1. Send email to [email protected] after handshake payment
2. I will then send you solutions to the work
3. We will rejoin in 24 to 30 hours to take the exam
4. 4 hour time limit
5. I will send you the questions
6. You will email it back
The test covers Chapter 6 Discounting Benefits and Costs in Future Time Periods, Chapter 7 Dealing with Uncertainty, Expected Values and Sensitivity Analysis, and Chapter 14 Valuing Observed Behavior Indirect Methods. Your time to finish the test is limited so make sure you prepare and study the posted notes, class recordings, and assignments. You need to remember and understand the concepts to be able to answer the questions and solve the problems correctly and within the allotted time. You will not have enough time to finish the test if you have to spend time looking for the answers on your notes or if you have to spend too much time figuring out the problem sets.
The test is composed of multiple choice, true or false, essay type questions, and problem sets.
Joseph Toppe
MondayDec 4 at 9:04am
Manage Discussion Entry
Passion and Objectivity
Quite often, reporters are asked to cover an issue they are passionate about. However, reporters must remain objective and accurate. The greatest challenge for even the most objective of reporters is to utilize an objective story angle as well.
But is this possible? Pure objectivity in journalism is difficult to achieve because of the human factor. Whether a writer knows it or not, the second they choose the story angle, the objectivity of the work has been diminished. Writing about passionate topics such as conservation and culture can stir the emotions of any staff writer, but the elements of the trade remain.
Professional reporters unlock new angles to trending topics and write passionately about it, but they do it with professional/acceptable objectivity and accuracy.
Essentially, provide a balanced debate and allow your readers to reach their own conclusions.
Week 4 - AssignmentEnvironmental/Cultural News Story and Broadcast Script
In today’s society, we hear a lot of discussion about the environment and about cultures. Environmental journalism and cultural journalism require that the journalist be committed to educating the public about aspects of each topic that audiences may know very little about.
This assignment requires you to choose a topic related to the environment or a specific culture. You will be writing the story as a feature for a national newspaper and preparing a script for a television program that appears on the Public Broadcasting Service. You will write a 450- to 500-word print story and a 3- to 5-minute broadcast script about the issue that you chose.
The assignment must
· Identify the media outlets where the story will appear.
· Summarize facts and/or statistics that are relevant to the story.
· Compare two opposing opinions about the topic derived from CQ Researcher.
· Incorporate one visual ...
Vani Magazine - Quarterly Magazine of Seshadripuram Educational Trust
1. Send email to [email protected] after handshake payment2. I w.docx
1. 1. Send email to [email protected] after handshake payment
2. I will then send you solutions to the work
3. We will rejoin in 24 to 30 hours to take the exam
4. 4 hour time limit
5. I will send you the questions
6. You will email it back
The test covers Chapter 6 Discounting Benefits and Costs in
Future Time Periods, Chapter 7 Dealing with Uncertainty,
Expected Values and Sensitivity Analysis, and Chapter 14
Valuing Observed Behavior Indirect Methods. Your time to
finish the test is limited so make sure you prepare and study the
posted notes, class recordings, and assignments. You need to
remember and understand the concepts to be able to answer the
questions and solve the problems correctly and within the
allotted time. You will not have enough time to finish the test if
you have to spend time looking for the answers on your notes or
if you have to spend too much time figuring out the problem
sets.
The test is composed of multiple choice, true or false, essay
type questions, and problem sets.
Joseph Toppe
MondayDec 4 at 9:04am
Manage Discussion Entry
Passion and Objectivity
Quite often, reporters are asked to cover an issue they are
passionate about. However, reporters must remain objective and
accurate. The greatest challenge for even the most objective of
reporters is to utilize an objective story angle as well.
But is this possible? Pure objectivity in journalism is difficult
to achieve because of the human factor. Whether a writer knows
it or not, the second they choose the story angle, the objectivity
2. of the work has been diminished. Writing about passionate
topics such as conservation and culture can stir the emotions of
any staff writer, but the elements of the trade remain.
Professional reporters unlock new angles to trending topics and
write passionately about it, but they do it with
professional/acceptable objectivity and accuracy.
Essentially, provide a balanced debate and allow your readers to
reach their own conclusions.
Week 4 - AssignmentEnvironmental/Cultural News Story and
Broadcast Script
In today’s society, we hear a lot of discussion about the
environment and about cultures. Environmental journalism and
cultural journalism require that the journalist be committed to
educating the public about aspects of each topic that audiences
may know very little about.
This assignment requires you to choose a topic related to the
environment or a specific culture. You will be writing the story
as a feature for a national newspaper and preparing a script for
a television program that appears on the Public Broadcasting
Service. You will write a 450- to 500-word print story and a 3-
to 5-minute broadcast script about the issue that you chose.
The assignment must
· Identify the media outlets where the story will appear.
· Summarize facts and/or statistics that are relevant to the story.
· Compare two opposing opinions about the topic derived from
CQ Researcher.
· Incorporate one visual element to enhance the story.
The print news story must be written according to the
Newspaper Feature Template and it must adhere to Associated
Press (AP) Style. The broadcast script must adhere to the
Broadcast Story Script Template. Be sure to provide proper
attribution for all sources of information included in the story
(facts, statistics, images/video, and opinions) and list each of
the sources in the Story Source List Template. View the Using
3. Templates document for assistance with modifying templates.
Check It! Your assignment must be submitted through
Grammarly prior to submission.
Saving Your Work: To maintain the formatting of your work,
you are strongly encouraged to save your assignment as a PDF
file. View Saving a Word Document as a PDF for steps on how
to do this.
Carefully review the Grading Rubric (Links to an external
site.)Links to an external site. for the criteria that will be used
to evaluate your assignment.
Tiffany VanVolkinburg
ThursdayDec 7 at 10:57pm
Manage Discussion Entry
I think that cultural competence is paramount to being a
successful reporter. If a reporter is unable to culturally
understand the people involved in a news story, as well as the
viewership/readership of that news story, then they are not able
to fully deliver a well-rounded or all-encompassing version of
the story.
The assigned reading, At the Community Level: Cultural
Competence and News Coverage of a City Neighborhood,
defines cultural competence as "the extent to which individuals
develop the awareness, knowledge, and skills necessary to
understand and work effectively with communities and people
from diverse cultures" (Garyantes, 2012). Therefore, in my own
community, reporters could not be successful without cultural
competence. I live in an extremely diverse community with
citizens from countless socioeconomic backgrounds and the
inability to interact and communicate with those people would
hinder any news report.
With the growth of diversity and cross-culture interaction
happening in the world, which I believe is largely due to
technology, the concept of cultural competence has expanded
beyond the journalism profession. When I was reviewing
4. varying analysis and commentary on cultural competency for
this assignment, I came across an overwhelming amount of
information geared toward teaching cultural awareness in
schools and varying professions. This vast amount of
information lends to my belief that cultural competence is
necessary for daily living, even beyond the workplace.
One article about enhancing a student's cultural competence
stated that "it is not sufficient to teach cultural knowledge or
language proficiency," (Bertolo & Kratzke, 2013). Further
saying that we must learn to examine our own cultural
knowledge, values, and beliefs to improve our cultural
competence; otherwise, our perceptions can limit our
willingness to work with other cultures.
I wholeheartedly agree with this statement in regards to the
journalistic profession. To work with and report on topics that
effect a multitude of backgrounds, our perception of those
varying cultures will be reflected in the stories we deliver. And
if, as reporters, we have a limited or obscured perception, I
believe it can only hinder our work. Garyantes wrote, "the ways
in which reporters are influenced by their social groups and
personal experiences have the potential to affect the way in
which they perceive and report on culturally diverse
communities and culturally different 'Others.' These perceptions
can make their way into news content, and audiences could in
turn be influenced by these texts" (2012). This makes
demonstrating cultural competence and absolute necessity in
news reporting.
Tiffany VanVolkinburg
References
Garyantes, D. M. (2012). At the community level: Cultural
competence and news coverage of a city neighborhood.
Community Journalism, 1(46). Retrieved from
http://journal.community-
journalism.net/sites/default/files/garyantes-cj1-2012.pdf (Links
to an external site.)Links to an external site.
5. Kratzke, C., & Bertolo, M. (2013). ENHANCING STUDENTS'
CULTURAL COMPETENCE USING CROSS-CULTURAL
EXPERIENTIAL LEARNING. Journal Of Cultural Diversity,
20(3), 107-111.
Tiffany VanVolkinburg
ThursdayDec 7 at 10:21pm
Manage Discussion Entry
After reading Climate Change in the Newsroom: Journalists’
Evolving Standards of Objectivity When Covering Global
Warming and evaluating objectivity in journalism, I do think
there is a significant difference in objective environmental
reporting from other types of reporting. Nevertheless, I don't
think that makes these news stories any less valid, I just think
the typical way objectivity is defined in most news reporting
isn't applicable to environmental journalism—as highlighted in
the article.
In one analysis of objective journalism techniques, the authors
wrote, "It was believed that objective journalism would benefit
the public by providing unembellished and unbiased
presentations of facts from which people could formulate their
own conclusions" (Holbert & Zubric, 2000). Environmental
journalism doesn't necessarily follow this form of objectivity
because it has already formulated certain conclusions, like
humans have contributed to climate change—though the how is
still debatable (Hiles & Hinnant, 2014)—because of consensus
among scientists in the field.
On the other hand, the analysis conducted by Holbert and
Zubric also stated that objectivity was "a way to delineate facts
from feelings, truths from opinions...It was hoped that the
extraction of reporter biases would yield a more pure form of
news reporting based singularly on facts—not absolute facts,
but verified, consensual facts" (2000). With this definition,
some aspects of objectivity carried over into environmental
journalism's altered form of objectivity—which was changed
out of necessity. The reason I believe aspects have carried over
6. is because of the end of that quote: "facts—not absolute facts,
but verified, consensual facts." In environmental journalism,
those facts about climate change are verified in the scientific
community and are the current consensual facts.
So, while journalists who cover this topic may have had to
redefine objectivity in their reporting to present a more
balanced and less argumentative story, they are still meeting
journalistic standards of reporting. Furthermore, I agree with
the notion that no story can be completely unbiased, and
subsequently objective, because of the human factor. But, as
stated in Hiles and Hinnant's article, "the very act of choosing a
certain story or a certain source is a subjective decision. The
best way to show your commitment is to write about it, in an
intelligent way, in a fair way, and when the situation calls for
it, in a balanced way" (2014).
Tiffany VanVolkinburg
References
Hiles, S. S., & Hinnant, A. (2014). Climate change in the
newsroom: Journalists’ evolving standards of objectivity when
covering global warming. Science Communication, 36(4), 428-
453. doi:10.1177/1075547014534077
Holbert, L. R., & Zubric, S. J. (2000). A comparative analysis:
Objective & public journalism techniques. Newspaper Research
Journal, (4),
Luis Torres
ThursdayDec 7 at 4:49pm
Manage Discussion Entry
I think cultural competence is an essential aspect of news
reporting; the knowledge about the community is shown on the
reports and this factor makes a significant impact on the public.
Understanding the way each community thinks and feels, helps
in the distribution of the news. According to Garyantes (2012),
"A culturally competent journalist would develop an
understanding of "macro" and "micro" aspects of a culture and
7. have the ability to convey those aspects of culture to a mass
media audience." (p. 51). Communicating with the public
showing knowledge of their community means not only
establishing a good connection but one that will grow roots.
There are many skills involved in creating a good relationship
that shows cultural competence, like avoiding stereotypes and
provide information in a way that makes sense for the people
listening, viewing or reading the news. Showing respect for
community values and addressing issues with respect are
essential factors for an excellent communication.
Cultural competence is perfect to establish a unique and
familiar connection with the public, making them feel identified
and appreciated; is quite popular among citizen journalists. "If
we take a closer look at the dominant criteria used by citizen
and professional journalists in their selection of news and
events, we observe a dramatic discrepancy between citizens' and
professionals' selection practices again." (Paulussen & D'heer,
2013). I have great respect for journalists in my community and
feel that cultural competence is smartly used in news media to
show appreciation and respect for the community.
Luis Torres
References
Garyantes, D. M. (2012). At the community level: Cultural
competence and news coverage of a city neighborhood .
Community Journalism,1(46). Retrieved from
http://journal.community-
journalism.net/sites/default/files/garyantes-cj1-2012.pdf
Paulussen, S., & D'heer, E. (2013). Using Citizens for
Community Journalism. Journalism Practice, 7(5), 588-603.
doi:10.1080/17512786.2012.756667
Luis Torres
ThursdayDec 7 at 4:51pm
Manage Discussion Entry
Writing in a fair an unbiased manner is the way to be objective
8. when we address any topic. However, not every issue is the
same; some problems like the environment and climate change
can awake passions because of the fixed relation between
damage to the environment and its consequences regarding the
survival of every species on earth, including humans. This view
of the effects of climate change could interfere with a
journalist's ability to write objectively and will be reflected in
the report. "Environmental journalists also face the challenge of
having scientists as primary sources." (Hiles & Hinnant, 2014).
Our sources will play a vital role in our objectivity of the
report. Having sources which represent only one side of the
story could be seen, and in fact, it is a factor that will interfere
with a balanced report. Something else to keep in mind is the
conflict of interests; for example, there've been scientists who
have refused evidence of global warming with the
unconscionable purpose of protecting the interests of the fossil
fuel industry.
Being objective on sensitive issues that concern every single
human being on earth isn't an easy task, and it takes a real
professional to report in a fair and unbiased manner. However,
the topic of global warming, or climate change which are
environmental issues, aren't only controversial; since these are
topics which have mainly been covered for several decades; is
also complicated to make an original and non-repetitive report
about it. Every contentious issue has two sides and is vital to
include both sides in the report. "In most cases, stories that
emphasize only one side of a controversial issue, lead the
audience to see a bias." (Akpan, Martin, Alexander & Uchenna,
2012). To be objective when reporting on environmental issues
a reporter has to maintain a neutral position about it and prevent
personal opinions to interfere with the facts to allow the reader
to reach their conclusions.
Luis Torres
References
Hiles, S. S., & Hinnant, A. (2014). Climate change in the
10. Valuing Impacts from Observed
Behavior: Indirect Market Methods
Using Revealed Preferences
Chapter 14
2
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2
Shadow Pricing
One of the key requirements of performing a CBA is
quantification
of costs and benefits.
However, there are a range of costs and benefits for which a
value
cannot be easily obtained.
Shadow pricing is suitable when there is no market value, or a
market value is not representative of the true value of a good.
3
Shadow Pricing
The methods can be broadly categorized into two:
1. Stated Preference Methods
11. a. Willingness to Pay – asking individuals how much they
would be willing to pay to continue to enjoy a
particular asset e.g. a park.
b. Willingness to Accept – asking individuals how much they
would be willing to accept in compensation for
continuing negative impacts e.g. pollution from a road.
2. Revealed Preference Methods
4
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3
Valuing Impacts from Observed
Behavior: Indirect Market Methods
Purpose: This chapter presents various methods for estimating
shadow
prices based on observed behavior when markets for the
(primary)
good, such as human life, do not exist.
• Considerable progress has been made during the past 30 years
to
value goods that were previously treated as “intangible”.
5
Valuing Impacts from Observed Behavior:
Indirect Market Methods
12. • Estimation of changes in social surplus requires knowledge
of entire demand and supply schedules.
• We have assumed that there is a market demand curve for
the good in question, where we can observe a least one point
on the demand curve.
• However, in many applications of CBA, the markets for
certain goods such as human life and pollution do not exist or
are imperfect.
• Economists have devised methods to value these goods or
their impacts enabling to have a comprehensive CBA.
6
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4
7
• In contrast to “stated” or “expressed” preferences (Chapter
15),
revealed preferences are not collected by asking individuals for
their views.
• They are, instead, collected through direct observation of
actual responses to complement or substitute goods.
• They provide indirect estimates of the value of a cost or
benefit
using surrogate market goods.
13. Valuing Impacts from Observed Behavior:
Indirect Market Methods (Revealed
Preferences)
Simple Valuation Methods
Valuing the impacts of projects using revealed preferences
can be conducted using the following methods:
1. MARKET ANALOGY METHOD
2. THE TRADE-OFF METHOD
3. INTERMEDIATE GOOD METHOD
4. ASSET VALUATION METHOD
5. PREVENTATIVE OR DEFENSIVE EXPENDITURES
APPROACH
6. HEDONIC PRICE METHOD
7. TRAVEL COST METHOD
8
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5
MARKET ANALOGY METHOD
• This method uses data on similar goods in the private market
14. to
estimate the implicit “price” or the demand curve for publicly
provided goods.
• Governments supply many goods that are also provided by the
private sector.
Examples: housing, campsites, university education, home care,
etc.
• The government usually provide these services free or at
significantly below market prices. Thus, the actual price paid
may not
be on the demand curve. However, it may be possible to obtain
an
estimate of the entire demand curve using data from a similar
good
produced by the private sector.
A. Using the Market Price of or Expenditures on an Analogous
Good
B. Using Information about an Analogous Private-Sector Good
to Estimate
the Demand Curve for a Publicly Provided Good
9
MARKET ANALOGY METHOD
A. Using the Market Price of or Expenditures on an Analogous
Good
Example: A local government project provides housing for 50
families and
charging a rent of $200 per month so that government revenue
is $10,000 a
month. This expenditure underestimates benefits because all
15. families
would be willing to pay $200 per month or more.
Suppose that comparable units in the private sector charge rent
of $500 a
month, then the estimated total monthly benefits of publicly
provided
housing would be $25,000 per month.
10
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6
11
MARKET ANALOGY METHOD
• The market price of a comparable good in the private sector
provides a
good estimate of the value of a publicly provided good if it
equals the
average amount that users of the publicly provided good would
be
willing to pay (WTP).
Where the government provides a good or service at a lower
than market
price, the price paid by occupants would generally
underestimate the
benefit of this service because users would be WTP at least this
amount;
some might pay more.
16. MARKET ANALOGY METHOD
B. Using Information about an Analogous Private-Sector Good
to
Estimate the Demand Curve for a Publicly Provided Good
• Rather than focusing on the average amount that users of a
publicly
provided good are willing to pay, it is conceptually better and
easier to think
about the demand curve for the good.
• We can use private-sector data to help map out the demand
curve for a
publicly-provided good if the goods and their markets are
similar.
• However, using expenditures alone underestimates total
benefits because
it ignores consumer surplus.
12
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7
MARKET ANALOGY METHOD
B. Using Information about an Analogous Private-Sector Good
to Estimate the Demand Curve for a Publicly Provided Good
Example: Suppose a municipal government wants to measure
the gross
17. benefits of a swimming pool that it owns and operates. It
doesn’t charge an
admission fee and the pool receives 300,000 visitors per year.
(point a in Figure
14-1).
In a comparable municipality, a privately operated swimming
pool charges $5
for admission and receives 100,000 visitors per year (point b).
If these two
municipalities and pools were comparable, it would be
reasonable to assume
that points a and b are both on the demand curve.
Using revenues at the private pool ($500,000) would
underestimate the
benefits of the public pool because it omits the consumer
surplus of those
willing to pay more than $5, the area of triangle cbd, and those
willing to pay
something less than $5, but more than $0, the area of triangle
bae.
13
Figure 14-1 Demand Curve for Visits to a
Municipal Swimming Pool
14
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8
18. THE TRADE-OFF METHOD
• Economists may use the opportunity cost as a measure of its
value.
• To measure the value of a good or commodity using
opportunity cost –
i.e. the value of what an individual would have to give up to
obtain
something – as a proxy for a good or commodity which has no
market
value.
For example, time saved could be valued using the after-tax
wage rate.
People make trade-offs between time and money wages and we
can use
the rate at which they make this trade-off to value time.
Similarly, the trade-off that people make between changes in
fatality risk
and wages can be used to value a statistical life.
A. The Value of Time Saved, VTTS
B. The Value of a Statistical Life, VSL
Forgone Earnings Method
Simple Consumer Purchase Studies
Simple Labor Market Studies
15
THE TRADE-OFF METHOD
A. The Value of Time Saved, VTTS
19. • The obvious analogous market for time saved is the labor
market.
• In the absence of market imperfections (i.e., people can
choose the
number of hours they work and there is no unemployment), the
wage
rate equals the marginal value of time.
However, using the wage rate is only a first approximation.
16
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9
THE TRADE-OFF METHOD
B. The Value a Statistical Life, VSL
1. Forgone earnings method - This method is an inappropriate
method. It suggests the value of a life saved equals the person’s
discounted future earnings.
• It generates higher values for young, high-income males than
old,
low-income females. For retired people, the resultant value of
life
may be negative.
• Conceptually most problematically, this method does not
reflect
what people are WTP for a small reduction in risk of their
20. death.
17
18
THE TRADE-OFF METHOD
B. The Value of a Statistical Life, VSL
2. Simple Consumer Purchase Studies - This method estimates
the
value of life by observing how much people pay for life-saving
devices, such as safety belts.
• Example: If people are indifferent between paying an extra
$300 to
reduce the probability that they will die by 1/10,000, then they
value
their life at $3 million.
3. Simple Labor Market Studies - Similarly, if a person is
willing to
forgo an extra $3,500/yr to increase the probability that he will
not
have a fatal on-the-job accident by 1/1,000, then he values his
life at
$3.5 million (or more).
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10
INTERMEDIATE GOOD METHOD
21. Intermediate goods – goods that are used as inputs to some
other
downstream business.
If a project produces an intermediate good that is not sold in a
well
functioning market, then its value can be imputed by
determining the
value added to the “downstream activity”:
Annual Benefit = NI(with project) – NI(without project)
where, NI = net income of downstream business. The total
benefit of a
project can be computed by discounting these annual benefits
over the
project’s life.
Example: This method can be used to value improvements in
human
capital, such as training programs, by comparing the average
incomes of
those in the program to those who are not.
19
INTERMEDIATE GOOD METHOD
Example: Valuing the benefits of education and training
programs.
The intermediate good method measures the annual benefit of
human
capital programs by comparing the average incomes of those
who have
22. been enrolled in them and the average incomes of those who
have not.
The total benefits is found by discounting the annual benefits
over the
years people work after graduation and multiplying by the
number of
participants.
Some problems with this method are:
1) It assumes the difference in income captures all of the
benefits (there
may be consumption benefits as well as investment benefits)
2) It assumes all other variables are held constant (e.g.,
educational
ability).
20
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11
ASSET VALUATION METHOD
Government projects often affect the prices of assets such as
land and
housing. The impacts are said to be capitalized into the market
value of
assets.
The impacts of a project or policy can be imputed from changes
23. in the
price for certain capital goods.
Observed increases or decreases in asset values can be used to
estimate the benefits or costs of projects.
This method is often used to value differences in housing. For
example,
data can be collected on average prices of houses with a large
garden,
or close access to a country park. These can be compared
against
houses without those attributes, to obtain an estimate of the
value of
having a large garden or local access to a country park.
21
ASSET VALUATION METHOD
22
More Examples:
• The “value” of noise can be inferred from comparing the price
of a house
in a noisy neighborhood to the price of a similar house in a
quiet
neighborhood.
• The difference in the market prices between houses with a
view and
houses with no view provides an estimate of how much
households are
willing to pay fro a view (assuming that these houses are similar
in all
24. other respects).
An advantage of using market prices is that information is
quickly and
efficiently capitalized into prices so that price changes or price
differences
provide a good estimate of the value of the policy change.
Also,
appropriate data are often available.
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12
PREVENTATIVE OR DEFENSIVE EXPENDITURES
APPROACH
23
• The preventative or defensive expenditure method estimates
the value of
a cost by observing the value of the costs incurred in attempting
to
mitigate or prevent the effects of a negative externality
(something
undesirable) such as pollution.
• If you hire someone to clean your windows periodically, the
cost of this
action in response to the smog is termed a defensive
expenditure – it is
the amount spent to mitigate or even eliminate the effect of a
negative
externality.
25. DEFENSIVE EXPENDITURES METHOD
24
The level of a public good or externality (e.g. smog) and other
goods
(window cleaners) are inputs to some production process
(window
cleaning).
For example, when the negative externality of smog is reduced,
less
labor is required to produce the same number of clean windows.
The
change in expenditures on the substitute input (window
cleaners) is
used as a measure of the benefit of reduction of the public good
or
externality.
The change in expenditures can be used as a measure of the cost
of
the change in pollution.
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13
PREVENTATIVE OR DEFENSIVE EXPENDITURES
APPROACH
25
26. Another Example:
• Using this measure could estimate the cost of noise pollution
from a
road by observing the expenditure of individuals living close to
the road
on double-glazing to block out noise pollution.
• If we wish to estimate the benefits of introducing boarding on
the
sides of the road to block out the noise, we could do so by
looking at
the changes in expenditure on double-glazing by households
located
close to the road over time.
• The limitation of this method is that some actions may be
taken for a
number of reasons, and not solely in order to mitigate a
negative
externality. For example, individuals may invest in double-
glazing to
reduce energy bills, or in order to make their home more
attractive to
potential buyers.
PROBLEMS WITH SIMPLE VALUATION
METHODS
1. Omitted Variable Problem
If a relevant explanatory variable is omitted from the model and
if it is
correlated with the included variables of interest, then the
estimated
coefficients will be biased.
27. Examples:
• The price of a house typically depends on factors such as its
distance
from the central business district and size, as well as whether it
has a
view.
26
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14
PROBLEMS WITH SIMPLE VALUATION
METHODS
2. Self-Selection Bias
The self-selection problem arises whenever different people
attach
different values to particular attributes.
Example: Suppose we want to use differences in house prices to
estimate a shadow price for noise.
People who are not bothered much by noise, possibly because of
hearing disabilities, naturally tend to move into noisy
neighborhoods.
As a result, the price differential between quiet houses and
noisy
houses may be quite small, which would lead to an
underestimation of
28. the shadow price of noise for the “average” person.
27
THE HEDONIC PRICE METHOD
The hedonic price method (sometimes called the hedonic
regression
method) can be used to value an attribute, or a change in an
attribute,
whenever its value is capitalized into the price of an asset, such
as
houses or salaries.
This method offers a way to overcome problems from omitted
variables
and self-selection bias.
It consists of two steps:
1. The first step estimates the relationship between the price of
an
asset and all of the attributes (characteristics) that affect its
value.
From this it derives the marginal effect of an attribute (e.g., a
better
scenic view) on the value of the asset, while controlling for
other
variables that affect the value of the asset.
2. The second step estimates the WTP for the attribute, after
controlling
for “tastes,” which are usually proxied by socioeconomic
factors.
28
29. 8/15/2017
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29
THE HEDONIC PRICE METHOD
Example: Suppose one wants to estimate the value of a scenic
view.
The first step estimates the effect of a marginally better scenic
view on the
value (price) of houses (a slope parameter in a regression
model), while
controlling for other variables that affect house prices.
House and other property prices are not simply determined by
one variable.
They are a product of a number of factors.
The hedonic price method is used to measure the relative
importance –
through use of regression analyses – of these independent
‘explanatory’
variables on house and property prices.
30
THE HEDONIC PRICE METHOD
For example, we may postulate the following multiplicative
model showing
30. the relationship between the price of a house (P) and all of its
attributes,
such as quality of its scenic view (VIEW), its distance from the
central
business district (CBD), its lot size (SIZE), and various
characteristics of its
neighborhood, NBHD:
(14.3)
Equation 14.3 is called a hedonic price function or implicit
price
function. The change in the price of a house that results from a
unit
change in a particular attribute (i.e., the slope) is called the
hedonic
price, implicit price, or rent differential of the attribute.
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31
THE HEDONIC PRICE METHOD
• In a well-functioning market, the hedonic price can naturally
be
interpreted as the additional cost of purchasing a house that is
marginally better in terms of a particular attribute.
• Usually researchers estimating hedonic prices assume the
hedonic
price function has a multiplicative functional form like
31. Equation 14.3.
This means that as a characteristic increases (or improves) the
house
prices increase but at a decreasing rate.
32
THE HEDONIC PRICE METHOD
• The hedonic price of a particular characteristic is therefore the
slope
of this equation with respect to that particular characteristic.
For
example, the hedonic price of scenic views, rv is expressed as:
rv measures the additional cost of buying a house with a slightly
better
(higher-level) scenic view.
In the model, the hedonic price of scenic views depends on the
value of
the parameter β3, the price of the house and the view from the
house.
The hedonic price of a characteristic can be interpreted as the
willingness to
pay of households for a marginal increase in that particular
characteristic.
(14.4)
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32. 33
THE HEDONIC PRICE METHOD
Households differ in their incomes and taste. Some are willing
to pay
a considerable amount of money for a scenic view, others are
not.
The second step of the hedonic regression analysis estimates the
willingness to pay of households but additionally accounts for
households having different incomes and tastes. To account for
different incomes and tastes, analysts should estimate the
following
WTP function (inverse demand function) for scenic views:
rv = W(VIEW, Y, Z) (14.5)
where, rv is estimated from equation (14.3), Y is household
income,
and Z is a vector of household characteristics that reflects tastes
(e.g., socioeconomic background, race, age, and family size).
34
THE HEDONIC PRICE METHOD
Using the methods described in Chapter 4, it is straightforward
to use
equation (14.5) to calculate the change in consumer surplus to a
household
due to a change in the level of scenic view. These changes in
individual
household consumer surplus can be aggregated across all
households to
33. obtain the total change in consumer surplus.
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Problems with Hedonic Models
35
There are several potential problems with hedonic models.
1. People must know and understand the implications of the
attribute that is being valued. For example, people should
know the level of pollution at the property they buy and know
the expected effect of this level of pollution on their health.
2. Variables should be measured without error (the errors in
variables problem).
3. The functional forms should be correct (specification error
problem).
4. The market should have enough alternatives so that people
can
locate at their optimum point on the curve.
5. There may be multicollinearity problems, e.g., fatality risk
and
non-fatality risk might be highly correlated. Dropping one
variable would lead to an omitted variable problem.
6. Markets are assumed to adjust immediately to changes in the
attributes of interest and to all other factors.
34. TRAVEL COST METHOD
36
• Most applications of the travel cost method (TCM) have been
to value
recreational sites.
Suppose that we want to estimate the value of a particular
recreational
site. We expect that the quantity of visits demanded by an
individual, q,
depends on its price, p; the price of substitutes, ps; the person’s
income,
Y; and variables that reflect the person’s tastes, Z:
q = f(p,ps,Y,Z) (14.7)
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37
TRAVEL COST METHOD
• TCM recognizes that the full price paid by persons for a visit
to a
recreational site is more than just the admission fee. It also
includes
the costs of traveling to and from the site.
Among these travel costs are the opportunity cost of time spent
35. traveling, the operating cost of vehicles used to travel, the cost
of
accommodations for overnight stays while traveling or visiting,
and
parking fees at the site.
The sum of all of these costs gives the total cost of a visit to the
site.
This total cost is used as an explanatory variable in place of the
admission price in a model similar to equation (14.7).
38
TRAVEL COST METHOD
The clever insight of the TCM is that, although admission fees
are usually
the same for all persons (indeed, they are often zero), the total
cost faced
by each person varies because of differences in the travel cost
component.
Consequently, usage also varies, thereby allowing researchers to
make
inferences about the demand curve for the site.
The travel cost method involves collecting data on the costs
incurred by each
individual travelling to the recreational site or amenity. This
‘price’ paid by visitors
is unique to each individual, and is calculated by summing the
travel costs from
each individuals original location to the amenity.
By aggregating the observed travel costs associated with a
number of individuals
accessing the amenity a demand curve can be estimated, and as
36. such a price can
be obtained for the non-price amenity.
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39
TRAVEL COST METHOD
Estimating the demand schedule (equation 14.7) for a particular
recreational site is conceptually straightforward.
1. Select a random sample of households within the market area
of the
site.
2. Survey these households to determine their numbers of visits
to the
site over some period of time, all of their costs involved in
visiting the
site, their costs of visiting substitute sites, their incomes, and
other
characteristics that may affect their demand.
3. Specify a functional form for the demand schedule and
estimate it
using the survey data.
It is worth emphasizing that when total cost replaces price in
equation
(14.7), this equation is not the usual demand curve that gives
visits as a
function of the price of admission. However, as shown in the
37. next
section, the TCM can be used to estimate the usual market
demand
curve.
40
Zonal Travel Cost Method
• Using this method, researchers survey actual visitors rather
than
potential ones.
Visitors are allocated to a particular zone, depending on their
“travel
costs” (usually distance). For each zone, the analyst computes
the
average number of visits per year and the average total travel
cost.
Using these observations it is possible to estimate the
relationship
between cost/trip and the number of trips per person. The
consumer
surplus for a visitor from a particular zone is given by the area
below
this curve and above the cost of a visit from that zone, as shown
in
Figure 14-4. By repeating this calculation for each zone, it is
possible
to calculate the total consumer surplus, as shown in Table 14-1.
TRAVEL COST METHOD
38. 8/15/2017
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Figure 14-4 “Representative” Individual’s Inverse Demand
Curve
for Visits to a Recreational Area as a Function of Total Cost per
Visit
42
Zonal Travel Cost Method
• The zonal travel cost method requires the analyst to specify
the
zones from which users of the site originate.
• Zones are easily formed by drawing concentric rings or iso-
time lines
around the site on a map.
• Ideally, households within a zone should face similar travel
costs as
well as have similar values of the other variables that would be
included in an individual demand function.
TRAVEL COST METHOD
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43
39. Zonal Travel Cost Method
Example
Consider an example of valuing a park.
In this example four zones have been designated by the
researcher. Zone A
has an average travel time of 1 hour, and a distance of 25km.
Zone B has an
average travel time of 1.5 hours and a distance of 40km. Zone C
has an
average travel time of approximately 2 hours and a distance of
80km. Finally,
zone D has an average travel time of 4 hours and a distance of
120km.
The admission cost for all users is the same, and is equal to
$10. The number
of visits per year has been observed by the researcher for each
zone. Zone A
has an average of 10,000 visits per year. Zone B has an average
of 12,000 visits
per year, zone C has 8,000 visits, and zone D has 4,000 visits
TRAVEL COST METHOD
44
Zonal Travel Cost Method
Example
TRAVEL COST METHOD
41. the simple equation as follows:
V = ((T x w) + (D x v) + Ca) x Va
Where,
T = travel time (in hours)
w = average wage rate (£/hour)
D = distance (in km)
v = marginal vehicle operating costs
Ca = cost of Admission to asset
Va = average number of visits per year
TRAVEL COST METHOD
46
Zonal Travel Cost Method
Example
In the example the average hourly wage rate is $10, and
marginal vehicle
operating costs are calculated at $0.16p per km. The researcher
can now
calculate the value of the country park for each zone to get an
overall value
for the asset.
TRAVEL COST METHOD
Zone Travel Time
(hours)
Travel
Distance (km)
Admission
42. Cost ($)
Visits per
Year
Zone Value
($)
A 1 25 10 10,000 240,000
B 1.5 40 10 12,000 376,800
C 2 80 10 8,000 342,400
D 4 120 10 4,000 276,800
$1,236,000
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Limitations of the TCM
47
1. It is restricted to sites where people (in the zones) have
different travel costs.
Without variation in total cost, it’s hard to estimate a demand
curve.
2. There may be analytical problems in measuring the total cost
of a visit. How
does one measure opportunity cost of travel time? Should
43. multiple purpose trips
be included in the data (desirable if costs can be accurately
apportioned to the
site)? Also, the journey may have value (and hence the trip has
multiple purposes).
Individuals may visit an amenity or recreational site in the
morning, but then visit
another site or enjoy some other activity in the afternoon. The
travel endured to
access the amenity was also undertaken to enable access to the
afternoon activity.
In this case the cost incurred in travelling to the amenity does
not represent the
value the individuals place on the amenity, but that which they
place on both the
amenity they visited in the morning and the one which they
visited in the
afternoon.
Limitations of the TCM
48
3. The method estimates the WTP for the entire site rather than
features of the
site. For example, we do not wish to value a whole park, but
instead the fishing
ponds within it.
It’s possible to value features if people in zones can choose
among
alternative sites with different attributes – by using the
“hedonic travel
cost method”, which treats total cost as a function of both
distance from
45. Discounting Benefits and
Costs in Future Time
Periods
Six
DISCOUNTING BENEFITS AND
COSTS IN FUTURE TIME PERIODS
CHAPTER 6
2
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Purpose: This chapter deals with the practical issues one
must know in order to compute the net present value of a
project.
• It assumes the social discount rate is given, which is
reasonable as the rate is often set by an oversight agency,
such as the Office of Management and Budget.
• Appendix 6A provides shortcut formulas for calculating the
present value of annuities and perpetuities.
DISCOUNTING BENEFITS AND COSTS IN FUTURE
TIME PERIODS
3
4
46. THE BASICS OF DISCOUNTING
Projects with Lives of One Year
Technically, discounting takes place over periods not years.
However, for expositional simplicity, we assume that each
period is a year. This section discusses projects that last
one year.
Example: A city government has the opportunity to buy a
parcel of land for $10 million . Also, suppose that if it buys
the land, then the land will be sold for $11 million one year
from now.
Should the city buy the land now?
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5
THE BASICS OF DISCOUNTING
Projects with Lives of One Year
• It is often useful to lay out the annual benefits and costs
of a project on a time line (Figure 6-1).
• The horizontal axis represents time measured in years.
Benefits appear above the time line and costs are below
it.
• A time line is particularly useful when the timing of
47. impacts is more complicated.
Time line
Figure 6-1 A Time Line Diagram for City Land
Purchase Example
6
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7
THE BASICS OF DISCOUNTING
Projects with Lives of One Year
To decide whether to buy the land, the city should compare the
land purchase project, which has a cost of $10 million now with
a
value of $11 million in one year to the best alternative – in this
case, the status quo (not buy the land and invest the money).
There are three possible methods to evaluate potential projects.
Each gives the same answer.
(1) Future Value Analysis
(2) Present Value Analysis
(3) Net Present Value Analysis
THE BASICS OF DISCOUNTING
48. Projects with Lives of One Year
(1) Future Value Analysis – Choose the project with the largest
future value, FV, where the future value in one year of an
amount X invested at interest rate i is:
FV = X (1 + i) (6.1)
Example: If the city does not buy the land and invest the money
at an interest rate of 5%, then it will have $10.5 million in one
year (the future value, FV).
If it buys the land, the future value is $11 million. In this case,
the city should buy the land.
8
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9
THE BASICS OF DISCOUNTING
Projects with Lives of One Year
(2) Present Value Analysis – Choose the project with the largest
present value, PV, where the present value of an amount Y
received in one year is:
PV = Y/(1 + i) (6.2)
Note that if the PV of a project equals X, and the FV of a
49. project
equals Y, both equations (6.1) and (6.2) imply:
This equation shows that discounting (the process of calculating
the present value of future amounts) is the opposite of
compounding (the process of calculating future values).
i) + (1
FV
= PV
10
THE BASICS OF DISCOUNTING
Projects with Lives of One Year
(2) Present Value Analysis
Example: The present value of the land that will be worth $11
million in one year is PV = $11,000,000/1.05 = $10,476,190
In contrast the present value of the best available alternative is
$10 million. Therefore, the city is better off in present value
terms if it buys the land.
i) + (1
FV
= PV
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50. 6
(3) Net Present Value Analysis – Choose the project with the
largest net present value, which calculates the sum of the
present values of all the benefits and costs of a project
(including the initial investment):
NPV = PV(benefits) – PV(costs) (6.3)
Example: NPV = $10,476,190 - $10,000,000 = $476,190
Figure 6-2 shows that as the NPV of buying the land is positive,
the city should buy the land.
THE BASICS OF DISCOUNTING
Projects with Lives of One Year
11
Figure 6-2 NPV of Buying the Land
12
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13
• Usually projects are evaluated relative to the status quo. If
there
is only one new potential project and its impacts are calculated
relative to the status quo, it should be selected if its NPV > 0,
and
51. should not be selected if its NPV < 0.
• If the impacts of multiple, mutually exclusive alternative
projects
are calculated relative to the status quo, one should choose the
project with the highest NPV, as long as this project’s NPV > 0.
If
the NPV < 0 for all alternative projects to the status quo, one
should maintain the status quo.
THE BASICS OF DISCOUNTING
Projects with Lives of One Year
COMPOUNDING AND DISCOUNTING
OVER MULTIPLE YEARS
14
(1) Future Value over Multiple Years
(2) Present Value over Multiple Years
(3) Net Present Value of a Project
We now generalize these results to apply to projects with
impacts
that occur over many years.
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15
52. COMPOUNDING AND DISCOUNTING
OVER MULTIPLE YEARS
(1)Future Value over Multiple Years – Interest is compounded
when an amount is invested for a number of years and the
interest earned each period is reinvested.
• Interest on reinvested interest is called compound interest. The
future value, FV, of an amount X invested for n years with
interest compounded annually at rate i is:
FV= X (1+i)n (6.4)
• The term (1+i)n is called the compound interest factor.
• If there is simple interest then interest iX is paid each year.
Unless
stated to the contrary we will assume interest is compounded
once
per year.
16
COMPOUNDING AND DISCOUNTING
OVER MULTIPLE YEARS
(1) Future Value over Multiple Years
Example: Suppose the city could invest the $10 million for 5
years with
5% interest per annum.
Under simple interest, each year interest is paid only on the
original
principal amount, and the city would receive $500,000 per year.
53. The
future value would be $12.5 million.
Under compounded interest, interest is earned on the principal
amount
and on the interest that has been reinvested.
If $10 million is invested for 5 years with interest compounded
annually
at 5%, then the future value is:
FV = $10 million (1 + 0.05)5 = $12.763 million
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17
COMPOUNDING AND DISCOUNTING
OVER MULTIPLE YEARS
(2) Present Value over Multiple Years – The present value, PV,
of an amount
Y received in n years, with interest compounded annually at rate
i is:
(6.5)
The term 1/(1+i)n is called the present value factor or discount
factor.
The present value of a stream of benefits or costs over n years
is:
54. (6.6)
(6.7)
or
18
COMPOUNDING AND DISCOUNTING OVER
MULTIPLE YEARS
(2) Present Value over Multiple Years
Example using Equation 6.6: Consider a government agency
that has to
choose between two alternative projects. Project I yields a
benefit of
$10,500 four years from now, whereas Project II yields $5,500
four years
from now and an additional $5,400 five years from now.
Assume that the
interest rate is 8%.
Which is the better project?
The present values of the projects are:
PV(I) = $10,500/(1+0.08)4 = $7,718
PV(II) = $5,500/(1+0.08)4 + $5,400/(1+0.08)5 = $4,043 +
$3,675 = $7,718
In this example, the present values of the two projects happen to
be
identical. Thus, one would be indifferent between them.
55. 8/15/2017
10
19
COMPOUNDING AND DISCOUNTING
OVER MULTIPLE YEARS
(3) Net Present Value of a Project – Inserting equations (6.6)
and (6.7) into (6.3) gives the following useful expression for
computing the NPV of a project:
Or, equivalently, the NPV of a project equals the present value
of the net benefits (NBi = Bi - Ci):
(6.9)
(6.8)
20
COMPOUNDING AND DISCOUNTING
OVER MULTIPLE YEARS
(3) Net Present Value of a Project
Example: Suppose a district library is considering purchasing a
new information system that would give users access to a
number of online databases for 5 years. The benefits are
estimated to be $100,000 per annum, including both cost
savings to the library and user benefits.
56. The information system costs $325,000 to purchase and set
up initially, and $20,000 to operate and maintain each year.
After 5 years, the system would be dismantled and sold,
resulting in a net cash inflow of $20,000 (terminal value or
liquidation value). Assume that the discount rate is 7 % and
there are no other costs or benefits.
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21
COMPOUNDING AND DISCOUNTING
OVER MULTIPLE YEARS
(3) Net Present Value of a Project
Table 6-2 contains the annual benefits, annual costs, and
annual net benefits of the library information system project.
Using Equation 6.9, the present value of the net benefits of
the project is $17,276, as shown in the last column of Table 6-
2.
22
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TIMING OF BENEFITS AND COSTS
57. 23
• Thus far, we have assumed that impacts occur immediately, or
at
the end of the first year, or at the end of the second year, and so
on.
• Time lines are very useful ways to specify exactly when
benefits
and costs do occur.
• If benefits arise throughout a year, rather than at the end as we
have assumed , one possibility is to compute the NPV as if the
benefits occurred in the middle of the year.
• Alternatively, one could compute the NPV under the
assumption
they occur at the beginning of the year and under the
assumption
that they occur at the end of the year and take the average.
COMPARING PROJECTS WITH DIFFERENT
TIME FRAMES
24
Analysts should not choose one project over another solely
based
on the NPV of each project if the time spans are different. Such
projects are not directly comparable.
Two appropriate methods to evaluate projects with different life
spans are:
(1)Roll-Over Method
58. (2) Equivalent Annual Net Benefits (EANB) Method
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25
COMPARING PROJECTS WITH DIFFERENT
TIME FRAMES
(1) Roll-Over Method
If project A spans n times the number of years as project B,
then
assume that project B is repeated n times and compare the NPV
of n
repeated project Bs to the NPV of (one) project A.
For example, if project A lasts 30 years and project B lasts 15
years,
compare the NPV of project A to the NPV of 2 back-to-back
project
B’s, where the latter is computed:
NPV = x + x/(1+i)15
where, x = NPV of one 15-year project B.
26
COMPARING PROJECTS WITH DIFFERENT
TIME FRAMES
59. (1) Roll-Over Method
Example: Suppose the utility decides to build the cogeneration
power plant. Further suppose that in 15 years time it builds
another new cogeneration plant; in 30 years it builds another
one; and it builds another again in 45 and 60 years.
The NPV of back-to-back cogeneration power plants denoted
5CGP, is:
NPV(5CGP) = $24,000,000 +$24,000,000/(1+0.08)15
+$24,000,000/(1+0.08)30 +$24,000,000/(1+0.08)45
+$24,000,000/(1+0.08)60
= $34.94 million9
The utility should select the option with the higher NPV.
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27
(2) Equivalent Annual Net Benefits (EANB) Method
The EANB is the amount received each year for the life of the
project that has the same NPV as the project itself.
It is computed by dividing the NPV of the project by the
annuity
60. factor ai
n:
EANB= NPV / ai
n (6.10) where
Where, ai
n is the present value of an annuity of $1 for the life of the
project (n years), where i = interest rate used to compute the
NPV.
Obviously, one would choose the project with the highest
EANB.
COMPARING PROJECTS WITH DIFFERENT
TIME FRAMES
28
COMPARING PROJECTS WITH DIFFERENT
TIME FRAMES
(2) Equivalent Annual Net Benefits (EANB) Method
Example:
EANB(HED) = $30/12.461 = $2.407 million
EANB(CGP) = $24/8.559 = $2.804 million
EANB of the cogeneration project implies that this project is
equivalent to an annuity of $2.804 million per year for 15 years.
In contrast, the net benefit of the hydroelectric alternative is
equivalent to an annuity of $2.407 million per year for 75 years.
61. Consequently, the cogeneration alternative is preferable,
assuming
replacement of both types of plant is possible at the end of their
useful lives.
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INFLATION AND REAL VERSUS NOMINAL
DOLLARS
29
Conventional private sector financial analysis measures
monetary amounts in nominal dollars (sometimes called current
dollars). But, due to inflation, one cannot buy as many goods
and services with a dollar today as one could one, two or more
years previously–“a dollar’s not worth a dollar anymore”. It is
important to control for inflation (i.e. general price increases).
We control for inflation by converting nominal dollars to real
dollars (sometimes called constant dollars). We usually use the
consumer price index (CPI) deflator, but sometimes use the
gross
national product (GNP) deflator.
30
INFLATION AND REAL VERSUS NOMINAL
DOLLARS
Problems with the CPI
62. The CPI is the most commonly used measure of inflation. Most
economists think that the CPI overstates inflation.
Two reasons for the overstatement are:
1) Commodity substitution effect: The CPI basket of goods does
not
accurately reflect consumers’ purchases because people quickly
switch to lower-priced substitutes as prices rise. One variant is
called
the discount stores effect. Another variant is called the “new
goods”
problem: consumers switch to new, cheaper generic drugs.
2) Quality improvements: The CPI does not accurately reflect
improvements in product quality to existing goods, e.g. cars are
more
safe or reliable.
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Analyzing Future Benefits and Costs in CBA
31
Analysts should either measure the benefits and costs in real
dollars and
discount using a real discount rate or measure the benefits and
costs in
nominal dollars and discount using a nominal discount rate.
Both methods
would result in the same numerical answer.
63. It is suggested to work in real dollars for public-sector project
evaluation as it
is usually easier and more intuitive.
APPENDIX 6A: SHORTCUT METHODS FOR
CALCULATING THE PRESENT VALUE OF ANNUITIES
AND PERPETUITIES
32
• Annuity - is an equal, fixed amount received (or paid) each
year
for a number of years.
• A perpetuity - is an annuity that continues indefinitely.
Many CBAs contain annuities or perpetuities. Fortunately,
there
are some simple formulas for calculating their PVs.
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33
APPENDIX 6A: SHORTCUT METHODS FOR
CALCULATING PV OF ANNUITIES & PERPETUITIES
Example: Suppose that in order to finance a new state highway,
a state
government issues $100 million worth of 30-year bonds with an
64. interest rate of 7% paid annually.
The annual interest payments of $70,000 are an annuity. If at
the end
of each 30-year period the state government refinances the debt
by
issuing another 30-year bond that also has an interest rate of
7%, then
the annual interest payments of $70,000 would continue
indefinitely,
which is a perpetuity.
34
Present Value of an Annuity
Using equation (6.6), the present value of an annuity of $A per
annum (with payments
received at the end of each year) for n years with interest at i
percent is given by:
This is the sum of n terms of a geometric series with the
common ratio equal to 1/(1 + i).
Consequently,
PV = A x (6A.1)
where , (6A.2)
The term , which equals the present value of an annuity of $1
per year for n years when
the interest rate is i percent, is called an annuity factor.
n
ia
APPENDIX 6A
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35
Present Value of an Annuity
APPENDIX 6A
Example: The library information system problem contains two
annuities: the
annual benefits of $100,000 per year for 5 years , which we
refer to as annuity A1,
and annual costs of $20,000 per year for five years, which we
refer to as annuity
A2.
From Figure 6-4 we see that the present value of A1 is $410,020
and the present
value of A2 is $82,004. But the easier way is to use Equation
6A1.
The present value of annuity A1 is:
PV(A1) = $100,000 x 1-(1+0.07)-5/0.07
= $100,000 x 4.1002
= $410,020
and
PV(A2) = $20,000 x 4.1002 = $82,004
66. 36
Present Value of a Perpetuity
Taking the limit of equation (6A.2) as n goes to infinity implies
that the present value of an amount, denoted by A, received (at
the end of) each year in perpetuity is given by:
if i > 0 (6A.3)
APPENDIX 6A: SHORTCUT METHODS
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APPENDIX 6A: SHORTCUT METHODS
Present Value of a Perpetuity
Example: Suppose that a municipality has an endowment of $10
million. If
interest rates are 6%, then this endowment will provide an
annual interest
payments of $600,000 indefinitely.
More generally, if the municipality has an endowment of X and
if the interest
rate is i, then the perpetual annual income from the endowment,
denoted by A,
is given by A = iX. Rearranging this equation shows the present
value of the
85. Calculating Expected Value of Net Benefits
In practice, treating expected values and certain amounts as
commensurate (risk
neutral) is generally reasonable when either the pooling of risk
over the collection
of policies, or the pooling of risk over the collection of persons
affected by a
policy, will make the actually realized values of costs and
benefits close to their
expected values.
For example, a policy that affects the probability of highway
accidents involves
reasonable pooling of risk across many drivers (some will have
accidents, others
will not) so that realized values will be close to expected
values.
In contrast, a policy that affects the risk of asteroid collision
does not involve
pooling across individuals (either everyone suffers from the
global harm if there is
a collision or no one does if there is no collision), so that the
realized value of
costs may be very far from their expected value.
90. Sensitivity Analysis
Partial Sensitivity Analysis
In partial sensitivity analysis, you select one variable, change
its value
while holding other variables constant, and see how much the
CBA
results in response.
In Figure 7-3, the probability of the epidemic in the current
year, p1, varies
from 0 to 0.5 by increments of 0.05.
The results are displayed as the line labeled L = $3 million.
The equation of net benefits were embedded in a spreadsheet on
a
computer, so it was easy to generate the points needed to draw
this line
by simply changing the values of p1.
As expected, this line is upward sloping: the higher the
probability of the
epidemic, the larger the net benefits of the program.
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94. Other Forms of Sensitivity Analysis
1. Discount rate
2. Wage rates used
3. The value of life, or risks associated with certain occupations
The researcher must determine how changes in these measures
affect the
outcome of the CBA. A researcher may wish to perform
additional sensitivity
analysis in any of these cases, especially if the result of the
CBA is close to zero
(using NPV), or the benefit-cost ratio is close to one. Moreover,
if certain
measures used are contentious sensitivity analysis may be
required. Or if a
particular cost or benefit that accounts for a large proportion of
the overall costs
or benefits associated with a project is calculated using a
measure which is
subject to some sort of arbitrary value.
8/15/2017
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Cost-Benefit Analysis: Concepts and Practice, Fourth Edition
Boardman • Greenberg • Vining • Weimer
Sensitivity Analysis
Example: Testing Sensitivity by Varying the Discount Rate
With a discount rate of 10% however the NPV of the project is
as follows:
$90,909.09 + $165,289.26 + $375,657.40 + $683,013.46
PV (B) = $1,314,869.20
NPV = $1,314,869.20 - $1.5 million
NPV = -$185,130.79
In this example, with a discount rate of 5% similarly there is
justification for the
project to go ahead. However, with a higher discount rate of
10% the costs
outweigh the discounted benefits by almost $200,000,
suggesting the project
should not go ahead. In this case the choice of discount rate
could have a