragraphs Unified—support must be focused on topic sentences
Ensure Paragraphs Cover Topic Sentence, But Do Not Write Extraneous Materials
Arrange Paragraphs in a Logical and Systematic Sequence
Vary Sentence and
Paragraph Length
Vary Sentence Length (Average—Short)
Vary Sentence Structure (Sentence Variety)
Vary Paragraph Length (Average—Short
8-10 Lines)
Changes in Tense, Voice, and Person in Paragraphs Are Discouraged
Revise to Grab
Reader’s Attention
Cultivate a Frame of Mind (Mind-set) for Revising and Proofreading
Have Your Revising/Editing Space/Room
View from Audience Perspective (You Attitude)
Revise until No More Changes Would Improve the Document
Be Willing to Allow Others to Make Suggestions (Writer’s Pride of Ownership?)
Ensure Error-Free Messages
Use Visual Enhancements for More Readability
Add Only When They Aid Comprehension
Create an A.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
Digital Artifact 2 - Investigating Pavilion Designs
CHAPTER 9Time Value of MoneyFuture valuePresent valueAnn.docx
1. CHAPTER 9
Time Value of Money
Future value
Present value
Annuities
Rates of return
Amortization
9-‹#›
1
Time lines
Show the timing of cash flows.
Tick marks occur at the end of periods, so Time 0 is today;
Time 1 is the end of the first period (year, month, etc.) or the
beginning of the second period.
CF0
CF1
CF3
CF2
0
3. $100 lump sum due in 2 years
9-‹#›
3
Future Value of Money
If you deposit $1,000 today at 10%, how much will you have
after 15 years?
Interest($) = Principal ∙ Interest Rate(%)
Simple Interest
The original principal stays the same.
There is no interest on interest. The interest is only on the
original principal.
Compound Interest
The principal changes through time.
There is “interest on interest”. The interest is on the new
principal.
9-‹#›
5. V3 = V2 + Interest = V2 + V2 ∙ I = V2(1 + I)
V2 = V1(1 + I) = V0(1 + I)(1 + I) = V0(1 + I)2
V3 = V2(1 + I) = V0(1 + I)2(1 + I) = V0(1 + I)3
Vn = V0 (1 + I)n
FVn = PV(1 + I)n = PV∙FVIF
V2 = V1 + Interest = V1 + (V0 + Interest) ∙ I
9-‹#›
Example
What is the future value of $20 invested for 2 years at 10%?
Simple: FV = PV(1+nI)
= 20(1+2I) = 20(1+0.2) = $24
Compound: FV = PV(1+I)n
= 20(1+I)2 = 20(1+0.1)2 = $24.2
What is the future value of $20 invested for 100 years at 10%?
Simple: FV = 20(1+ ) =
Compound : FV = 20(1.1)100 = 275,612.25
9-‹#›
The Power of Compounding
The Value of Manhattan
In 1626, the land was bought from American Indians at $24.
6. In 2018, value = $24(1+I)392
9-‹#›
Solving for FV:
The formula method
Solve the general FV equation:
FVN = PV∙(1 + I)N = PV ∙ FVIF
FV15 = PV∙(1 + I)15 = $1,000∙(1.10)15 = $4,177.25
= $1,000∙4.177 = $4,177
(Table A)
9-‹#›
Present Value of Money
If you want to have $4,177.25 after 15 years, how much do you
have to deposit today at 10%?
9-‹#›
7. PV = ?
4,177.25
Present Value of Money
Finding the PV of a cash flow or series of cash flows is called
discounting (the reverse of compounding).
0
1
2 …
15
10%
9-‹#›
13
Solving for PV:
The formula method
Solve the general FV equation for PV:
PV = = ∙
= FVN ∙ PVIF
PV = = = $4,177.25 ∙
= $4,177.25∙0.239
(Table C)
= $998.36, but $4,177.25∙0.2394 = $1,000
8. 9-‹#›
14
Examples
If you want $10,000 after 10 years, how much do you have to
deposit today at 5%?
If you want $100,000 someday for a world tour, how long will it
take at 7% if you deposit $10,000 today?
If you want $50,000 in 10 years, at what rate do you have to
invest your money if you have $10,000 today?
9-‹#›
9-‹#›
9. 9-‹#›
9-‹#›
9-‹#›
Calculation
You deposit $1000 today at 6%. After one year (t=1), you
withdraw $300, after two years (t=2), you deposit $500 more,
and no deposit or withdrawal after that, then how much will you
have in year 5 (t=5) ?
9-‹#›
Answer
Step by step solution
0 1 2 5
$1,000 -$300 $500 ?
1000 PV, 6 I/Y, 1 N, CPT FV =>1060
1060
10. ( )PV, 6 I/Y, ( )N, FV => ( )
( ) + ( ) = ( )
( ) PV, 6 I/Y, ( ) N, FV => ( )
9-‹#›
Annuity
A series of cash flows of the same amount with fixed intervals
for a specified number of periods.
0 1 2 3 4
$20 $20 $30 $20
$20 $30 $40 $50
$20 $20 $0 $20
$0 $0 $20 $20
$20 $30 $20 $30
9-‹#›
FV of Annuity
100
100
100
12. = 100[(1+I)2 + (1+I) + 1]
= 100∙
For n periods,
FVA = PMT∙
= PMT∙FVAIF
9-‹#›
PV of Annuity
100
100
100
0
1
2
3
I%
9-‹#›
PV of Annuity
13. PVA = + +
= 100 [ + + ]
= 100
For n periods,
PVA = PMT
= PMT∙PVAIF
9-‹#›
9-‹#›
9-‹#›
9-‹#›
Examples
If you deposit $3,000 a year for 10 years at 7%, how much will
14. you have after 10 years?
If you want to receive $5o,000 per year for 20 years, how much
do you have to deposit today at 5%?
9-‹#›
More examples
You need $100,000 in year 15 to start your own business. If
your bank’s interest rate is 6%, how much do you have to
deposit each year to get $100,000?
You need $100,000 for a world tour. If you deposit $10,000
each year, how long will it take for you to accumulate $100,000
at 7%?
9-‹#›
9-‹#›
Investment Choice
You have $10,000 to invest. There are two choices for your
15. investment.
Choice A: Buying an annuity at $10,000 and receiving $1,000
for 20 years.
Choice B: Depositing $10,000 in a bank that pays 8% interest
rate.
9-‹#›
9-‹#›
Harder Problem
You need to accumulate $11,000. To do so, you plan to deposit
$1,350 per year in a bank that pays 6% interest. Your last
deposit will be less than $1,350 if less is needed to round out to
$11,000.
A. How many years will it take to reach your goal?
B. How large will the last deposit be for you to have exactly
$11,000 in your account?
9-‹#›
16. 9-‹#›
Answer
Two ways
A: The FV at year 6 will be $9,416.68, and the money will grow
in the account for a year to $9,981.68.
B: The FV at year 7 will be $11,331.68.
9-‹#›
9-‹#›
What is the difference between an ordinary annuity and an
annuity due?
Ordinary Annuity
PMT
PMT
PMT
18. PVADUE = PVA(1+I)
9-‹#›
PV of Annuity Due
What is the PV of 3-year annuity due of $100 payments at 10%?
Now, $100 payments occur at the beginning of each period.
PVAdue= PVA (1+I) = $248.69(1.1) =$273.55.
Alternatively, set calculator to “BEGIN” mode and solve for the
FV of the annuity:
9-‹#›
FV of Annuity Due
What is the FV of 3-year annuity due of $100 payments at 10%?
Now, $100 payments occur at the beginning of each period.
FVAdue= FVA (1+I) = $331(1.1) = $364.10.
Alternatively, set calculator to “BEGIN” mode and solve for the
FV of the annuity:
19. 9-‹#›
9-‹#›
What is the (future) value of this annuity at t = 1? At t = 2?
100(1+I) + 100 +
9-‹#›
9-‹#›
9-‹#›
20. 9-‹#›
Question
If you can receive $50,000 per year forever, how much are you
willing to pay for that?
9-‹#›
Perpetuity
Perpetuity
PV =
If I = 10%, PV = = $0.5M
If I= 5%, PV = = $1M
9-‹#›
52
Growing Perpetuity
If the payments grow at a constant rate, g, it is a growing
21. perpetuity.
PV =
=
Example: If I = 10%, g = 5%,
PMT0 = $50,000,
PV = = $1.05M
9-‹#›
The Power of Compound Interest
A 20-year-old student wants to save $3 a day for her retirement.
Every day she places $3 in a drawer. At the end of the year, she
invests the accumulated savings ($1,095) in a brokerage account
with an expected annual return of 12%.
How much money will she have when she is 65 years old?
9-‹#›
Solving for FV:
If she begins saving today, how much will she have when she is
65?
If she sticks to her plan, she will have $( ) when she
22. is 65.
( ) N, 12 I/YR, -1095 PMT, FV =>
( )
9-‹#›
Solving for FV:
If you don’t start saving until you are 40 years old, how much
will you have at 65?
If a 40-year-old investor begins saving today, and sticks to the
plan, he or she will have $146,000.59 at age 65. This is $1.3
million less than if starting at age 20.
Lesson: It pays to start saving early.
25 N, 12 I/Y, 1095 PMT,
FV =› 146,000.59
9-‹#›
Solving for PMT:
How much must the 40-year old deposit annually to catch the
20-year old?
To find the required annual contribution, enter the number of
years until retirement and the final goal of $1,487,261.89, and
solve for PMT.
25 N, 12 I/Y, 1,487,261.89 FV,
PMT = › 11,154.42
24. 90.91
247.93
225.39
-34.15
530.08 = PV
9-‹#›
59
Solving for PV:
Uneven cash flow stream
Input cash flows in the calculator’s “CF” register:
CF0 = 0
C01 = 100
F01 = 1
C02 = 300
F02 = 2
C03 = -50
Press NPV button, then enter I = 10, and hit CPT=> $530.087.
(Here NPV = PV.)
9-‹#›
25. NPV (Net Present Value)
NPV is calculated net of costs.
If your project’s PV of cash inflows is greater than the PV of
cash outflows, the project will enhance your company’s
profitability.
In chapter 9, generally there is no cost at time 0, so the NPVs
are positive, but in chapter 12, when we evaluate projects, the
NPVs can be negative.
Example: 0 1 2 3 (I = 10%)
-1000 300 300 500
9-‹#›
9-‹#›
9-‹#›
26. 9-‹#›
CHAPTER 9
Time Value of Money
Future value
Present value
Annuities
Rates of return
Amortization
9-‹#›
1
Time lines
Show the timing of cash flows.
Tick marks occur at the end of periods, so Time 0 is today;
Time 1 is the end of the first period (year, month, etc.) or the
beginning of the second period.
CF0
CF1
CF3
CF2
28. $100 lump sum due in 2 years
9-‹#›
3
Future Value of Money
If you deposit $1,000 today at 10%, how much will you have
after 15 years?
Interest($) = Principal ∙ Interest Rate(%)
Simple Interest
The original principal stays the same.
There is no interest on interest. The interest is only on the
original principal.
Compound Interest
The principal changes through time.
There is “interest on interest”. The interest is on the new
principal.
9-‹#›
30. V2 = V1 + Interest = V1 + V1 ∙ I = V1(1 + I)
V3 = V2 + Interest = V2 + V2 ∙ I = V2(1 + I)
V2 = V1(1 + I) = V0(1 + I)(1 + I) = V0(1 + I)2
V3 = V2(1 + I) = V0(1 + I)2(1 + I) = V0(1 + I)3
Vn = V0 (1 + I)n
FVn = PV(1 + I)n = PV∙FVIF
V2 = V1 + Interest = V1 + (V0 + Interest) ∙ I
9-‹#›
Example
What is the future value of $20 invested for 2 years at 10%?
Simple: FV = PV(1+nI)
= 20(1+2I) = 20(1+0.2) = $24
Compound: FV = PV(1+I)n
= 20(1+I)2 = 20(1+0.1)2 = $24.2
What is the future value of $20 invested for 100 years at 10%?
Simple: FV = 20(1+ ) =
Compound : FV = 20(1.1)100 = 275,612.25
9-‹#›
The Power of Compounding
The Value of Manhattan
31. In 1626, the land was bought from American Indians at $24.
In 2018, value = $24(1+I)392
9-‹#›
Solving for FV:
The formula method
Solve the general FV equation:
FVN = PV∙(1 + I)N = PV ∙ FVIF
FV15 = PV∙(1 + I)15 = $1,000∙(1.10)15 = $4,177.25
= $1,000∙4.177 = $4,177
(Table A)
9-‹#›
Present Value of Money
If you want to have $4,177.25 after 15 years, how much do you
have to deposit today at 10%?
9-‹#›
32. PV = ?
4,177.25
Present Value of Money
Finding the PV of a cash flow or series of cash flows is called
discounting (the reverse of compounding).
0
1
2 …
15
10%
9-‹#›
13
Solving for PV:
The formula method
Solve the general FV equation for PV:
PV = = ∙
= FVN ∙ PVIF
PV = = = $4,177.25 ∙
= $4,177.25∙0.239
(Table C)
= $998.36, but $4,177.25∙0.2394 = $1,000
33. 9-‹#›
14
Examples
If you want $10,000 after 10 years, how much do you have to
deposit today at 5%?
If you want $100,000 someday for a world tour, how long will it
take at 7% if you deposit $10,000 today?
If you want $50,000 in 10 years, at what rate do you have to
invest your money if you have $10,000 today?
9-‹#›
9-‹#›
34. 9-‹#›
9-‹#›
9-‹#›
Calculation
You deposit $1000 today at 6%. After one year (t=1), you
withdraw $300, after two years (t=2), you deposit $500 more,
and no deposit or withdrawal after that, then how much will you
have in year 5 (t=5) ?
9-‹#›
Answer
Step by step solution
0 1 2 5
$1,000 -$300 $500 ?
1000 PV, 6 I/Y, 1 N, CPT FV =>1060
35. 1060
( )PV, 6 I/Y, ( )N, FV => ( )
( ) + ( ) = ( )
( ) PV, 6 I/Y, ( ) N, FV => ( )
9-‹#›
Annuity
A series of cash flows of the same amount with fixed intervals
for a specified number of periods.
0 1 2 3 4
$20 $20 $30 $20
$20 $30 $40 $50
$20 $20 $0 $20
$0 $0 $20 $20
$20 $30 $20 $30
9-‹#›
FV of Annuity
100
100
38. PV of Annuity
PVA = + +
= 100 [ + + ]
= 100
For n periods,
PVA = PMT
= PMT∙PVAIF
9-‹#›
9-‹#›
9-‹#›
9-‹#›
Examples
39. If you deposit $3,000 a year for 10 years at 7%, how much will
you have after 10 years?
If you want to receive $5o,000 per year for 20 years, how much
do you have to deposit today at 5%?
9-‹#›
More examples
You need $100,000 in year 15 to start your own business. If
your bank’s interest rate is 6%, how much do you have to
deposit each year to get $100,000?
You need $100,000 for a world tour. If you deposit $10,000
each year, how long will it take for you to accumulate $100,000
at 7%?
9-‹#›
9-‹#›
Investment Choice
40. You have $10,000 to invest. There are two choices for your
investment.
Choice A: Buying an annuity at $10,000 and receiving $1,000
for 20 years.
Choice B: Depositing $10,000 in a bank that pays 8% interest
rate.
9-‹#›
9-‹#›
Harder Problem
You need to accumulate $11,000. To do so, you plan to deposit
$1,350 per year in a bank that pays 6% interest. Your last
deposit will be less than $1,350 if less is needed to round out to
$11,000.
A. How many years will it take to reach your goal?
B. How large will the last deposit be for you to have exactly
$11,000 in your account?
9-‹#›
41. 9-‹#›
Answer
Two ways
A: The FV at year 6 will be $9,416.68, and the money will grow
in the account for a year to $9,981.68.
B: The FV at year 7 will be $11,331.68.
9-‹#›
9-‹#›
What is the difference between an ordinary annuity and an
annuity due?
Ordinary Annuity
PMT
PMT
43. PVADUE = PVA(1+I)
9-‹#›
PV of Annuity Due
What is the PV of 3-year annuity due of $100 payments at 10%?
Now, $100 payments occur at the beginning of each period.
PVAdue= PVA (1+I) = $248.69(1.1) =$273.55.
Alternatively, set calculator to “BEGIN” mode and solve for the
FV of the annuity:
9-‹#›
FV of Annuity Due
What is the FV of 3-year annuity due of $100 payments at 10%?
Now, $100 payments occur at the beginning of each period.
FVAdue= FVA (1+I) = $331(1.1) = $364.10.
Alternatively, set calculator to “BEGIN” mode and solve for the
FV of the annuity:
44. 9-‹#›
What is the (future) value of this annuity at t = 1? At t = 2?
100(1+I) + 100 +
9-‹#›
9-‹#›
9-‹#›
Question
If you can receive $50,000 per year forever, how much are you
willing to pay for that?
45. 9-‹#›
Perpetuity
Perpetuity
PV =
If I = 10%, PV = = $0.5M
If I= 5%, PV = = $1M
9-‹#›
50
Growing Perpetuity
If the payments grow at a constant rate, g, it is a growing
perpetuity.
PV =
=
Example: If I = 10%, g = 5%,
PMT0 = $50,000,
PV = = $1.05M
9-‹#›
46. The Power of Compound Interest
A 20-year-old student wants to save $3 a day for her retirement.
Every day she places $3 in a drawer. At the end of the year, she
invests the accumulated savings ($1,095) in a brokerage account
with an expected annual return of 12%.
How much money will she have when she is 65 years old?
9-‹#›
Solving for FV:
If she begins saving today, how much will she have when she is
65?
If she sticks to her plan, she will have $( ) when she
is 65.
( ) N, 12 I/YR, -1095 PMT, FV =>
( )
9-‹#›
Solving for FV:
If you don’t start saving until you are 40 years old, how much
will you have at 65?
47. If a 40-year-old investor begins saving today, and sticks to the
plan, he or she will have $146,000.59 at age 65. This is $1.3
million less than if starting at age 20.
Lesson: It pays to start saving early.
25 N, 12 I/Y, 1095 PMT,
FV =› 146,000.59
9-‹#›
Solving for PMT:
How much must the 40-year old deposit annually to catch the
20-year old?
To find the required annual contribution, enter the number of
years until retirement and the final goal of $1,487,261.89, and
solve for PMT.
25 N, 12 I/Y, 1,487,261.89 FV,
PMT = › 11,154.42
9-‹#›
What is the PV of this uneven cash flow stream?
0
100
1
49. Input cash flows in the calculator’s “CF” register:
CF0 = 0
C01 = 100
F01 = 1
C02 = 300
F02 = 2
C03 = -50
Press NPV button, then enter I = 10, and hit CPT=> $530.087.
(Here NPV = PV.)
9-‹#›
NPV (Net Present Value)
NPV is calculated net of costs.
If your project’s PV of cash inflows is greater than the PV of
cash outflows, the project will enhance your company’s
profitability.
In chapter 9, generally there is no cost at time 0, so the NPVs
are positive, but in chapter 12, when we evaluate projects, the
NPVs can be negative.
Example: 0 1 2 3 (I = 10%)
-1000 300 300 500
9-‹#›
CHAPTER 9
50. Time Value of Money
Future value
Present value
Annuities
Rates of return
Amortization
9-‹#›
1
Time lines
Show the timing of cash flows.
Tick marks occur at the end of periods, so Time 0 is today;
Time 1 is the end of the first period (year, month, etc.) or the
beginning of the second period.
CF0
CF1
CF3
CF2
0
1
2
3
I%
52. 9-‹#›
3
Future Value of Money
If you deposit $1,000 today at 10%, how much will you have
after 15 years?
Interest($) = Principal ∙ Interest Rate(%)
Simple Interest
The original principal stays the same.
There is no interest on interest. The interest is only on the
original principal.
Compound Interest
The principal changes through time.
There is “interest on interest”. The interest is on the new
principal.
9-‹#›
54. Vn = V0 (1 + I)n
FVn = PV(1 + I)n = PV∙FVIF
V2 = V1 + Interest = V1 + (V0 + Interest) ∙ I
9-‹#›
Example
What is the future value of $20 invested for 2 years at 10%?
Simple: FV = PV(1+nI)
= 20(1+2I) = 20(1+0.2) = $24
Compound: FV = PV(1+I)n
= 20(1+I)2 = 20(1+0.1)2 = $24.2
What is the future value of $20 invested for 100 years at 10%?
Simple: FV = 20(1+ ) =
Compound : FV = 20(1.1)100 = 275,612.25
9-‹#›
The Power of Compounding
The Value of Manhattan
In 1626, the land was bought from American Indians at $24.
In 2018, value = $24(1+I)392
55. 9-‹#›
Solving for FV:
The formula method
Solve the general FV equation:
FVN = PV∙(1 + I)N = PV ∙ FVIF
FV15 = PV∙(1 + I)15 = $1,000∙(1.10)15 = $4,177.25
= $1,000∙4.177 = $4,177
(Table A)
9-‹#›
Present Value of Money
If you want to have $4,177.25 after 15 years, how much do you
have to deposit today at 10%?
9-‹#›
PV = ?
4,177.25
Present Value of Money
Finding the PV of a cash flow or series of cash flows is called
56. discounting (the reverse of compounding).
0
1
2 …
15
10%
9-‹#›
13
Solving for PV:
The formula method
Solve the general FV equation for PV:
PV = = ∙
= FVN ∙ PVIF
PV = = = $4,177.25 ∙
= $4,177.25∙0.239
(Table C)
= $998.36, but $4,177.25∙0.2394 = $1,000
57. 9-‹#›
14
Examples
If you want $10,000 after 10 years, how much do you have to
deposit today at 5%?
If you want $100,000 someday for a world tour, how long will it
take at 7% if you deposit $10,000 today?
If you want $50,000 in 10 years, at what rate do you have to
invest your money if you have $10,000 today?
9-‹#›
9-‹#›
9-‹#›
58. 9-‹#›
9-‹#›
Calculation
You deposit $1000 today at 6%. After one year (t=1), you
withdraw $300, after two years (t=2), you deposit $500 more,
and no deposit or withdrawal after that, then how much will you
have in year 5 (t=5) ?
9-‹#›
Answer
Step by step solution
0 1 2 5
$1,000 -$300 $500 ?
1000 PV, 6 I/Y, 1 N, CPT FV =>1060
1060
( )PV, 6 I/Y, ( )N, FV => ( )
( ) + ( ) = ( )
( ) PV, 6 I/Y, ( ) N, FV => ( )
59. 9-‹#›
Annuity
A series of cash flows of the same amount with fixed intervals
for a specified number of periods.
0 1 2 3 4
$20 $20 $30 $20
$20 $30 $40 $50
$20 $20 $0 $20
$0 $0 $20 $20
$20 $30 $20 $30
9-‹#›
FV of Annuity
100
100
100
0
1
2
3
61. FVA = PMT∙
= PMT∙FVAIF
9-‹#›
PV of Annuity
100
100
100
0
1
2
3
I%
9-‹#›
PV of Annuity
PVA = + +
= 100 [ + + ]
= 100
For n periods,
62. PVA = PMT
= PMT∙PVAIF
9-‹#›
Examples
If you deposit $3,000 a year for 10 years at 7%, how much will
you have after 10 years?
If you want to receive $5o,000 per year for 20 years, how much
do you have to deposit today at 5%?
9-‹#›
More examples
You need $100,000 in year 15 to start your own business. If
your bank’s interest rate is 6%, how much do you have to
deposit each year to get $100,000?
You need $100,000 for a world tour. If you deposit $10,000
each year, how long will it take for you to accumulate $100,000
at 7%?
63. 9-‹#›
Investment Choice
You have $10,000 to invest. There are two choices for your
investment.
Choice A: Buying an annuity at $10,000 and receiving $1,000
for 20 years.
Choice B: Depositing $10,000 in a bank that pays 8% interest
rate.
9-‹#›
Harder Problem
You need to accumulate $11,000. To do so, you plan to deposit
$1,350 per year in a bank that pays 6% interest. Your last
deposit will be less than $1,350 if less is needed to round out to
$11,000.
A. How many years will it take to reach your goal?
B. How large will the last deposit be for you to have exactly
$11,000 in your account?
9-‹#›
Answer
Two ways
A: The FV at year 6 will be $9,416.68, and the money will grow
in the account for a year to $9,981.68.
64. B: The FV at year 7 will be $11,331.68.
9-‹#›
What is the difference between an ordinary annuity and an
annuity due?
Ordinary Annuity
PMT
PMT
PMT
0
1
2
3
i%
PMT
PMT
0
1
2
3
65. i%
PMT
Annuity Due
9-‹#›
35
Ordinary Annuity and Annuity Due
FVADUE = FVA(1+I)
PVADUE = PVA(1+I)
9-‹#›
PV of Annuity Due
What is the PV of 3-year annuity due of $100 payments at 10%?
Now, $100 payments occur at the beginning of each period.
PVAdue= PVA (1+I) = $248.69(1.1) =$273.55.
Alternatively, set calculator to “BEGIN” mode and solve for the
FV of the annuity:
66. 9-‹#›
FV of Annuity Due
What is the FV of 3-year annuity due of $100 payments at 10%?
Now, $100 payments occur at the beginning of each period.
FVAdue= FVA (1+I) = $331(1.1) = $364.10.
Alternatively, set calculator to “BEGIN” mode and solve for the
FV of the annuity:
9-‹#›
What is the (future) value of this annuity at t = 1? At t = 2?
100(1+I) + 100 +
9-‹#›
Question
If you can receive $50,000 per year forever, how much are you
willing to pay for that?
67. 9-‹#›
Perpetuity
Perpetuity
PV =
If I = 10%, PV = = $0.5M
If I= 5%, PV = = $1M
9-‹#›
41
Growing Perpetuity
If the payments grow at a constant rate, g, it is a growing
perpetuity.
PV =
=
Example: If I = 10%, g = 5%,
PMT0 = $50,000,
PV = = $1.05M
68. 9-‹#›
The Power of Compound Interest
A 20-year-old student wants to save $3 a day for her retirement.
Every day she places $3 in a drawer. At the end of the year, she
invests the accumulated savings ($1,095) in a brokerage account
with an expected annual return of 12%.
How much money will she have when she is 65 years old?
9-‹#›
Solving for FV:
If she begins saving today, how much will she have when she is
65?
If she sticks to her plan, she will have $( ) when she
is 65.
( ) N, 12 I/YR, -1095 PMT, FV =>
( )
9-‹#›
Solving for FV:
69. If you don’t start saving until you are 40 years old, how much
will you have at 65?
If a 40-year-old investor begins saving today, and sticks to the
plan, he or she will have $146,000.59 at age 65. This is $1.3
million less than if starting at age 20.
Lesson: It pays to start saving early.
25 N, 12 I/Y, 1095 PMT,
FV =› 146,000.59
9-‹#›
Solving for PMT:
How much must the 40-year old deposit annually to catch the
20-year old?
To find the required annual contribution, enter the number of
years until retirement and the final goal of $1,487,261.89, and
solve for PMT.
25 N, 12 I/Y, 1,487,261.89 FV,
PMT = › 11,154.42
9-‹#›
What is the PV of this uneven cash flow stream?
0
100
71. Solving for PV:
Uneven cash flow stream
Input cash flows in the calculator’s “CF” register:
CF0 = 0
C01 = 100
F01 = 1
C02 = 300
F02 = 2
C03 = -50
Press NPV button, then enter I = 10, and hit CPT=> $530.087.
(Here NPV = PV.)
9-‹#›
NPV (Net Present Value)
NPV is calculated net of costs.
If your project’s PV of cash inflows is greater than the PV of
cash outflows, the project will enhance your company’s
profitability.
In chapter 9, generally there is no cost at time 0, so the NPVs
are positive, but in chapter 12, when we evaluate projects, the
NPVs can be negative.
Example: 0 1 2 3 (I = 10%)
-1000 300 300 500
9-‹#›
72. 9’-‹#›
Classifications of interest rates
Nominal rate (INOM) – also called the quoted or stated rate.
An annual rate that ignores compounding effects.
INOM is stated in contracts. Periods must also be given, e.g.
8% Quarterly or 8% Daily interest.
Periodic rate (IPER) – amount of interest charged each period,
e.g. monthly or quarterly.
IPER = INOM / M, where M is the number of compounding
periods per year. M = 4 for quarterly and M = 12 for monthly
compounding.
9’-‹#›
2
Compounding More than Once per Year
Annual Compounding
0 8% 1
|______________________|
Semiannual Compounding
0 4% 1 4% 2
|__________|___________|
Quarterly Compounding
73. 0 2% 1 2% 2 2% 3 2% 4
|_____|_____|_____|_____|
9’-‹#›
Effective Annual Rate (EAR)
Effective (or equivalent) annual rate (EAR = EFF%): The
annual rate of interest actually being earned, accounting for
compounding.
EFF% for 8% semiannual investment
EFF% = ( 1 + )M - 1
= (1 + )2 – 1 = 8.16%
Should be indifferent between receiving 8.16% annual interest
and receiving 8% interest, compounded semiannually. EAR is
used to compare investment returns.
9’-‹#›
4
9’-‹#›
74. Calculator
Use ICONV key
NOM = INOM
EFF = EAR
C/Y = # of compounding per year
9’-‹#›
What is the FV of $100 after 3 years under 10% semiannual
compounding? Quarterly compounding?
9’-‹#›
7
calculator
10% semi-annual compounding
5 I/Y, 100 PV, 6 N, FV => 134.01
Quarterly compounding
2.5 I/Y, 100 PV, 12 N, FV => 134.49
75. 9’-‹#›
What is the future value of an annuity with $100 monthly
payments at 7% after 5 years?
FV = PMT
= 100
OR,
100 PMT
( ) I/Y
( ) N
FV =
9’-‹#›
GM Incentives
You need $12,000 loan to buy a car.
There are two financing options to choose:
A: 2.9% financing with a 36 month loan
B: A rebate of $1,000 is available and the remaining $11,000 is
to be financed at 10% for 36 months.
Which option would you choose?
9’-‹#›
Quarterly Compounding
A. If you deposit $1,000 in a bank that pays 8% quarterly
compounding, what is the rate of return if you withdraw after 10
76. months?
B. How much in dollars will you get if you withdraw after 10
months?
9’-‹#›
9’-‹#›
9’-‹#›
What’s the FV of a 3-year $100 annuity, if the quoted interest
rate is 10%, compounded semiannually?
Payments occur annually, but compounding occurs every 6
months.
Cannot use normal annuity valuation techniques.
77. 9’-‹#›
Method 1:
Compound each cash flow
FV3 = $100(1.05)4 + $100(1.05)2 + $100
FV3 = $331.80
9’-‹#›
Method 2:
Financial calculator
Find the EAR and treat as an annuity.
EAR = ( 1 + )2 – 1 = 10.25%.
10.25 I/Y, 3 N, -100 PMT, ---
9’-‹#›
Calculator 2
78. 1 P/Y, 2 C/Y, 100 PMT, 3 N, 10 I/Y,
FV => 331.8006 => 331.80
9’-‹#›
Find the PV of this 3-year ordinary annuity.
Could solve by discounting each cash flow, or …
Use the EAR and treat as an annuity to solve for PV.
10.25 I/Y, 3 N, 100 PMT, --
9’-‹#›
Calculator 2
1 P/Y, 2 C/Y, 100 PMT, 3 N, 10 I/Y,
PV => 247.5947 => 247.59
9’-‹#›
P/Y, C/Y
What is the future value of a three-year annuity with quarterly
payments of $50 each at 7%, monthly compounding?
79. 9’-‹#›
Loan amortization
Amortization tables are widely used for home mortgages, auto
loans, business loans, retirement plans, etc.
Financial calculators and spreadsheets are great for setting up
amortization tables.
EXAMPLE: Construct an one-year amortization table for a
$100,000, 8%, semiannual payment, 30-year loan.
9’-‹#›
21
Step 1:
Find the required annual payment
All input information is already given.
60 N, 4 I/Y, 100,000 PV,
PMT = 4,420.18
9’-‹#›
80. 22
Step 2:
Find the interest paid in Period 1
The borrower will owe interest upon the initial balance at the
end of the first period. Interest to be paid in the first period can
be found by multiplying the beginning balance by the periodic
interest rate.
INTt = Beg balt (I)
INT1 = $100,000 (0.04) = $4,000
9’-‹#›
23
Step 3:
Find the principal repaid in Period 1
If a payment of $4,420.18 was made at the end of the first
period and $4,000 was paid toward interest, the remaining value
must represent the amount of principal repaid.
PRIN REPAYMENT = PMT – INT
= $4,420.18 - $4,000 = $420.18
9’-‹#›
81. 24
Step 4:
Find the ending balance after Period 1
To find the balance at the end of the period, subtract the amount
paid toward principal from the beginning balance.
END BAL= BEG BAL – PRIN REP.
= $100,000 - $420.18
= $99,579.82
9’-‹#›
25
Constructing an amortization table:
Repeat steps 1 – 4 until end of loanPBEG BALPMTINTPRIN
REPAYEND
BAL1$100,000$4,420.18$4,000$420.18$99,579.822 99,579.82
4,420.18
3,983.19 436.99 99,142.83
Interest paid declines with each payment as the balance
declines. What are the tax implications of this?
9’-‹#›
82. 26
Illustrating an amortized payment:
Where does the money go?
Constant payments.
Declining interest payments.
Declining balance.
$
0
1
2
3
4,420.18
Interest
420.18
Principal Repayments
9’-‹#›
27
Continuous Compounding
= ℮
83. 9’-‹#›
If compounding takes place continuously,
FVt = PV∙℮It
Alternatively,
PV = = FVt∙℮-It
Example 1: Suppose you invest $200 at 12% continuously
compounded for two years. How much are you going to receive
at the end of two years?
9’-‹#›
Continued …
Answer: It = 0.12×2 = 0.24, e0.24 = 1.2712. So, FVt = FV2 =
$200×1.2712 = $254.25
Example 2: What is the PV of $300 in one year’s time if I =
5%, and continuously compounded?
Answer: It = 0.05×1 = 0.05,
e-It = e-0.05= 0.9512,
so, PV = $300×0.9512 = $285.37
9’-‹#›
$134.49
86. Amortization
9-‹#›
1
Time lines
Show the timing of cash flows.
Tick marks occur at the end of periods, so Time 0 is today;
Time 1 is the end of the first period (year, month, etc.) or the
beginning of the second period.
CF0
CF1
CF3
CF2
0
1
2
3
I%
88. 3
Future Value of Money
If you deposit $1,000 today at 10%, how much will you have
after 15 years?
Interest($) = Principal ∙ Interest Rate(%)
Simple Interest
The original principal stays the same.
There is no interest on interest. The interest is only on the
original principal.
Compound Interest
The principal changes through time.
There is “interest on interest”. The interest is on the new
principal.
9-‹#›
9-‹#›
90. 9-‹#›
Example
What is the future value of $20 invested for 2 years at 10%?
Simple: FV = PV(1+nI)
= 20(1+2I) = 20(1+0.2) = $24
Compound: FV = PV(1+I)n
= 20(1+I)2 = 20(1+0.1)2 = $24.2
What is the future value of $20 invested for 100 years at 10%?
Simple: FV = 20(1+ ) =
Compound : FV = 20(1.1)100 = 275,612.25
9-‹#›
The Power of Compounding
The Value of Manhattan
In 1626, the land was bought from American Indians at $24.
In 2018, value = $24(1+I)392
9-‹#›
Solving for FV:
91. The formula method
Solve the general FV equation:
FVN = PV∙(1 + I)N = PV ∙ FVIF
FV15 = PV∙(1 + I)15 = $1,000∙(1.10)15 = $4,177.25
= $1,000∙4.177 = $4,177
(Table A)
9-‹#›
Present Value of Money
If you want to have $4,177.25 after 15 years, how much do you
have to deposit today at 10%?
9-‹#›
PV = ?
4,177.25
Present Value of Money
Finding the PV of a cash flow or series of cash flows is called
discounting (the reverse of compounding).
92. 0
1
2 …
15
10%
9-‹#›
13
Solving for PV:
The formula method
Solve the general FV equation for PV:
PV = = ∙
= FVN ∙ PVIF
PV = = = $4,177.25 ∙
= $4,177.25∙0.239
(Table C)
= $998.36, but $4,177.25∙0.2394 = $1,000
9-‹#›
14
93. Examples
If you want $10,000 after 10 years, how much do you have to
deposit today at 5%?
If you want $100,000 someday for a world tour, how long will it
take at 7% if you deposit $10,000 today?
If you want $50,000 in 10 years, at what rate do you have to
invest your money if you have $10,000 today?
9-‹#›
9-‹#›
Calculation
You deposit $1000 today at 6%. After one year (t=1), you
withdraw $300, after two years (t=2), you deposit $500 more,
and no deposit or withdrawal after that, then how much will you
have in year 5 (t=5) ?
9-‹#›
94. Answer
Step by step solution
0 1 2 5
$1,000 -$300 $500 ?
1000 PV, 6 I/Y, 1 N, CPT FV =>1060
1060
( )PV, 6 I/Y, ( )N, FV => ( )
( ) + ( ) = ( )
( ) PV, 6 I/Y, ( ) N, FV => ( )
9-‹#›
Annuity
A series of cash flows of the same amount with fixed intervals
for a specified number of periods.
0 1 2 3 4
$20 $20 $30 $20
$20 $30 $40 $50
$20 $20 $0 $20
$0 $0 $20 $20
$20 $30 $20 $30
9-‹#›
FV of Annuity
100
100
95. 100
0
1
2
3
I%
9-‹#›
FV of Annuity
FVA = 100(1+I)2 + 100(1+I) + 100
= 100[(1+I)2 + (1+I) + 1]
= 100∙
For n periods,
FVA = PMT∙
= PMT∙FVAIF
9-‹#›
PV of Annuity
100
96. 100
100
0
1
2
3
I%
9-‹#›
PV of Annuity
PVA = + +
= 100 [ + + ]
= 100
For n periods,
PVA = PMT
= PMT∙PVAIF
9-‹#›
Examples
If you deposit $3,000 a year for 10 years at 7%, how much will
97. you have after 10 years?
If you want to receive $5o,000 per year for 20 years, how much
do you have to deposit today at 5%?
9-‹#›
More examples
You need $100,000 in year 15 to start your own business. If
your bank’s interest rate is 6%, how much do you have to
deposit each year to get $100,000?
You need $100,000 for a world tour. If you deposit $10,000
each year, how long will it take for you to accumulate $100,000
at 7%?
9-‹#›
Investment Choice
You have $10,000 to invest. There are two choices for your
investment.
Choice A: Buying an annuity at $10,000 and receiving $1,000
for 20 years.
Choice B: Depositing $10,000 in a bank that pays 8% interest
rate.
98. 9-‹#›
Harder Problem
You need to accumulate $11,000. To do so, you plan to deposit
$1,350 per year in a bank that pays 6% interest. Your last
deposit will be less than $1,350 if less is needed to round out to
$11,000.
A. How many years will it take to reach your goal?
B. How large will the last deposit be for you to have exactly
$11,000 in your account?
9-‹#›
Answer
Two ways
A: The FV at year 6 will be $9,416.68, and the money will grow
in the account for a year to $9,981.68.
B: The FV at year 7 will be $11,331.68.
9-‹#›
What is the difference between an ordinary annuity and an
annuity due?
Ordinary Annuity
100. 9-‹#›
29
Ordinary Annuity and Annuity Due
FVADUE = FVA(1+I)
PVADUE = PVA(1+I)
9-‹#›
PV of Annuity Due
What is the PV of 3-year annuity due of $100 payments at 10%?
Now, $100 payments occur at the beginning of each period.
PVAdue= PVA (1+I) = $248.69(1.1) =$273.55.
Alternatively, set calculator to “BEGIN” mode and solve for the
FV of the annuity:
9-‹#›
FV of Annuity Due
What is the FV of 3-year annuity due of $100 payments at 10%?
Now, $100 payments occur at the beginning of each period.
FVAdue= FVA (1+I) = $331(1.1) = $364.10.
101. Alternatively, set calculator to “BEGIN” mode and solve for the
FV of the annuity:
9-‹#›
What is the (future) value of this annuity at t = 1? At t = 2?
100(1+I) + 100 +
9-‹#›
Question
If you can receive $50,000 per year forever, how much are you
willing to pay for that?
9-‹#›
Perpetuity
Perpetuity
PV =
102. If I = 10%, PV = = $0.5M
If I= 5%, PV = = $1M
9-‹#›
35
Growing Perpetuity
If the payments grow at a constant rate, g, it is a growing
perpetuity.
PV =
=
Example: If I = 10%, g = 5%,
PMT0 = $50,000,
PV = = $1.05M
9-‹#›
The Power of Compound Interest
A 20-year-old student wants to save $3 a day for her retirement.
Every day she places $3 in a drawer. At the end of the year, she
invests the accumulated savings ($1,095) in a brokerage account
with an expected annual return of 12%.
How much money will she have when she is 65 years old?
103. 9-‹#›
Solving for FV:
If she begins saving today, how much will she have when she is
65?
If she sticks to her plan, she will have $( ) when she
is 65.
( ) N, 12 I/YR, -1095 PMT, FV =>
( )
9-‹#›
Solving for FV:
If you don’t start saving until you are 40 years old, how much
will you have at 65?
If a 40-year-old investor begins saving today, and sticks to the
plan, he or she will have $146,000.59 at age 65. This is $1.3
million less than if starting at age 20.
Lesson: It pays to start saving early.
25 N, 12 I/Y, 1095 PMT,
FV =› 146,000.59
104. 9-‹#›
Solving for PMT:
How much must the 40-year old deposit annually to catch the
20-year old?
To find the required annual contribution, enter the number of
years until retirement and the final goal of $1,487,261.89, and
solve for PMT.
25 N, 12 I/Y, 1,487,261.89 FV,
PMT = › 11,154.42
9-‹#›
What is the PV of this uneven cash flow stream?
0
100
1
300
2
300
3
10%
-50
105. 4
90.91
247.93
225.39
-34.15
530.08 = PV
9-‹#›
41
Solving for PV:
Uneven cash flow stream
Input cash flows in the calculator’s “CF” register:
CF0 = 0
C01 = 100
F01 = 1
C02 = 300
F02 = 2
C03 = -50
Press NPV button, then enter I = 10, and hit CPT=> $530.087.
(Here NPV = PV.)
106. 9-‹#›
NPV (Net Present Value)
NPV is calculated net of costs.
If your project’s PV of cash inflows is greater than the PV of
cash outflows, the project will enhance your company’s
profitability.
In chapter 9, generally there is no cost at time 0, so the NPVs
are positive, but in chapter 12, when we evaluate projects, the
NPVs can be negative.
Example: 0 1 2 3 (I = 10%)
-1000 300 300 500
9-‹#›
9’-‹#›
Classifications of interest rates
Nominal rate (INOM) – also called the quoted or stated rate.
107. An annual rate that ignores compounding effects.
INOM is stated in contracts. Periods must also be given, e.g.
8% Quarterly or 8% Daily interest.
Periodic rate (IPER) – amount of interest charged each period,
e.g. monthly or quarterly.
IPER = INOM / M, where M is the number of compounding
periods per year. M = 4 for quarterly and M = 12 for monthly
compounding.
9’-‹#›
2
Compounding More than Once per Year
Annual Compounding
0 8% 1
|______________________|
Semiannual Compounding
0 4% 1 4% 2
|__________|___________|
Quarterly Compounding
0 2% 1 2% 2 2% 3 2% 4
|_____|_____|_____|_____|
9’-‹#›
Effective Annual Rate (EAR)
108. Effective (or equivalent) annual rate (EAR = EFF%): The
annual rate of interest actually being earned, accounting for
compounding.
EFF% for 8% semiannual investment
EFF% = ( 1 + )M - 1
= (1 + )2 – 1 = 8.16%
Should be indifferent between receiving 8.16% annual interest
and receiving 8% interest, compounded semiannually. EAR is
used to compare investment returns.
9’-‹#›
4
9’-‹#›
Calculator
Use ICONV key
NOM = INOM
EFF = EAR
C/Y = # of compounding per year
109. 9’-‹#›
What is the FV of $100 after 3 years under 10% semiannual
compounding? Quarterly compounding?
9’-‹#›
7
calculator
10% semi-annual compounding
5 I/Y, 100 PV, 6 N, FV => 134.01
Quarterly compounding
2.5 I/Y, 100 PV, 12 N, FV => 134.49
9’-‹#›
What is the future value of an annuity with $100 monthly
payments at 7% after 5 years?
FV = PMT
= 100
OR,
100 PMT
( ) I/Y
110. ( ) N
FV =
9’-‹#›
GM Incentives
You need $12,000 loan to buy a car.
There are two financing options to choose:
A: 2.9% financing with a 36 month loan
B: A rebate of $1,000 is available and the remaining $11,000 is
to be financed at 10% for 36 months.
Which option would you choose?
9’-‹#›
Quarterly Compounding
A. If you deposit $1,000 in a bank that pays 8% quarterly
compounding, what is the rate of return if you withdraw after 10
months?
B. How much in dollars will you get if you withdraw after 10
months?
9’-‹#›
111. What’s the FV of a 3-year $100 annuity, if the quoted interest
rate is 10%, compounded semiannually?
Payments occur annually, but compounding occurs every 6
months.
Cannot use normal annuity valuation techniques.
9’-‹#›
Method 1:
Compound each cash flow
FV3 = $100(1.05)4 + $100(1.05)2 + $100
FV3 = $331.80
9’-‹#›
Method 2:
Financial calculator
112. Find the EAR and treat as an annuity.
EAR = ( 1 + )2 – 1 = 10.25%.
10.25 I/Y, 3 N, -100 PMT, ---
9’-‹#›
Calculator 2
1 P/Y, 2 C/Y, 100 PMT, 3 N, 10 I/Y,
FV => 331.8006 => 331.80
9’-‹#›
Find the PV of this 3-year ordinary annuity.
Could solve by discounting each cash flow, or …
Use the EAR and treat as an annuity to solve for PV.
10.25 I/Y, 3 N, 100 PMT, --
9’-‹#›
Calculator 2
1 P/Y, 2 C/Y, 100 PMT, 3 N, 10 I/Y,
PV => 247.5947 => 247.59
113. 9’-‹#›
P/Y, C/Y
What is the future value of a three-year annuity with quarterly
payments of $50 each at 7%, monthly compounding?
9’-‹#›
Loan amortization
Amortization tables are widely used for home mortgages, auto
loans, business loans, retirement plans, etc.
Financial calculators and spreadsheets are great for setting up
amortization tables.
EXAMPLE: Construct an one-year amortization table for a
$100,000, 8%, semiannual payment, 30-year loan.
9’-‹#›
19
114. Step 1:
Find the required annual payment
All input information is already given.
60 N, 4 I/Y, 100,000 PV,
PMT = 4,420.18
9’-‹#›
20
Step 2:
Find the interest paid in Period 1
The borrower will owe interest upon the initial balance at the
end of the first period. Interest to be paid in the first period can
be found by multiplying the beginning balance by the periodic
interest rate.
INTt = Beg balt (I)
INT1 = $100,000 (0.04) = $4,000
9’-‹#›
21
Step 3:
Find the principal repaid in Period 1
115. If a payment of $4,420.18 was made at the end of the first
period and $4,000 was paid toward interest, the remaining value
must represent the amount of principal repaid.
PRIN REPAYMENT = PMT – INT
= $4,420.18 - $4,000 = $420.18
9’-‹#›
22
Step 4:
Find the ending balance after Period 1
To find the balance at the end of the period, subtract the amount
paid toward principal from the beginning balance.
END BAL= BEG BAL – PRIN REP.
= $100,000 - $420.18
= $99,579.82
9’-‹#›
23
Constructing an amortization table:
Repeat steps 1 – 4 until end of loanPBEG BALPMTINTPRIN
116. REPAYEND
BAL1$100,000$4,420.18$4,000$420.18$99,579.822 99,579.82
4,420.18
3,983.19 436.99 99,142.83
Interest paid declines with each payment as the balance
declines. What are the tax implications of this?
9’-‹#›
24
Illustrating an amortized payment:
Where does the money go?
Constant payments.
Declining interest payments.
Declining balance.
$
0
1
2
3
4,420.18
Interest
420.18
Principal Repayments
117. 9’-‹#›
25
Continuous Compounding
= ℮
9’-‹#›
If compounding takes place continuously,
FVt = PV∙℮It
Alternatively,
PV = = FVt∙℮-It
Example 1: Suppose you invest $200 at 12% continuously
compounded for two years. How much are you going to receive
at the end of two years?
9’-‹#›
Continued …
Answer: It = 0.12×2 = 0.24, e0.24 = 1.2712. So, FVt = FV2 =
$200×1.2712 = $254.25
118. Example 2: What is the PV of $300 in one year’s time if I =
5%, and continuously compounded?
Answer: It = 0.05×1 = 0.05,
e-It = e-0.05= 0.9512,
so, PV = $300×0.9512 = $285.37
9’-‹#›
$134.49
(1.025)
$100
FV
$134.01
(1.05)
$100
FV
)
2
0.10
1
120. =
´
´
Term Paper on the TVM
The first part of your term paper should include a summary of
all the concepts of Time value money covered in class, for
example, Future value of single sum, present value of single
sum, annuity, etc., in your own words. You must include a
simple numerical example to explain each concept. Do not
simply copy the textbook, and you should follow the rule of
quotation if you want to quote a sentence from the book.
Include all the concepts covered in class.
The second part of the paper is about the application of Time
value money to your own financial problems. Try to use the
concepts you learn from the class to solve practical financial
issues in your life, for example, your retirement planning, your
mortgage payments or car loan payments, credit card interest
rates, to name a few. Since you use a numerical example for
each concept in the first part, it is encouraged to analyze one
big problem rather than several small problems in the second
part. It has to be your own and specific problem. If you cannot
think of your own problem, you may make up a case that is
interesting.
Do not mix the first part and the second part, that is, the second
part should have a separate heading. There is a penalty of 20%
for mixing the two parts. Two sample papers are on reserve in
the library for your perusal.
Include word count on the front page. The word count should be
at least 2,500. Simply type the word count shown on your MS
Word or other word processors.
Grading:
First Part 50%
Second Part 40%
Writing Quality 10%
121. The emphasis on the first part is thoroughness, that is, you have
to explain every concept covered from time lines to loan
amortization.
The second part is comprised of creativity/originality (10%),
correctness (10%), sophistication (10%), and overall content
(10%).