8.11: Essay Questions
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48 .
Write an essay discussing the role of self-efficacy in a child’s academic achievement during middle childhood. Explain how a child’s belief in their ability to succeed influences their approach to learning tasks and their overall academic performance. Use specific examples to illustrate how high and low self-efficacy can lead to different academic outcomes. Additionally, suggest strategies that teachers and parents can use to help boost a child’s self-efficacy in school.
49 .
Write an essay examining the development of gender identity in middle childhood. Discuss how children’s understanding of gender norms evolves during this period and how societal expectations, media, and peer interactions influence their gender identity. Provide examples of how children might challenge or reinforce gender stereotypes and discuss the implications for their overall self-concept.
50 .
Discuss the role of emotional regulation in middle childhood. How do children develop the ability to manage their emotions, and what factors contribute to their success or struggles in this area? Include examples of coping strategies that children might use during this stage of development.
51 .
Consider the role of resilience in a child’s ability to cope with stress and adversity during middle childhood. What factors contribute to building resilience, and how can caregivers and educators support this process? Include examples of how resilient children might handle challenges differently than their peers.
52 .
Analyze the factors that contribute to a child’s peer status during middle childhood. Discuss how the different categories of peer status (popular, rejected, neglected, controversial, and average) can influence a child’s social development and future relationships.
53 .
Examine the role of family dynamics in shaping a child’s social and emotional development during middle childhood. Consider how parenting styles, sibling relationships, and family structure can impact a child’s interactions with peers and their overall well-being.
54 .
Imagine you are the principal of a school that currently offers only a limited number of extracurricular activities. You believe that expanding the range of extracurricular activities will greatly benefit students. Write an essay in which you make the case for adding more extracurricular activities to the school’s offerings. In your essay, be sure to address how these activities could improve the overall school climate, strengthen teacher-student relationships, and support positive youth development. Use specific examples to illustrate your points and explain how these changes could lead to better outcomes for the students in your school.
55 .
Imagine you are a school guidance counselor working with a group of teachers who are concerned about a student displaying both internalizing and externalizing behaviors. The teachers are unsure how to approach this student to support their mental health and promote resilience. Write a letter to the teachers outlining specific strategies they can use to address these behaviors, and explain how these strategies can help improve the student’s socioemotional well-being.


14.5: Junction Diodes
Selenium oxide rectifiers were used before modern power diode rectifiers became available. These and the Cu 2 O rectifiers were polycrystalline devices. Photoelectric cells were once made from Selenium.
Before the modern semiconductor era, an early diode application was as a radio frequency detector , which recovered audio from a radio signal. The “semiconductor” was a polycrystalline piece of the mineral galena, lead sulfide, PbS. A pointed metallic wire known as a cat whisker was brought in contact with a spot on a crystal within the polycrystalline mineral. (Figure below) The operator labored to find a “sensitive” spot on the galena by moving the cat whisker about. Presumably, there were P and N-type spots randomly distributed throughout the crystal due to the variability of uncontrolled impurities. Less often the mineral iron pyrites, fools gold, was used, as was the mineral carborundum, silicon carbide, SiC, another detector, part of a Presumably there were P and N-type spots randomly distributed throughout the crystal due to the variability of uncontrolled impurities. Less often the mineral iron pyrites, fools gold, was used, as was the mineral carborundum, silicon carbide, SiC, another detector, part of a foxhole radio , consisted of a sharpened pencil lead bound to a bent safety pin, touching a rusty blue-blade disposable razor blade. These all required searching for a sensitive spot, easily lost because of vibration.
Crystal detector
Replacing the mineral with an N-doped semiconductor (Figure below(a) ) makes the whole surface sensitive, so that searching for a sensitive spot was no longer required. This device was perfected by G.W.Pickard in 1906. The pointed metal contact produced a localized P-type region within the semiconductor. The metal point was fixed in place, and the whole point contact diode encapsulated in a cylindrical body for mechanical and electrical stability. (Figure below(d) ) Note that the cathode bar on the schematic corresponds to the bar on the physical package.
Silicon point contact diodes made an important contribution to radar in World War II, detecting giga-hertz radio frequency echo signals in the radar receiver. The concept to be made clear is that the point contact diode preceded the junction diode and modern semiconductors by several decades. Even to this day, the point contact diode is a practical means of microwave frequency detection because of its low capacitance. Germanium point contact diodes were once more readily available than they are today, being preferred for the lower 0.2 V forward voltage in some applications like self-powered crystal radios. Point contact diodes, though sensitive to a wide bandwidth, have a low current capability compared with junction diodes.
Silicon diode cross-section: (a) point contact diode, (b) junction diode, (c) schematic symbol, (d) small signal diode package.
Most diodes today are silicon junction diodes. The cross-section in Figure above(b) looks a bit more complex than a simple PN junction; though, it is still a PN junction. Starting at the cathode connection, the N + indicates this region is heavily doped, having nothing to do with polarity. This reduces the series resistance of the diode. The N - region is lightly doped as indicated by the (-). Light doping produces a diode with a higher reverse breakdown voltage, important for high voltage power rectifier diodes. Lower voltage diodes, even low voltage power rectifiers, would have lower forward losses with heavier doping. The heaviest level of doping produces zener diodes designed for a low reverse breakdown voltage. However, heavy doping increases the reverse leakage current. The P + region at the anode contact is heavily doped P-type semiconductor, a good contact strategy. Glass encapsulated small signal junction diodes are capable of 10’s to 100’s of mA of current. Plastic or ceramic encapsulated power rectifier diodes handle to 1000’s of amperes of current.
Review
- Point contact diodes have superb high-frequency characteristics, usable well into the microwave frequencies.
- Junction diodes range in size from small signal diodes to power rectifiers capable of 1000’s of amperes.
- The level of doping near the junction determines the reverse breakdown voltage. Light doping produces a high voltage diode. Heavy doping produces a lower breakdown voltage, and increases reverse leakage current. Zener diodes have a lower breakdown voltage because of heavy doping.


Discuss the connection between
genetic inheritance
and
genotype
Identify common inherited and
genetic disorder
s
Describe the ways genes and environments interact
To say that Arjun is outgoing or extraverted would be an understatement. He thrives on time spent with others—loud parties, packed professional conferences, and crowded sports bars. His brother Ajay is more introverted and prefers quiet meals with his partner or a close friend, reading, and solo hikes. Despite their differences in personality, Arjun and Ajay have a strong physical resemblance. Their parents often wonder how their children can look so similar but have such distinct personalities when they have the same biological parents and grew up in the same home.
To understand how human development occurs, and how similarities and differences like those observed by Arjun and Ajay’s parents arise, we need to examine the role of genetic inheritance (nature), environment and experiences (nurture), and the interplay between genetic and environmental effects (nurture and nature). Connections between chromosomes, DNA, genes, genetic inheritance, inherited and genetic disorders, and the way our genetics and environments interact contribute to the similarities and individual differences observed across human development.
Chromosomes, DNA, and Genes
The first step in grasping the way genetics influence development is to understand chromosomes, DNA, and genes, and the way each functions within a cell–the focus of the field of molecular genetics. Cells duplicate themselves through a process of cell division called
mitosis
, which allows organisms to grow and replace old or damaged cells. Mitosis accounts for the replication of most types of cells in the body and ensures that each new cell includes all forty-six chromosomes, organized in twenty-three pairs located in the cell nucleus. A
chromosome
is a rodlike structure in the cell nucleus, composed of long molecules of DNA.
DNA (deoxyribonucleic acid)
molecules contain an individual’s genetic information; they coil around each other to form a double helix, a twisted ladderlike structure (Figure 2.2).
 These cells replicate through a different type of cell division called meiosis. During
meiosis
, a sex cell, whether an
ovum
in a female or a
sperm
cell in a male, splits into two new cells that each also contain only twenty-three chromosomes. Thus, gametes contain only half the genetic information of each parent, ensuring that after fertilization of the ovum, the resulting offspring will have a total of forty-six chromosomes, twenty-three from the biological mother and twenty-three from the biological father. Which particular chromosomes these are is largely random: eight million different combinations are possible, contributing to the wide genetic variation seen among humans.
A human nonsex cell, called an
autosome
, is what is present in chromosome pairs one through twenty-two. The twenty-third pair—the sex chromosomes—may look the same or different (Figure 2.3). The sex chromosomes are called the X and Y chromosomes, based on their shapes. The combination of these chromosomes determines the child’s sex at conception: XX for a biological female and XY for a biological male.
Females have two X chromosomes, so each of their ova contains an X chromosome in the twenty-third position; males have both X and Y chromosomes, so each of their sperm cells contains one or the other, and thereby determines the baby’s sex.
Intersex is an umbrella term for people who have one or more of a range of variations in sex characteristics or chromosomal patterns that do not fit the typical conceptions of male or female; the prefix
inter
- means “between” and refers here to an apparent biological state “between” male and female. There are many causal factors that can make a person intersex; these are often referred to as differences in sex development (DSD), though there is debate over which DSDs make a person intersex. Genetically, the baby may have a different number of sex chromosomes. Rather than two X chromosomes (associated with females) or one X and one Y chromosome (associated with males), babies are sometimes born with an alternative number of sex chromosomes, such as XO (only one chromosome) or XXY (three chromosomes). In other cases, hormonal activity or even chance occurrences in the womb can affect the baby’s anatomy. The number of people born intersex has been expressed to be as high as 1.7 percent of births; however, based on different interpretations of what makes someone intersex, you may see other statistics or ranges quoted (Fausto-Sterling, 2000; Becker, Chin & Bates, 2022).
While some conditions or disorders associated with being intersex may require treatment or intervention, being intersex is not a disorder. The intersex community and many medical groups view surgery to support the assignment of an infant to a specific sex to be unethical and even abusive. For example, Medical ethicist Kevin Behrens (2020) argues that surgical interventions for intersex children should only be carried out when surgery serves the best medical interests of the child.
The most commonly occurring twenty-third chromosome pairings are XX and XY (National Organization for Rare Disorders, n.d.; Genetic and Rare Diseases Information Center, n.d.). However, differences may occur during cell division that result in
aneuploidy
, an atypical number of autosomal or sex chromosomes that may result in various syndromes (Gottlieb et al., 2023; Skuse et al., 2018) (Table 2.1).
Sex Chromosome Combinations
Medical Terminology
Prevalence
XX
Biological female
Majority
XY
Biological male
Majority
XO
Turner syndrome
1 in 2,500 females
XXY
Klinefelter syndrome
1 in 500 to 1,000 males
XXX
Trisomy X
1 in 1,000 females
XYY
XYY syndrome
1 in 1,000 males
XXYY
XXYY syndrome
1 in 18,000 to 50,000 male births
Table 2.1
Types of Sex Chromosomes Combinations
Our genetic inheritance is carried in the genes that make up our chromosomes. A
gene
is a segment of
DNA
that contains the instructions for making proteins that regulate the structure and functioning of the body. It’s estimated that humans have between 20,000 and 25,000 genes (National Human Genome Research Institute, 2022). The rungs of the chromosome’s ladderlike structure, which house the DNA sequence, consist of four nucleic acid bases: guanine (G), adenine (A), thymine (T), and cytosine (C). These nucleic acids pair up in specific ways (Klug et al., 2016). However, not all of our genes code for proteins; some regulate gene expression, or how genes work and interact with each other.
The complete sequence of an organism’s DNA is called its
genome
. Each human being shares about 99.9 percent of their genome with all other humans on the planet; the remaining 0.01 percent contributes to the differences we observe in physical and behavioral differences, as well as the variations in our risk of developing certain types of diseases (Duello et al., 2021; National Human Genome Research Institute, 2022).
Genetic Inheritance
Have you ever wondered why you share some physical characteristics with your biological parents but not others? Maybe you have your mother’s freckles, or perhaps a different eye color than either of your parents. How do these similarities and differences occur?
Recall that humans receive twenty-three chromosomes each from their biological parents’ sperm and ovum. During fertilization, these chromosomes fuse to create one cell with twenty-three pairs of chromosomes, each carrying two copies of each gene. The particular composition of the genes we inherit makes up our unique
genotype
, which cannot be directly observed. Some genes have a slightly different alternate forms, called an
allele
, and the specific alleles in our genotype can lead to differences in gene expression (National Human Genome Research Institute, 2022). These differences, in turn, result in a different
phenotype
, or set of characteristics that can be observed, such as hair or eye color. Biological parents may both give their child the same allele, or each parent may contribute a different allele.
The genes for certain traits, such as eye color, have both dominant and recessive alleles. If an allele is dominant, we need to inherit only one copy of it for the
dominant trait
, such as brown eyes, to be observed. However, we need two copies of a recessive allele, such as that for blue eyes, for the
recessive trait
to be observed. This pattern of inheritance is called the recessive/dominant pattern. If a child inherits the same eye color allele from both parents, the child is considered
homozygous
for this trait. The child who inherits different eye color alleles from both parents is
heterozygous
for this trait (Figure 2.4).
Another inheritance pattern for traits such as hair texture, skin color, and height demonstrates incomplete or partial dominance, which occurs when an individual is heterozygous for a particular trait and neither allele is completely dominant or recessive. The result is
incomplete dominance
, an intermediate phenotype in which both alleles are expressed (Figure 2.5). For instance, if one parent is homozygous for curly hair and the other is homozygous for straight hair, incomplete dominance will result in the child’s having wavy hair, because alleles for both straight and curly hair are simultaneously expressed (Omoto & Lurquin, 2004).
For other traits, a codominant inheritance pattern holds. With a
codominant trait
, an individual inherits both alleles of a gene, and each is fully expressed (National Human Genome Research Institute, 2024). For example, the ABO blood group has three alleles, A, B, and O, all encoded by the same gene. A child will inherit one of these alleles from each parent, which results in one of four possible phenotypes (A, B, AB, or O), commonly known as your blood type (Dean, 2005) (Figure 2.6).
Another factor that can influence the way genes are expressed is whether they are located on the X chromosome, meaning they are X-linked (Figure 2.7). For example, the genes identified for red-green colorblindness, a recessive trait, are located on the X chromosome. Biological males are more frequently affected than biological females by recessive X-linked traits such as red-green colorblindness. Females need to receive the recessive allele for this trait from both biological parents, whereas males need to receive it only from their biological mother.
The traits described rely on one or a few genes, but the vast majority of physical, behavioral, and health traits are a type of
polygenic trait
, meaning they are governed by multiple genes. Together, the effects of all the individual genes add up to create the observed phenotype. Scientists are beginning to identify which combinations of genes are associated with a range of complex traits and diseases such as cognitive ability, major depressive disorder, type 2 diabetes, and coronary heart disease (Tam et al., 2019). Not all the phenotypic variation observed is accounted for by genes, however, environmental factors also contribute to the expression of a trait. Complex traits and diseases are likely a result of
multifactorial inheritance
; that is, their occurrence depends on both genetic and environmental factors.
In addition, a single gene can influence multiple traits and produce a variety of phenotypic outcomes, a characteristic referred to as
pleiotropy
(Figure 2.8). For example, PKU (phenylketonuria) is a single-gene recessive disorder. This mutation results in the ineffective metabolism of phenylalanine (found in milk and other foods), bringing about a variety of issues if untreated, such as cognitive disability, eczema, and delayed growth (Elhawary et al., 2022; Targum & Lang, 2010). Another type of pleiotropic effect occurs when genes referred to as generalist genes affect different but related phenotypes. For example, the same genetic variants are shared across verbal and nonverbal cognitive abilities (Bearden & Glahn, 2017), and shared genetic variants are indicated across several psychiatric disorders (Cross-Disorder Group of the Psychiatric Genomics Consortium, 2019).
Inherited and Genetic Disorders
Genes contribute to all aspects of human development, functioning, and trait expression, including inherited and genetic disorders. There are three main types of genetic disorders: single-gene disorders, chromosomal disorders, and multifactorial inherited disorders.
A
single-gene disorder
occurs in a single gene and can happen in two ways: (1) Individuals may inherit a pair of recessive alleles responsible for a disorder, or (2) mutations to the DNA sequence can result spontaneously, from errors during cell division or from exposure to environmental toxins or other hazards such as x-rays or pollution. Mutations occur when the DNA sequence of a gene is altered; this can occur in a variety of ways but most commonly through a change in a single nucleic acid base pairing substitution. Examples of single-gene disorders include PKU, Tay-Sachs disease, cystic fibrosis, and sickle cell anemia (Table 2.2).
A
chromosomal disorder
is due to errors during cell division and result in structural or numerical abnormalities. Structural abnormalities occur when sections within a chromosome are deleted, duplicated, or inverted (a section of the chromosome flips its orientation), or when sections are rearranged within or across the chromosome pairs. Numerical abnormalities happen during cell division and result in one of the twenty-three chromosome pairs containing only one chromosome (monosomy) or having an extra chromosome (trisomy). For example, individuals with Down syndrome will have three twenty-first chromosomes rather than two (Figure 2.9). Because each chromosome contains a large number of genes, deviation in chromosome number (more or less than two) will affect a range of characteristics.
A disorder resulting from
multifactorial inheritance
occurs when both polygenic effects (controlled by many genes) and environmental effects contribute to a phenotype. Studies have identified several genes that contribute to the risk of developing type 2 diabetes, heart disease, obesity, autism spectrum disorder, and anxiety disorders (Dickerson & Dickerson, 2023; Genovese, & Butler, 2023; Li et al., 2024; National Human Genome Research Institute, 2020b). Many of these disorders are also influenced by multiple genes and a range of environmental influences, such as the prenatal environment, nutrition, socioenvironmental experiences, and environmental conditions.
Known inherited and genetic disorders can be screened for before pregnancy, prenatally, and shortly after birth. Table 2.2 offers an overview of some of these disorders.
Disorder
Prevalence
Symptom Description
Treatments
Phenylketonuria (PKU)
1 in 10,000 to 15,000 live births
Range of intellectual disability, eczema, lighter skin due to pigment defects
Limit on foods containing phenylalanine; nutritional supplements
Tay-Sachs disease
1 in 320,000 live births; more frequent in people of central or eastern European Jewish descent
1 in 3,200 live births; people of European ancestry at highest risk
Thick, sticky mucus that clogs the lungs; vulnerability to pulmonary infections
Treatments to manage symptoms, prevent complications
Sickle cell anemia
1 in 365 live births; Black and African American individuals at greatest risk
Sickle-shaped red blood cells; anemia; acute chest pain; pain episodes; organ damage
Treatments to manage symptoms, recently approved cell-based gene therapy
Fragile X syndrome
1 in 7,000 male and 1 in 11,000 female live births
Mild to moderate learning disabilities; distractibility and impulsivity
Early intervention, special education, treatment for attention-deficit/hyperactivity disorder (ADHD)
Down syndrome
1 in 1,000 live births
Range of intellectual disabilities; unique facial features; poor muscle tone; possible heart, digestion, or hearing problems
Physical, occupational, speech, and educational therapy; medical intervention as needed
Table 2.2
Examples of Inherited and Genetic Disorders
(sources: Centers for Disease Control and Prevention, 2024a, 2024b; Elhawary et al., 2022; National Human Genome Research Institute, 2013, 2014, 2020a; Ramani & Sankaran, 2023; U.S. Food and Drug Administration, 2023)
Gene Environment Intersections
Genetic research has helped us understand human traits that rely on one or two genes. However, most human traits, such as personality traits, are more complex and result from a combination of genetic (nature) and environmental (nurture) influences. Understanding how, and how much, genes and environments influence gene expression together is the focus of the field of
behavioral genetics
. As described in 1.2 Themes of Development,
heritability estimate
s indicate the degree to which genetics contribute to individual differences for a trait within a population. A high heritability estimate, near 100 percent, indicates that genetic effects explain a lot of variability within a population; a low heritability, closer to 0 percent, indicates that most of the variability is environmental (Mayhew & Meyre, 2017) (Table 2.3).
The goal of behavioral genetics is to explain 100 percent of the observed variance for a trait. Interpreting a heritability estimate also reveals to what degree environmental influences account for differences in a trait. For example, the heritability of intelligence is 50 percent, which means that genetics explains half the observed differences in this complex trait, and the remaining 50 percent is due to environmental effects. Note that heritability is a population statistic and cannot be applied to a specific individual. In other words, heritability can’t tell you how much your intelligence is due to the specific genes you inherited. Consider the examples in Table 2.3.
Trait
Heritability
Height
80–90 %
Blood pressure
30–70 %
Intelligence
50 %
Big Five personality traits
40–60 %
Autism spectrum disorder
64–91 %
Depression
37 %
Alcohol dependence
50 %
Table 2.3
Heritability Estimates for Common Human Traits
(sources: Doris, 2010; Plomin & von Stumm, 2018; Power & Pluess, 2015; Schrempft et al., 2018; Sullivan et al., 2000; Tick et al., 2015; Verhulst et al., 2014)
Heritability helps us understand understand the magnitude of individual genetic and environmental effects on a complex trait. But how do genes and environments work together to create the range of phenotypes observed for traits like personality or depression? The answer involves exploring the way genetic and environmental effects are intertwined via epigenetic effects, gene and environment interactions (G × E), and gene and environment correlations (rGE), and epigenetic effects.
Epigenetics
As you learned in 1.2 Themes of Development,
epigenetics
investigates the way environments, experiences, and behaviors influence the expression of inherited genes without altering the DNA sequence of those genes (National Human Genome Research Institute, 2022). How do epigenetic effects influence gene expression? One common way
gene expression
is regulated is by the addition and removal of chemical tags through the process of
DNA methylation
(Figure 2.10). The addition of methyl groups to the nucleotide base(s) of the gene, prevents expression of or silences the gene. Conversely, when a methyl group is removed from the nucleotide base(s) of the gene, it increases gene expression (Moore et al., 2012; Villicaña & Bell, 2021).
Epigenetic effects can be activated by chemical and environmental exposures such as (lead, air and water pollutants, PCBs, and BPA), diet and food availability (such as lack of folate, or prenatal malnutrition), lifestyle habits (such as smoking, high alcohol consumption, stress, and exercise), and a range of drug treatments (Toraño et al., 2016). These can occur throughout the lifespan and are linked to increased risks for chronic illness and disease and development of mental and physical health issues. Early studies of epigenetic effects examined the records of children whose mothers were pregnant during the Dutch famine of 1944–1945 during World War II (Heijmans et al., 2008). Prenatal exposure to the famine was linked to a greater risk for the development of type 2 diabetes and heart disease later in life (De Rooij et al., 2021). The children of mothers exposed to prenatal famine were larger at birth, while the children of fathers exposed to prenatal famine were heavier in adulthood (De Rooij et al., 2021). These studies indicate that epigenetic effects may be transmitted to future generations.
More recent investigations have focused on the effects of early childhood stress exposure. In children who had experienced earlier traumatic events, often called adverse childhood experiences, epigenetic effects were observed in areas of the brain that control the stress response. These children were more reactive to stress, even low levels, and more prone to depression and anxiety due to the epigenetic changes identified (Turecki & Meaney, 2016). Whether epigenetic effects are passed to the next generation in humans is just beginning to be examined. Although the chemical tags connected to epigenetic effects are usually removed during gamete production, research suggests some can be passed to future generations in animals (Gillette et al., 2018).
Regardless of whether epigenetic effects are passed to the next generation, providing health services and nutritional support to pregnant individuals, infants, and toddlers can reduce preventable illnesses with long-lasting implications that occur through epigenetic mechanisms (National Scientific Council on the Developing Child, 2010). For example, improved health care, exercise, and nutritional resources may serve as important environmental epigenetic factors that can improve mental and physical health. Nutrition and exercise show promise as protective factors in reducing risks of metabolic disease and other health risks (Abraham et al., 2023; Bekdash, 2024).
Genotype × Environment Interactions
Another way genes and environments work together to create a
phenotype
is through a
genotype × environment interaction
. In these events, the effect of the genotype (nature) on a phenotype (observed trait) depends on our environment (nurture). In other words, some genes will have an effect only under certain environmental conditions.
A classic example of a genotype × environment interaction is PKU (Widaman, 2009). Recall that
PKU
is a recessive disorder but will negatively affect development only if a low-phenylalanine diet isn’t followed. A genetic risk (two affected alleles) must interact with a high-risk environment (a high-phenylalanine diet) for the PKU phenotype to occur. Other gene × environment interaction models indicate that some genotypes may show differential susceptibility, which means they are sensitive to both protective and risk environments. A group of adolescent males with the short allele of a certain gene associated with serotonin reported more depressive episodes when experiencing lower family support, and fewer episodes with more family support. However, this interaction was not found for the long allele of this gene (Li et al., 2013).
As mentioned in Chapter 1 Lifespan Psychology and Developmental Theories, there are several types of
genotype-environment correlation
s, which indicates that our genes and environments are not randomly distributed but are instead connected.
Gene and Environment Correlations
The understanding of how gene and environment interact suggests that our genes play a role in shaping our environments and experiences. Three types of genotype-environment correlations (rGEs) are evident across the lifespan: passive, evocative, and active (Plomin et al., 1977; Scarr & McCartney, 1983).
A
passive genotype-environment correlation
occurs when biological parents provide both the genes and environment for children. Therefore, children inherit a genotype that covaries, or varies in correlation with, their family’s environment. For example, if your inherited genes predispose you for musical ability, and you are raised by biologically related caregivers, you are also likely to be provided a family environment that supports musicality. For example, the father already had a drum set and the mother regularly plays ukulele. This type of genotype-environment correlation is observed during infancy and early childhood when children have little control over their environment.
An
evocative (or reactive) genotype-environment correlation
is evident when an individual’s genetically influenced traits or behaviors evoke a response from those around them. In other words, people evoke environmental effects that covary with their genetic predispositions. For example, an inclination for musical ability will likely be noticed by a music teacher, who works with the individual challenging music pieces and encourages trying out for the school orchestra. Evocative genotype-environment correlations steadily occur across the lifespan, from infancy through late adulthood.
An
active genotype-environment correlation
is present when our genes influence the experiences and environments an individual seeks out or selects to match their genetic predispositions. In other words, people construct environments that covary with their genotypes. This effect is also referred to as
niche-picking
, which means we actively choose the environment (niche) where we feel most comfortable. In this example, you recognize your musical ability and select environments and experiences that allow you to pursue personal and professional opportunities connected to music. Active genotype-environments increase over the lifespan as individuals gain more control over their environment.
The interplay between genes and environment is challenging to untangle. For any given human behavior, multiple connections and mutual influences between genotypes and environments work together to create the similarities and differences observed across human behavior (Figure 2.11).
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18: Leases
After completing this chapter, you should be able to: (1) understand how leasing can provide an alternative method for gaining control of and access to capital resources; and (2) evaluate leases using present value (PV) models developed earlier.
To achieve your learning goals, you should complete the following objectives:
- Learn how leasing arrangements offer a different method for gaining control of and access to capital resources.
- Distinguish between the different forms of leases including the sale and leaseback lease, the operating lease, and the financial or capital lease.
- Learn the differences between leases and rental agreements.
- Learn how lease agreements are taxed.
- Learn the advantages and disadvantages of entering a lease agreement versus owning a capital resource.
- Learn how to find the break-even purchase price when compared to a leasing option.
Introduction
Control of a durable can be transferred between parties in several ways. A lease agreement is one important way. A lease is a contract through which control over the right to use a durable is transferred from one party, the lessor, to another party, the lessee who acquires control of the durable. In exchange for the right to use or control a durable for a specified time period, the lessee pays the lessor a rental payment or share in the output produced by the leased durable. The lease payment or shared output must cover the opportunity cost of funds invested in the leased item, depreciation of the durable, and other incidental ownership costs incurred by the lessor. Thus, leasing is a method of financing the control of a durable that separates its use from its ownership.
There are several kinds of lease arrangements and several kinds of durables that are leased. Farmland is frequently leased as are machines, houses, cars, computers, coping equipment, buildings, breeding livestock, and many kinds of management services. In this chapter, we describe various types of leases, evaluate their advantages and disadvantages, and apply present value (PV) tools to analyze leasing benefits for both the lessor and the lessee.
Types of Lease Agreements
Sale and leaseback. Under the sale-and-leaseback agreement, a firm owning a durable to be leased sells the durable to a financial institution and simultaneously executes an agreement to lease the durable back. Thus, the lease becomes the alternative to a purchase with a specific advantage to the lessee: namely, he or she is allowed to write off the entire lease payment as an expense instead of just interest costs and depreciation. The lessor will not enter into this type of lease agreement unless the lease payments are sufficient to return the full purchase price plus a return on the investment to the lessor.
Operating leases. Operating leases, sometimes called service leases, provide for both financing and maintenance. These leases ordinarily call for the lessor to maintain the leased equipment. The cost of the maintenance is built into the lease payment. Computers and office copiers, together with cars and trucks, are the primary types of equipment involved in operating leases.
In the case of operating leases, lease payments are often insufficient to recover the full cost of the equipment. To offset this feature, the lease is written for a time period considerably less than the expected life of the leased equipment, leaving the lessor to recover his or her investment in renewal payments of the lease or through disposal of the leased equipment.
One of the main advantages of the operating lease for lessees is the cancellation of the short lease period which allows them to adopt and bring into use more advanced equipment. Thus, for durables subject to rapid changes in technology, an operating lease is often a preferred method for gaining control of a durable.
Financial or capital leases. A financial lease is a fully amortized lease whose PV of the lease payments equals the full price of the leased equipment. It does not provide for maintenance service nor may it be canceled. The financial lease begins with a lessee selecting the specific items it requires and agreeing with the lessor about the price and the delivery of the item. The lessor arranges with a bank or another financial institution to purchase the equipment and simultaneously executes a financial lease with the lessee intending to use the equipment. The purchase of the equipment builds into the lease payments a rate of return equivalent to what would be charged on a loan, and the lease is canceled when the purchase price of the durable plus a return for the lessor is paid.
Under financial leases, lessees generally pay property taxes and insurance and, in many cases, can acquire ownership of the durable at the end of the lease. The significant difference between the sale-and-leaseback lease and the financial lease is that the lessee purchases the durable directly from the manufacturer rather than from the lessor under the terms of the financial lease.
Lease Agreements and Taxes
One of the major effects of the lease is to alter the tax obligations of the lessee and lessor. Therefore, special attention is required to make sure that lease agreements are acceptable under current tax codes as interpreted in the United States by the Internal Revenue Service. There is an important distinction between a lease agreement and a loan for tax purposes. If the lease agreement cannot be distinguished from an ordinary loan agreement, then any special tax provisions associated with the lease agreement are lost.
To distinguish a lease from a sale agreement, the term over which the investment durable is leased must be less than 75 percent of the economic life of the durable. Nor should the lessee be granted any special repurchase option not available to others not involved in the lease. There are other conditions as well; tax codes are evolving documents that are constantly being updated.
Lease Liquidity and Risk
Normally, the decision to acquire the durable is not at issue in the typical lease analysis. The issue at hand is whether to acquire control of the durable through a lease or by purchasing it—often by borrowing funds to finance the purchase. The decision requires a careful examination of the advantages of leasing. Leasing offers several possible advantages relative to owning a durable that we describe next.
Release of cash and credit. When a firm leases or sells a durable on a leaseback arrangement, the lessee avoids the cash down payment required to purchase the investment. More generally, the liquidity of a lease versus the liquidity of a purchase depends on which option requires the most accelerated payments.
Some texts discuss in detail the effect on the firm’s credit reserve as a result of leasing. If leasing uses up credit at a slower rate than borrowing, there may be credit incentives for leasing rather than borrowing. However, lenders are likely to recognize that long-term lease agreements place the same requirements on the firm’s future cash flow as loans do.
Obsolescence risk. Investments may experience significant obsolescence risks. In addition, there is some risk that the need for durables’ services will change before the durables’ service capacity is exhausted. Part of this obsolescence and use risk may be reduced through a lease arrangement for a short time period, especially if the lessor is less subject to obsolescence risk than the lessee. This is likely the case where the leased equipment has alternative uses in other firms or industries and where the risk can be spread over many lessees.
Idle capacity risk. Another risk that can often be reduced through lease arrangement is the risk of holding idle equipment. If the demand for services from a durable is not sufficient to employ the durable full time, the lessee can reduce idle capacity risk by leasing rather than owning the durable. From the lessor’s point of view, the durable can be completely employed because many lessees will use the equipment.
Foreclosure risk. In many respects, leasing is similar to borrowing because it represents an obligation of the firm to a series of future cash payments. There is one significant difference between agreeing to lease and borrowing to purchase the durable. In the case of financial difficulties, the lessor simply takes back the equipment because he or she holds the legal title. In the case of a loan, inability to meet loan payments may result in more complex foreclosure proceedings.
Tax advantages. A tax advantage may be gained when the term of the lease is shorter than the allowable tax depreciation period for ownership. However, tax incentives for the lessee must be a result of a lower total tax burden for the lessee and lessor. This situation implies that the lease arrangement has legitimately allowed for a reduction in the total amount of taxes paid. Needless to say, the Internal Revenue Service imposes conditions on what does and does not constitute a legal lease.
Net Present Cost of Leasing versus Purchasing
The decision to lease or to buy a durable depends on the net present cost (NPC) of leasing versus NPC of purchasing the durable. Since the size and timing of the cash flow, influence of taxes, and risks associated with buying and leasing are different, they represent two different investment opportunities which are amenable to analysis using PV models. In the following discussion, the after-tax cash flow is considered risk-adjusted, and the problem is treated as riskless.
To compare the lease with the purchase option, the firm considers itself in both roles—that of a lessee and lessor—and finds the maximum lease payment it could pay and be indifferent between purchasing or leasing the durable. We begin by describing the NPC of the lease (NPC L ). Because we are describing the NPC of the lease, cash costs are treated as positive flow, and income that reduces the cost of leasing is treated as negative cash flow. For simplicity, we will assume a maximum constant lease payment equal to C. Then we assume the lease payment at age t is C t , the lessee’s constant marginal tax rate is T, the lessee’s before-tax opportunity cost of capital is r, and the lessee’s tax adjustment coefficient is θ as described in Chapter 11. With these definitions in place, the net present cost of a lease for n periods, NPC L , can be expressed as:
\[-N P C^{L}=C(1-T)+\frac{C(1-T)}{[1-r(1-\theta T)]}+\cdots+\frac{C(1-T)}{[1-r(1-\theta T)]^{n-1}} \label{18.1}\]
Notice in Equation \ref{18.1} that the first lease payment is made at the beginning of the lease payment rather than at the end of the lease period, which would be the case of a loan. Therefore, leases can be viewed as an annuity due type of financial arrangement. Multiplying both sides of Equation \ref{18.1} by and summing the resulting geometric series, we write the result as:
\[N P C^{L}=C(1-T)\left\{1+U S_{0}[r(1-\theta T), n-1]\right\} \label{18.2}\]
where:
\[U S_{0}[r(1-\theta T), n-1]=\frac{C(1-T)}{[1-r(1-\theta T)]}+\cdots+\frac{C(1-T)}{[1-r(1-\theta T)]^{n-1}} \label{18.3}\]
We now consider the net present cost of a cash purchase, NPC P , for the same financial manager who previously considered the lease option. We begin by assuming that the market value of the durable leased or purchased is equal to V 0 . We also assume that is the book value of the depreciable durable at age t. We continue to assume that the purchaser’s opportunity cost of capital is r , the average tax rate is T , and is the percentage of the investment’s value allowed to be deducted in year t where t = 1, …, n , and the tax adjustment coefficient is . Of course, the sum of the amount deducted cannot exceed the value of the investment so that . All these assumptions allow us to write the NPC P as:
\[\begin{align} N P C^{P}=V_{0}-\frac{T \gamma_{1} V_{0}}{[1+r(1-\theta T)]}-\cdots \\[4pt] -\frac{T \gamma_{n} V_{0}}{[1+r(1-\theta T)]^{n}}-\frac{V_{n}-T \gamma_{n} V_{n}}{[1+r(1-\theta T)]^{n}} \label{18.4} \end{align}\]
The purchaser’s cost on the right-hand side of Equation \ref{18.4} is the purchase price V 0 , less n periods of tax savings from depreciation equal to in the period discounted to the present period. The liquidation value V n minus a tax adjustment term reduces the purchaser’s cost. The adjustment term accounts for the tax consequences of a difference between the liquidation value and the book value of the investment. If the investment is completely depreciated by the n th period, and the liquidation value is zero, then the NPC P can be written as:
\[N P C^{P}=V_{0}-\frac{T \gamma_{1} V_{0}}{[1+r(1-\theta T)]}-\cdots-\frac{T \gamma_{n} V_{0}}{[1+r(1-\theta T)]^{n}} \label{18.5}\]
Finally, if the NPC L , expressed as the right-hand side of Equation \ref{18.2}, is equated to NPC P , expressed as the left-hand side of Equation \ref{18.5}, we can solve for the lease payment C, a maximum bid lease, which equates the two alternatives for controlling the services from the durable.
\[C=\frac{N P C^{p}}{(1-T)\left\{1+U S_{0}[r(1-\theta T), n-1]\right\}} \label{18.6}\]
Consider an example. Go Green is a lawn service that requires a new truck to service its customers. It wants to know the largest lease payment it could afford and still be as well off as it would be if it purchased the truck. The truck in question has a new sticker price of $30,000 and can be depreciated using a straight-line method over five years. At the end of the lease, the truck has a liquidation value of $5,000. To find the maximum bid payment, the following assumptions are used: T = 32%, for t = 1, …, 5, r = 14%, = 1, n = 5, V n = $5,000, and . Finally, the after-tax discount rate is r (1 – T ) = .14(1 – .32) = .095
To find the maximum bid payment, we first find NPC P by substituting numerical values into Equation \ref{18.6}:
\[N P C^{P}=\$ 30,000-(.32)(\$ 6,000) U S_{0}(0.095,5)-\frac{\$ 5,000(1-.32)}{(1.0952)^{5}} \label{18.7}\]
We record the solution to this problem using Excel in Table 18.1 below.
| C10 | Function : | =NPV(C3,C4:C9) | ||
| A | B | C | D | |
| 1 | Finding the NPC of the Purchase | |||
| 2 | Purchase Price | $30,000.00 | ||
| 3 | rate | .095 | ||
| 4 | Depreciation tax savings period 1 | ($1,920) | ||
| 5 | Depreciation tax savings period 2 | ($1,920) | ||
| 6 | Depreciation tax savings period 3 | ($1,920) | ||
| 7 | Depreciation tax savings period 4 | ($1,920) | ||
| 8 | Depreciation tax savings period 5 | ($1,920) | ||
| 9 | After-tax salvage value period 6 | ($3,100) | ||
| 10 | NPV of depreciation tax savings + after-tax salvage | ($9,170.60) | “=NPV(rate, value1:value6) | |
| 11 | NPC: purchase price – (PV of tax-savings + salvage value) | $20.829.40 | “=NPV of depreciation tax savings + after-tax salvage plus the purchase price (C10+C2) |
In cell C10 we enter the function: = NPV(rate,values) = NPV(C3,C4:C9) which returns the value ($9,170.60). In cell C11 we add the purchase price of $30,000 to the NPC of after-tax depreciation savings plus the liquidation value which returns the NPC of the purchase equal to $20,829.36.
Having found equal to $20,829.40, we can find C using Equation \ref{18.6}.
We solve this problem using Excel in Table 18.2 by finding the present value of Annuity Due with 5 payments of –1. We enter the arguments of the PV function and label the terms in adjacent cells. Excel’s PV function has the following arguments listed in column A: rate (rate), number of payments (nper), annuity (pmt), future value (FV), annuity type (type). For this problem, the discount rate is 9.5% = .095, the number of payments equals 5, the payments are –1, the future value FV is zero, and the type of annuity is an annuity due which requires we enter 1.
Table 18.2. Finding the PV
of the Annuity Due
Open Table 18.2 in Microsoft Excel
| B6 | Function : | =PV(B1,B2,B3,B4,B5) | |
| A | B | C | |
| 1 | rate | .095 | |
| 2 | nper | 5 | |
| 3 | pmt | -1 | |
| 4 | FV | 0 | |
| 5 | type | 1 | |
| 6 | PV | $4.20 | “=PV(rate,nper,pmt,FV,type) |
In cell B6 we type in the PV function: = PV(B1,B2,B3,B4,B5). The result returned is PV = $4.20. Then we multiply by (1 – T ) as required in Equation \ref{18.6}. Finally we find C:
\[C=\frac{N P C^{P}}{(1-T)\left\{1+U S_{0}[r(1-\theta T), n-1]\right\}}=\frac{\$ 20,829.40}{.68(4.2)}=\$ 7,283.01 \label{18.8}\]
Now suppose that we wanted to know the number of periods required to reach a future value of $2,000. With the data already entered, we turn to the “goal seek” option in Excel. To access goal seek from the main menu, press the [Data] tab, then on the ribbon menu press the [What-if Analysis] button, and on the drop down menu press [Goal Seek…]. The goal seek menu allow us to identify a target value for a particular cell and a variable to change. In our case the target cell is B6 and the target amount is $2,000. The cell we allow to vary is the number of periods cell, B2. Then entering these into Excel’s solver, the solution returned is 18.57. Thus, by continuing to invest for 8.57 periods, we obtain a future value of $2,000 compared to the future value of $1,005.18 reached after 10 years of investing.
Alternatively, we could have asked what is the payment amount required to reach a future value of $2,000 during the original term. In this case we vary the annuity in cell is B3, and the solver returns the value of $182.65. Thus, by increasing our annuity due from $90 to $182.65, we reach a future value amount of $2,000 in the same term required to reach a future value of $1,005.18 with $90 annuity due payments.
What we have found in this example is that we would be indifferent between purchasing the truck for $30,000 and making five lease payments of $7,283.01. Obviously, the high discount rate of 14% and making the payment for the truck up front contributes to the high lease payment. In the questions at the end of this chapter, students will be asked to repeat the problem assuming the same values except that the opportunity cost of capital is 5%.
Comparative Advantages for Leasee and Leasor
So far, we have described the technical properties of leases and how a financial manager may decide between gaining control of a durable through a lease or purchase arrangement. In this section, we allow the lessee and the lessor to be two different persons whose comparative advantages lead them into an exchange arrangement in which one party purchases an asset and then leases it to another party. The solution in this case considers the NPC from the lessee’s (lessor’s) position, assuming that the lessor (lessee) pays their maximum bid purchase price (lease payment). What makes this an interesting problem is that differences in the lessee’s and lessor’s tax rates, as well as opportunity costs of capital, can create incentives to exchange.
Comparative advantage. A fundamental principle of economics is that firms should specialize in tasks for which nature, institutions, or luck has granted them an advantage. To illustrate, suppose two farmers, A and B, can both produce dry edible beans and carrots. Also assume A can grow dry edible beans and carrots more profitably than B, and B can grow carrots more profitably than it can grow dry beans. If both beans and carrots must be produced, then A should produce beans, and B should grow carrots. They could then trade to obtain what they did not produce, and both would be better off.
Even though A produced both beans and carrots more profitably than B, it would still be to A’s and B’s advantage to specialize. They should decide in which product A had the greatest advantage in production, or B had the least comparative disadvantage, and then specialize and trade as before.
An application of the law of comparative advantage explains why two firms may lease. Suppose firm A is able to purchase a durable at a lower price than firm B. But firm B, not firm A, has need of the services of the durable. In this case, firm A’s advantage is in purchasing while B’s advantage is in using the durable. Thus, A might purchase the durable and either sell or lease to B.
Another reason why A and B might both agree to lease has to do with relative tax rates. Suppose A, the purchaser of a durable, pays taxes at an average rate T P , which is higher than T L , the average rate at which B, the lessee, pays taxes. As the durable is depreciated, the depreciation creates a tax shield of greater value to the purchaser than to the lessee. Thus, we might say that A, the purchaser, has a comparative tax advantage over B, the lessee, in claiming tax depreciation. The lease allows the purchaser, A, and the lessee, B, to benefit from their comparative advantages associated with the tax shields created by depreciation.
Still further reasons why A and B might purchase and lease a durable are that they face different opportunity costs of capital, have different opportunities for using the durable’s services, or face different marginal costs of credit.
Comparative advantages for lessee and lessor created by different tax rates and opportunity costs of capital. To demonstrate the idea of comparative advantage with a lease agreement, consider that person B, the lessee, will not lease for more than it would cost to control the durable through a purchase agreement. We want to find B’s NPC if the durable were purchased. To simplify, assume the purchase price of the durable is V 0 , the book value depreciation rate in year t is where t = 0, …, n – 1, r B is B’s opportunity cost of capital, T B is B’s average tax rate, and assume the lessee tax adjustment coefficient is 1. The NPC P of the purchase for B is:
\[N P C^{L}(\text {purchase})=V_{0}-\frac{T^{B} \gamma V_{0}}{\left[1+r^{B}\left(1-T^{B}\right)\right]}-\frac{T^{B} \gamma V_{0}(1-\gamma)}{\left[1+r^{B}\left(1-T^{B}\right)\right]^{2}} -\frac{T^{B} \gamma V_{0}(1-\gamma)^{2}}{\left[1+r^{B}\left(1-T^{B}\right)\right]^{3}}-\cdots \label{18.9}\]
Equation \ref{18.9} is equivalent to Equation \ref{18.4} except that it is expressed in a form that makes it analytically tractable. Obviously, more detailed expressions with finite time horizons could easily be calculated. What makes Equation \ref{18.9} tractable is that it is expressed as an infinite series whose solution can be written as:
\[N P C^{L}(\text {purchase})=V_{0}-\frac{T^{B} \gamma V_{0}}{r^{B}\left(1-T^{B}\right)+\gamma} \label{18.10}\]
Now consider what happens to B’s NPC resulting from the purchase if B’s tax rate increases. We find the change in B’s NPC associated with the purchase of the durable by differentiating NPC P with respect to T B . (This operation in essence examines the change in NPC P with respect to a small change in T A . The results is that NPC P decreases with an increase in T B . Thus, a firm in a higher tax bracket can buy a durable at a lower after-tax cost than someone in a lower tax bracket.
Next, we find B’s NPC L associated with leasing the durable which, after summing geometrically, can be expressed as:
\[\begin{align} N P C^{L}(\text {lease}) &=\frac{C\left(1-T^{B}\right)}{\left[1+r^{L}\left(1-T^{B}\right)\right]}+\frac{C\left(1-T^{B}\right)}{\left[1+r^{L}\left(1-T^{B}\right)\right]^{2}} +\frac{C\left(1-T^{B}\right)}{\left[1+r^{L}\left(1-T^{B}\right)\right]^{3}}+\cdots \\[4pt] &=\frac{C\left[1+r^{L}\left(1-T^{B}\right)\right]}{r^{L}} \label{18.11} \end{align}\]
To illustrate Equation \ref{18.10} consider the following example: Suppose Affordable Assets (AA) buys durables and leases them to other firms. As a well-to-do established firm, AA’s tax rate, T A is high—45 percent. On the other hand, the Unendowed User (UU) lacks capital and prefers to lease rather than own in order to protect its limited credit. Because of its lower earnings, UU’s average tax rate T U is 21 percent. In addition, assume that the leased durable wears out at the rate of = 10 percent, and assume the market rate of return for both AA and UU is 14 percent. Finally, assume that the purchase price of the durable is $4,000.
Making the appropriate substitutions into Equation \ref{18.10}, we find the NPC of purchasing the durable for UU is:
\[N P C^{U U}=\$ 4,000-\frac{[(.21)(.1)(\$ 4,000)]}{[(0.14)(1-0.21)+0.1]}=\$ 3,600 \label{18.12}\]
In other words, the after-tax purchase price of the durable for UU is $3,600.
Now consider the after-tax NPC of the purchase for firm AA. Making the appropriate substitutions into Equation \ref{18.10}, we find the NPC of purchasing the durable for AA is:
\[N P C^{A A}=\$ 4,000-\frac{[(0.45)(0.1)(\$ 4,000)]}{[(0.14)(1-0.45)+0.1]}=\$ 3,000 \label{18.13}\]
In other words, the after-tax cost of the durable purchase for AA was only $3,000 compared to $3,600 for UU.
Having calculated NPC for purchasing the durable for firms UU and AA, we can find their respective maximum bid lease prices. Making the appropriate substitutions into Equation \ref{18.11}, we find
\[NPC^{UU} (leasing) = \dfrac{C^{UU}[1 + (0.14)(1 – 0.21)]}{0.14} = \$3,600.\]
Solving for \(C^{UU}\) we find \(C^{UU} = \$453.81\).
Similarly we find
\[NP^{AA} (leasing) = \dfrac{C^{AA}[1 + (0.14)(1 – 0.45)]}{0.14} = \$3,000.\]
Solving for \(C^{AA}\) we find \(C^{AA} = \$389.97\).
Reflections on comparative advantages for firms UU and AA. Because of their differences in tax rates, firms UU and AA have different effective after-tax cost of the durable even though the market price of the durable is the same for each firm. In this case, the effective cost for AA is less than for firm UU—$3,000 versus $3,600. On the other hand and as a result of the differences in the effective after tax cost of the durable, the maximum bid lease price for firm UU is greater than for firm AA: $453.81 versus $389.97.
These results provide opportunities for firms AA and UU to take advantage of their comparative advantages: firm AA purchases the durable at a lower effective cost than is available to UU. UU, on the other hand, is quite willing to pay a higher lease price than AA’s maximum bid lease price. Under these arrangements, both firms AA and UU are made better off.
Leases and NPV. Assume that firm AA buys the durable and UU leases the durable from AA. Now the lease price in an expense for firm UU but an income for AA. We may want to ask: what is the minimum lease payment AA could accept from UU and still break even? To find this amount we set AA’s NPV as:
\[N P V^{A A}=\frac{C\left[1+r\left(1-T^{A A}\right)\right]}{r-N P C^{A A}(\text {purchase})} \label{18.14}\]
After making the appropriate substitutions we find
\[C=\frac{N P C^{A A}(\text {purchase})\left(r^{A A}\right)}{\left[1+r^{A A}\left(1-T^{A A}\right)\right]}=\frac{\$ 3,000(.14)}{[1+(.14)(1-.45)]}=\$ 389.97 \label{18.15}\]
Thus, any arrangement with UU which generates a lease payment more than $389.97 will result in a positive NPV for AA.
Summary and Conclusions
Trades occur when each party to the exchange gives up something of value in return for something of greater value. In most trades, a physical object or service is exchanged for an agreed-on amount of cash. Moreover, in most cases, ownership is transferred along with the good or service.
This chapter has considered leasing, a different kind of trade, in which the control over the use of a durable is transferred, but ownership of the durable is not. Leasing exists because it provides benefits to the lessee and lessor that might not be realized if control of a durable also required ownership.
Different types of leases described in this chapter include sale-and-leaseback agreements, operating leases, and financial or capital leases. Leases offer particular advantages for lessees including the avoidance of capital requirements associated with a purchase. As a result, lessees may use their limited credit for other purchases or as a credit reserve. Obsolescence risk of ownership is also reduced for lessees. Additionally, leasing offers the chance to better match service requirements to the delivery of services. Ownership of durables may require holding idle capacity—less likely when services of a durable are leased.
Tax considerations are critical in the decision to lease or to purchase. Ownership allows for tax depreciation shields; leasing allows the entire lease payment to be claimed as an expense.
An important principle of comparative advantage is involved in the lease decision. If the tax depreciation from ownership is greater for one firm than for another, leasing permits the firm which can benefit the most from the depreciation shield to claim it by purchasing the asset and leasing it to another firm. Not only can comparative tax advantages be optimally used through leasing, there can also be comparative advantages in acquiring financing. Comparative advantage and the incentive to lease may also result from differences in opportunity costs, access to credit, and use for the durables’ services. In essence, leasing is a critical tool that allows firms to benefit from their comparative advantages.
Questions
- Describe three different lease types and their essential differences.
- For every lease agreement, there is a lessor and a lessee who both believe they will be better off by executing the lease. Describe how a sale and leaseback agreement might make both the lessor and lessee better off.
- Assume a lease agreement that requires $100 payments at the beginning of each period for 15 years. The lessee’s marginal tax bracket is 25% and opportunity cost of capital is 8%. The tax adjustment coefficient is assumed to equal 80%. Find the NPC of this lease. Now assume that the lessor agreed to accept payments at the end of each period instead of the beginning. What would be the NPC of the lease agreement under the new arrangement?
- Resolve the Go Green lease problem assuming that the firm’s opportunity cost of capital is 5% rather than 14%. Compare your solution with the previous one. Did the lease payment go up or down? Can you explain why?
- Resolve the Go Green lease problem by assuming that the lessee will lease the durable for an extra period. The lessee will make 6 lease payments instead of 5, but the depreciation schedule will not change. In other words, find the maximum lease payment and explain your results.
- Explain in your own words the concept of comparative advantage. Provide one example of how the concept of comparative advantage has influenced your choice or the choice of others.
- Explain how the principle of comparative advantage might explain why two firms may agree to a lease arrangement.
- In the example of a lessee UU and a lessor AA, the lessee and lessor are in different average tax brackets (45 versus 21 percent) but were assumed to face the same opportunity cost of capital. Resolve the example by assuming UU’s opportunity cost of capital is 7% instead of 14%. Find the effective after-tax purchase price of the durable for the two firms. Then find the maximum bid lease price for the two firms. Do the results allow for the two firms to take advantage of the principle of comparative advantage? Please explain.
- Consider the case of firms UU and AA described in the text. Since AA has the lowest NPC for purchasing the durable, it should do so. Meanwhile the maximum bid lease price for UU is higher than for AA, so UU should lease rather than purchase the durable. Suppose that UU agrees to pay AA a lease price of $410.00. What is AA’s NPV from buying the durable and leasing it back to UU? (Hint: In this arrangement, the lease cost for UU is an income for AA.)


2.0: What Does Psychology Say?
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Luisa is ten weeks pregnant with her first child and has been struggling with morning sickness. Nothing tastes right except for her favorite avocado roll from the sushi place nearby. Luisa knows she isn’t supposed to have raw fish but is unsure whether that means all sushi is risky. She’s already concerned about the half glass of wine she had at Thanksgiving before she knew she was expecting, and she just heard that the cup of coffee she enjoys every morning might be dangerous to the developing baby. She has started wondering whether her child will inherit her curly hair and height. On top of that, Luisa is interested in learning about home birth. When she suggested this, her mother insisted that she should give birth only in a hospital. At least she and her partner agree that they want only one biological child, and he will get a vasectomy after the baby’s birth. Lately, he has been hesitant and nervous about the procedure and has questions about recovery. Like many expecting and new parents, she wonders:
In this chapter, you’ll find out what current research says about questions like these and more.


10.5: Keeping Management Issues in Perspective
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There are two primary messages from this chapter. One is that management issues are important, complex, and deserving of serious attention. The other is that strategies exist that can reduce, if not eliminate, management problems when and if they occur. We have explained some of those strategies— including some intended to prevent problems and others intended to remedy problems.
But there is an underlying assumption about management that this chapter emphasized fully: that good classroom management is not an end in itself, but a means for creating a classroom where learning happens and students are motivated. Amidst the stresses of handling a problem behavior, there is a risk of losing sight of this idea. Telling a student to be quiet is never a goal in itself, for example; it is desirable only because (or when) it allows all students to hear the teacher's instructions or classmates' spoken comments, or because it allows students to concentrate on their work. There may actually be moments when students' keeping quiet is not appropriate, such as during a "free choice" time in an elementary classroom or during a group work task in a middle school classroom. As teachers, we need to keep this perspective firmly in mind. Classroom management should serve students' learning, and not the other way around. The next chapter is based on this idea, because it discusses ways not just to set the stage for learning, as this chapter has done, but ways to plan directly for students' learning.


4.15: The Endomembrane System and Proteins - Peroxisomes
- Name the various functions that peroxisomes perform inside the cell
Peroxisomes
A type of organelle found in both animal cells and plant cells, a peroxisome is a membrane-bound cellular organelle that contains mostly enzymes. Peroxisomes perform important functions, including lipid metabolism and chemical detoxification. They also carry out oxidation reactions that break down fatty acids and amino acids.
In contrast to the digestive enzymes found in lysosomes, the enzymes within peroxisomes serve to transfer hydrogen atoms from various molecules to oxygen, producing hydrogen peroxide (H 2 O 2 ). In this way, peroxisomes neutralize poisons, such as alcohol, that enter the body. In order to appreciate the importance of peroxisomes, it is necessary to understand the concept of reactive oxygen species.
Reactive oxygen species (ROS), such as peroxides and free radicals, are the highly-reactive products of many normal cellular processes, including the mitochondrial reactions that produce ATP and oxygen metabolism. Examples of ROS include the hydroxyl radical OH, H 2 O 2 , and superoxide (O −2 ). Some ROS are important for certain cellular functions, such as cell signaling processes and immune responses against foreign substances. Many ROS, however, are harmful to the body. Free radicals are reactive because they contain free unpaired electrons; they can easily oxidize other molecules throughout the cell, causing cellular damage and even cell death. Free radicals are thought to play a role in many destructive processes in the body, from cancer to coronary artery disease.
Peroxisomes oversee reactions that neutralize free radicals. They produce large amounts of the toxic H 2 O 2 in the process, but contain enzymes that convert H 2 O 2 into water and oxygen. These by-products are then safely released into the cytoplasm. Like miniature sewage treatment plants, peroxisomes neutralize harmful toxins so that they do not cause damage in the cells. The liver is the organ primarily responsible for detoxifying the blood before it travels throughout the body; liver cells contain an exceptionally high number of peroxisomes.
Contributions and Attributions
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- Lysosome. Provided by : Wikipedia. Located at : en.Wikipedia.org/wiki/Lysosome . License : CC BY: Attribution
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Key Points
- Lipid metabolism and chemical detoxification are important functions of peroxisomes.
- Peroxisomes are responsible for oxidation reactions that break down fatty acids and amino acids.
- Peroxisomes oversee reactions that neutralize free radicals, which cause cellular damage and cell death.
- Peroxisomes chemically neutralize poisons through a process that produces large amounts of toxic H 2 O 2 , which is then converted into water and oxygen.
- The liver is the organ primarily responsible for detoxifying the blood before it travels throughout the body; as a result, liver cells contain large amounts of peroxisomes.
Key Terms
- enzyme : a globular protein that catalyses a biological chemical reaction
- free radical : Any molecule, ion or atom that has one or more unpaired electrons; they are generally highly reactive and often only occur as transient species.