Solution Manual For Investments: Analysis and Management, 12th Edition
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Chapter 1: Understanding Investments
CHAPTER OVERVIEW
Chapter 1 is designed to be a standard introductory chapter. As such, its purpose is to
introduce students to the subject of Investments, explain what Investments is concerned with
from a summary viewpoint, and outline what the remainder of the text will cover. It defines
important terms such as investments, security analysis, portfolio management, expected
and realized rate of return, risk-free rate of return, risk, and risk tolerance.
IT IS IMPORTANT TO NOTE that Chapter 1 discusses some important issues, such
as the expected return–risk tradeoff that governs the investment process, the uncertainty that
dominates investment decisions, the globalization of investments, and the impact of
institutional investors. As such, the chapter sets the tone for the entire text and explains to
the reader what Investments is all about. It establishes a basic framework for the course
without going into too much detail at the outset.
Chapter 1 also contains some material that will be of direct interest to students,
including the importance of studying investments (using illustrations of the wealth that can be
accumulated by compounding over long periods of time) and investments as a profession.
The CFA designation is discussed, and the Appendix for Chapter 1 contains a more detailed
description of the CFA program.
Equally important, Chapter 1 does not cover calculations and statistical concepts, data
on asset returns, and so forth, either in the chapter or an appendix. The author feels strongly
that Chapter 1 is not the place to do this when most students have little knowledge of what
the subject is all about. They are not ready for this type of important material, and since it
will not be used immediately they will lose sight of why it was introduced. The author
believes that it is much more effective to introduce the students thoroughly to what the
subject involves.
It is highly desirable for instructors to add their own viewpoints at the outset of the
course, perhaps using recent stories from the popular press to emphasize what investments is
concerned with, why students should be interested in the subject, and so forth. One
interesting and important topic that can be discussed in class is investment fraud. Scams
continue day after day, and many people lose their life savings. Most people will have at
least heard of the alleged Ponzi scheme revealed in late 2008 involving Bernie Madoff. By
learning a few basic investing principles, students will be able to avoid these โscams,โ
thereby possibly saving themselves or their family and friends from misfortune.
Chapter 1 also discusses ethics in investing, setting the stage for examples of ethical
issues in other chapters.
CHAPTER OBJECTIVES
To introduce students to the subject matter of Investments from an overall viewpoint,
including terminology.
To explain the basic nature of the investing decision as a tradeoff between expected
return and risk.
To explain that the decision process consists of security analysis and portfolio
management and that external factors affect this decision process. These
factors
include uncertainty, the necessity to think of investments in a global context,
the
environment involving institutional investors, and the impact of the internet on
investing.
To organize the remainder of the text.
MAJOR CHAPTER HEADINGS [Contents]
An Overall Perspective On Investing
Just Say NO!
Establishing A Framework For Investing
Some Definitions
[investment; investments; financial and real assets;
marketable securities; portfolio]
A Perspective on Investing
[investing is only one part of overall financial decisions; take a portfolio
perspective]
Why Do We Invest?
[to increase monetary wealth]
Take a Portfolio Perspective
The Importance of Studying Investments
for
the
The Personal Aspects
[most people make some type of investment decisions; examples of wealth
accumulation as a result of compounding; people will be largely responsible
making investing decisions affecting their retirement; how an understanding of
subject will help students when reading the popular press]
Investments as a Profession
[various jobs such as security analysts, portfolio managers, stockbrokers, and
financial advisors; financial planners; CFA designation]
Understanding the Investment Decision Process
free
The Basis of Investment DecisionsโReturn and Risk
[expected return; realized return; risk; risk-averse investor; risk tolerance; the
Expected-Return–Risk Tradeoff; diagram of tradeoff; ex post vs. ex ante; riskrate of return, RF]
Structuring the Decision Process
[a two-step process: security analysis and portfolio management]
Important Considerations in the Investment Decision Process for Todayโs Investors
The Great Unknown
[uncertainty dominates decisions–the future is unknown!]
A Global Perspective
[the importance of foreign markets; the Euro; emerging markets]
The Importance of the Internet
[using the internet to invest]
Individual Investors vs. Institutional Investors
[individual investors compete with institutional investors, but individuals are the
beneficiaries of institutional investor activity; Regulation FD; spin-offs]
Ethics in Investing
Organizing the Text
[Background; Realized and Expected Returns and Risk; Bonds; Stocks; Security
Analysis, including both fundamental and technical analysis; Derivative
Securities;
Portfolio Theory and Capital Market Theory; the Portfolio
Management Process and
Measuring Portfolio Performance]
POINTS TO NOTE ABOUT CHAPTER 1
Exhibits, Figures and Tables
Exhibit 1-1 discusses some professional designations used by people in the money
management business. It offers a good opportunity to discuss with students the opportunities
in the field, such as financial planner.
Figure 1-1 is an important figure because it is the basis of investing decisions–indeed,
it is the basis of all finance decisions. It shows the expected return–risk tradeoff available to
investors. This diagram should be emphasized because it can be used to generate much
useful discussion, including:
โข
โข
โข
โข
โข
The upward-sloping tradeoff that dominates Investments.
The role of RF, the risk-free rate of return.
The importance of risk in all discussions of investing.
The different types of financial assets available.
The distinction between realized and expected return.
NOTE: This diagram is relevant on the first day of class, and the last. It is a good way to start
the course, and to end it.
NOTE: Example 1-1 shows wealth accumulations possible from an IRA-type investment. It
typically generates considerable student interest to see the ending wealth that can be
produced by compounding over time. This type of example can be related to 401 (k) plans,
which are quickly becoming of primary importance to many people.
SOME RECOMMENDATIONS WHEN DISCUSSING CHAPTER 1:
1.
The expected return-risk tradeoff is fundamental to any understanding of Investments.
While it seems to be a straightforward concept, I find that students have problems
with it.
These problems revolve around understanding the realized tradeoff (what did
happen) vs. the anticipated tradeoff (what is expected to happen). I discuss the following
relationships to show the various tradeoffs.
(a) The expected tradeoff (illustrated in the text) which is always upward sloping
because rational investors must expect to receive a larger return if they are to
assume
more risk. This is the basis of decision-making when investing.
(b) The long-term (for example, 50 or more years) realized tradeoff, as illustrated
by
the Ibbotson data and the returns data used in Chapter 6. This tradeoff must
slope
upward if what is taught in Investments is to make sense; that is, we have a
real
problem if over long periods of time risky assets do not return more than safe
assets..
And, of course, they have done so in the past. Stocks have returned more than
bonds,
which have returned more than T-bills, over very long periods of time.
(c) The shorter-term realized tradeoff, where safe assets outperform risky assets.
2000-2002 and 2008 offer the perfect examples. The market declined sharply
in each
case, and therefore T-bills returned more than stocks. On a realized basis,
investors
were penalized for assuming risk. Obviously, they did not expect this
to occur.
vertical
2.
Thus, diagrams for (a) and (b) look similar. The difference is the label on the
axis: expected return for (a), and realized return for (b).
The decline in the economy and in the stock market in 2000-2002 is a good
illustration of risk, and of using the recent past to predict the future. During the late
1990s and into part of 2000, we heard a lot about day traders, and how we were now
in a new environment where the old standards of valuation such as profitability were
much less important. Of course, many of the high-flyers crashed and/or went out of
business. Today there is a renewed appreciation for the traditional methods of stock
valuation.
The stock market decline of 2008 is a dramatic example of the risk that can impact
investors. The decline was dramatic, and most investors who held stocks lost
money.
Many well known investors and professionally managed funds failed to
anticipate this
market decline or the extent and severity of it. Many investors found
their retirement
accounts significantly diminished.
3.
of
It may be good practice to start talking about the dollar, and the Euro, at the beginning
the course. Movements in the dollar are a popular topic, and an important one.
ANSWERS TO END-OF-CHAPTER QUESTIONS
1-1.
to
The term Investments can be thought of as representing the study of the investment
process. An investment is defined as the commitment of funds to one or more assets
be held over some future time period.
1-2.
and
Traditionally, the investment decision process has been divided into security analysis
portfolio management.
is,
โช Security analysis involves the analysis and valuation of individual securities; that
estimating value, a difficult job at best.
โช Portfolio management utilizes the results of security analysis to construct
portfolios.
As explained in Part II, this is important because a portfolio taken as
a whole is not
equal to the sum of its parts.
1-3.
has
lives.
is
The study of investments is important to many individuals because almost everyone
wealth of some kind and will be faced with investment decisions sometime in their
One important area where many individuals can make important investing decisions
that of retirement plans, particularly 401 (k) plans. In addition, individuals often have
some say in their retirement programs, such as allocation decisions to cash
equivalents, bonds, and stocks.
The dramatic stock market gains of 1995-1999 and the sharp losses in 2000-2002 and
2008 illustrate well the importance of studying investments. Investors who were
persuaded in the past to go heavily, or all, in stocks reaped tremendous gains in their
retirement assets as well as in their taxable accounts in 1995-1999 and then often
suffered sharp losses in 2000-2002 and 2008.
1-4.
A financial asset is a piece of paper evidencing some type of financial claim on an
issuer, whether private (corporations) or public (governments).
A real asset, on the other hand, is a tangible asset such as gold coins, diamonds, or
land.
1-5.
Investments, in the final analysis, is simply a risk-return tradeoff. In order to have a
chance to earn a return above that of a risk-free asset, investors must take risk. The
larger the return expected, the greater the risk that must be taken.
The risk-return tradeoff faced by investors making investment decisions has the
following characteristics:
๏ The risk-return tradeoff is upward sloping because investment decisions involve
expected returns (vertical axis) versus risk (horizontal axis).
๏ The vertical intercept is RF, the risk-free rate of return available to all investors.
1-6. An investor would expect to earn the risk-free rate of return (RF) when he or she
invests in a risk-free asset. This is the zero risk point on the horizontal axis in Figure 1-1.
1-7.
Disagree. Risk-averse investors will assume risk if they expect to be adequately
compensated for it.
1-8.
The basic nature of the investment decision for all investors is the upward-sloping
tradeoff between expected return and risk that must be dealt with each time an
investment
decision is made.
1-9. Expected return is the anticipated return for some future time period, whereas
realized return is the actual return that occurred over some past period.
1-10. In general, the term risk as used in investments refers to adverse circumstances
affecting the investorโs position. Risk can be defined in several different ways. Risk is
defined
here as the chance that the actual return on an investment will differ from its
expected return.
Beginning students will probably think of default risk and purchasing power risk very
quickly. Some may be aware of interest rate risk and market risk without fully
understanding these concepts (which are explained in later chapters). Other risks
include
political risk and liquidity risk. Students may also remember financial
risk and business risk from their managerial finance course.
1-11. As explained in Chapter 21, return and risk form the basis for investors establishing
their objectives. Some investors think of risk as a constraint on their activities. If so, risk
is
the most important constraint. Investors face other constraints, including:
๏ time
๏ taxes
๏ transaction costs
๏ income requirements
๏ legal and regulatory constraints
๏ diversification requirements
1-12. All rational investors are risk averse because it is not rational when investing to
assume
risk unless one expects to be compensated for doing so.
All investors do not have the same degree of risk aversion. They are risk averse to
varying degrees, requiring different risk premiums in order to invest.
1-13. Investors should determine how much risk they are willing to take before investingโ
this is their risk tolerance. Based on their risk tolerance, investors can then decide
how to invest. Investors may seek to maximize their expected return consistent with the
amount of risk they are willing to take.
1-14. The external factors affecting the decision process are:
(1) uncertaintyโthe great unknown
(2) the global investments arena
(3) the importance of the internet
(4) individual investors vs. institutional investors
The most important factor is uncertainty, the ever-present issue with which all
investors must deal. Uncertainty dominates investments, and always will.
1-15. Institutional investors include bank trust departments, pension funds, mutual funds
(investment companies), insurance companies, and so forth. Basically, these financial
institutions own and manage portfolios of securities on behalf of various clienteles.
They affect the investing environment (and therefore individual investors) through
their actions in the marketplace, buying and selling securities in large dollar amounts.
However, although they appear to have several advantages over individuals (research
departments, expertise, etc.); reasonably informed individuals should be able to
perform as well as institutions, on average, over time. This relates to the issue of market
efficiency.
1-16. Required rates of return differ as the risk of an investment varies. Treasury bonds,
generally accepted as being free from default risk, are less risky than corporates, and
therefore have a lower required rate of return.
1-17. Investors should be concerned with international investing for several important
reasons. First, international investing offers diversification opportunities, and
diversification is
extremely important to all investors as it provides risk reduction.
Second, the returns may
be better in foreign markets than in the U. S. markets. Third,
many U. S. companies are
increasingly affected by conditions abroad–for example, Coca
Cola derives most of its
revenue and profits from foreign operations. U. S. companies
clearly are significantly
affected by foreign competitors.
The exchange rate (currency risk) is an important part of all decisions to invest
internationally. As discussed in Chapter 6 and other chapters, currency risk affects
investment returns, both positively and negatively.
1-18. The long run ex ante tradeoff between expected return and risk should be an upward
sloping line indicating that the greater the risk taken, the greater the expected return.
if
less
The long run ex post tradeoff between return and risk should also be upward sloping
investing is to make sense. Over long periods riskier assets should return more than
risky assets.
1-19. Disagree. If investors always attempted to minimize their risk, they would only
invest in Treasury bills. Instead, investors must seek a balance between expected return
and risk.
1-20. Disagree. If investors sought only to maximize their returns, they would purchase the
riskiest assets, ignoring the risk they would be taking. Once again, investors must
seek a balance between expected return and risk.
Chapter 2: Investment Alternatives
CHAPTER OVERVIEW
The purpose of Chapter 2 is to provide an overview of the major types of financial
assets available to investors and discussed in later chapters. It also outlines the important
alternatives of direct and indirect investing, thereby providing the foundation for Chapter 3.
Obviously, these assets cannot be discussed in detail in this chapter; however,
instructors can provide additional details as they see fit. What is important here is for
students to be exposed to the major types of financial assets early in the course in order for
them to understand the basics of alternative investment opportunities. For example, if an
instructor were to refer to an example or concept involving a call option or a convertible
security, the student may have no idea what is being discussed. A good example is
derivatives, a topic of public discussion in 2009 because of the financial crisis.
Chapter 2 first discusses the non-marketable alternatives available to investors, such
as savings accounts, because many students have encountered these already. Also, they offer
a good contrast to the marketable securities, which are the focus of the text.
Money market securities are discussed briefly, primarily because these assets
typically are owned by individual investors in the form of money market mutual funds.
Chapter 2 concentrates on the major capital market assets, bonds and stocks, while
providing a very brief coverage of derivative securities.
The idea of indirect investing–the ownership of investment company shares–is
introduced in Chapter 2 in Exhibit 2-1. This is because of the important alternative that such
ownership provides all investors. They can turn their funds over to a mutual fund or ETF and
not have to make investment decisions. It is desirable for students to think about this
alternative early in their study. Many investors will opt for a combination of direct and
indirect investing, and this alternative needs to be explained early in the course. Chapter 3 is
devoted to indirect investing and provides a detailed discussion of investment companies.
CHAPTER OBJECTIVES
To provide an overview of the major financial assets available to investors and
discussed
in subsequent chapters.
To provide some detail on the financial assets of most importance bonds and stocks.
To explain investorsโ alternatives, which consist of direct investing, indirect
investing, or,
as is often done, a combination of the two.
MAJOR CHAPTER HEADINGS [Contents]
Organizing Financial Assets
Direct Investing
[invest directly and indirectly in money market, capital market and other
securities]
A Global Perspective
[why this is important in today’s investing environment]
Nonmarketable Financial Assets
[savings accounts; certificates of deposit (CDs); money market deposit accounts
(MMDAs); U. S. government savings bonds–key features summarized in
table form]
Money Market Securities
The Treasury Bill
[discussion of important money market securities in table form; emphasis on
Treasury
bills as the risk-free (RF) rate; calculating the discount yield]
Money Market Rates
Capital Market Securities
Fixed-Income Securities
Bonds
[definition; characteristics–par value, maturity, zero coupon bond, call feature,
bond prices, accrued interest, discounts and premiums]
Types of Bonds
Government Agency Securities
Asset-backed Securities
[definition, examples; securitization trends; why investors buy asset-backed
securities]
Rates on Fixed-Income Securities
[general relationships]
Equity Securities
Preferred Stock
[definition; characteristics; new forms]
Common Stock
[definition; characteristics–book value, market value, dividends, dividend yield,
payout ratio, stock dividends and stock splits, the P/E ratio; investing
internationally
in equities]
Investing Internationally in Equities
[ADRsโdefinition and examples]
Derivative Securities
[Corporate-created securities: warrants; options; futures contracts]
Options
[definition; very brief basics of puts and calls]
Futures Contracts
[definition; purposes]
A Final Note
POINTS TO NOTE ABOUT CHAPTER 2
Exhibits, Figures and Tables
Exhibit 2-1 is useful for organizing financial assets into one diagram. It illustrates
both direct and indirect investing.
Exhibit 2-2 outlines the major non-marketable financial assets in order that this topic
can be covered quickly and efficiently.
Exhibit 2-3 discusses the major money market securities in table format, relieving the
student and instructor from even more tedious details in the body of the chapter. This table
contains the relevant facts about these assets. THE IMPORTANT POINT TO STRESS IS
THAT MOST INDIVIDUAL INVESTORS WILL OWN THESE ASSETS INDIRECTLY
THROUGH MONEY MARKET MUTUAL FUNDS.
Exhibit 2-4 contains a basic summary of S&P debt rating definitions.
ANSWERS TO END-OF-CHAPTER QUESTIONS
2-1. Indirect investing involves the purchase and sale of investment company shares.
Since investment companies hold portfolios of securities, an investor owning investment
company shares indirectly owns a pro-rata share of a portfolio of securities.
2-2.
value
an
the
Treasury bills are auctioned weekly in a bid process. Bills are sold at less than face
(a discount) and redeemed at maturity for the face value, with this spread constituting
investorโs return. The greater the discount (the smaller the price paid for the bills),
larger the return.
2-3. Negotiable certificates of deposit (CDs) are marketable deposit liabilities of the
issuing
bank that pay a stated interest rate and are redeemable from the issuer at maturity
by the holder. The minimum deposit is $100,000. Because they are negotiable, they can be
sold in the open market before maturity.
Non-marketable certificates of deposit are sold by banks and other institutions.
Penalties may exist for early withdrawal of funds remains in effect. Most importantly, these
CDs are nonnegotiable. The owner (purchaser) must deal directly with the issuing
institution.
2-4.
Bonds are issued by the federal government, federal government agencies,
municipalities, and corporations. The last two are the most risky. If one has to be
chosen as the most risky, it presumably would be corporates since general obligation
municipals
(as opposed to revenue bonds) are backed by the taxing power of the issuer.
2-5.
Fannie Maes are issued by the Federal National Mortgage Association, a governmentsponsored agency which became a privately owned corporation traded on the NYSE.
In September, 2008, the government seized control of Fannie Mae and Freddie Mac,
placing them in a government conservatorship, somewhat similar to a bankruptcy
reorganization. These securities are much more risky now than before the crisis of
2008.
Ginnie Maes are issued by the Government National Mortgage Association, a whollyowned government agency issuing fully-backed securities. Ginnie Mae is known for
its
pass-through certificates, where both principal and interest are passed through
monthly to
the certificate holders.
2-6.
the
The two basic types of municipals are general obligation bonds, which are backed by
โfull faith and creditโ of the issuer, and revenue bonds, which are repaid from the
revenues generated by the project they were sold to finance.
2-7.
As a result of mortgage refinancings, investors in Ginnie Maes face the risk that the
mortgages may be repaid earlier than expected by borrowers refinancing their
obligations.
2-8. The advantages of Treasury bonds include:
(1)
the practical elimination of default risk
(2)
(3)
the minimization of call risk
a very liquid and viable market
The possible disadvantages of Treasury bonds are the lower rates of return and the
exposure to inflation risk (unless the new inflation-adjusted bonds are used).
2-9. A savings bond represents the non-marketable part of the U. S. government debt. It
cannot be sold in the open market. Treasury bonds represent the marketable portion
of
federal debt, and can be sold at virtually any time.
2-10. Preferred stock is referred to as a hybrid security because it has some features similar
to
fixed-income securities (it pays a fixed return and has a meaningful par value) and
some features similar to equity securities (it never matures and it pays dividends).
2-11. Common stockholders are the residual claimants of a corporation because they are
entitled to all earnings after payment of any debt interest and any preferred dividends.
In
case of liquidation, they are entitled to any assets remaining after bondholder and
preferred stockholder claims have been satisfied.
2-12. There is no requirement for a company to pay a dividend on the common stock. Any
payment is decided by the companyโs board of directors, who can change the
dividend (or abolish it) at any time.
2-13. A derivative security is a security that derives its value from other more basic
underlying assets, such as securities, commodities, or currencies. Derivative
securities are also referred to as contingent claims.
Equity derivative securities derive all, or part, of their value from the underlying
common stock; that is, part, or all, of their value is due to their claim on the common.
k.
Corporate-created equity-derivative securities include rights, warrants and
convertibles, all of which are issued by corporations while investor-created equityderivative securities involve options (puts and calls), which are written and bought by
investors (both
individuals and institutions).
Futures contracts are also derivative securities.
2-14. Securitization refers to the transformation of illiquid risky individual loans into more
liquid, less risky securities.
2-15. The classic example of asset-backed securities is the mortgage-backed securities
issued by
the federal agencies to support the mortgage market, such as Ginnie
Maes. Other recent examples include car loans, aircraft leases, credit-card
receivables, railcar leases, smallbusiness loans, and so forth.
2-16. For practical purposes, Treasury bills, like other Treasury securities, are considered to
be
default-free securities. Although very safe, both bank CDs and commercial paper
carry some risk of default, however small. Therefore, T-bills should have a lower return.
2-17. The call feature is a disadvantage to investors who must give up a higher-yielding
bond and replace it (to continue having a position) with a lower-yielding bond. Issuers will
call in bonds when interest rates have dropped substantially (e.g., two or three
percentage
points) from a period of very high rates.
Of course, the bonds may be protected from call for a certain period and cannot be
called although the issuer would like to do so. Generally, once unprotected, issuers will call
bonds when it is economically attractive to do so, which is when the discounted
benefits outweigh the discounted costs of calling the bonds.
2-18. Investors are more likely to hold zero coupon bonds in a non-taxable account because
holders must pay taxes each year on zero coupons as if they actually received the
interest. By holding zeros in a non-taxable account, the tax can be deferred.
2-19. Direct Access Notes (DANs) are sold by high credit-quality firms at $1,000, thereby
eliminating discounts and premiums and accrued interest. Coupon rates are fixed, and
maturities vary widely. Maturities and rates on a new issue are posted for one week,
allowing investors to shop around.
2-20. An ADR represents indirect ownership of a specified number of shares of a foreign
company. These shares are held on deposit in a bank in the issuerโs home country,
and
the ADRs are issued by U. S. banks called depositories. In effect, then, ADRs are
tradable receipts.
2-21. Stock dividends and splits do not, other things being equal, represent additional
value. Of course, if a stock dividend is accompanied by a higher cash dividend, the
stockholder gains, but this is a change in the dividend policy. Some people believe that
these transactions increase the ownership of a stock by bringing it into a more favorable
price range, but even if true it is doubtful this would add real value.
2-22. A stockholder is the residual claimant in a corporation, entitled to the earnings
remaining after the bondholders and preferred stockholders are paid (of course, all earnings
are not usually paid out to stockholders). Also, in case of liquidation, the stockholders are
entitled to the residual assets after the bondholders and preferred stockholders (as well
as
other) claims are settled.
In the case of financially sound corporations, the bondholder has considerable
assurance of receiving the interest payments. However, the bondholder will never
receive more than the stated interest and principal payments. While stockholders
assume the risk that returns will be negative in some years, they expect some large
returns in other years and, also expect, on average, to earn more than the bondholders.
2-23. The $3.20 dividend is the annual dividend. The stock goes ex-dividend on August 11.
An investor must buy the stock on or before August 10 to receive the dividend.
With 150 shares, 150 ($.80) = $120 will be received (the quarterly dividend is 1/4 of
$3.20, or $.80).
2-24. (b)โratings reflect the relative likelihood of default.
2-25. (a)
2-26. (d)โstockholders receive what is left over after the fixed claimants have been paid.
2-27. The Treasury bill is considered the safest of all assets because of its short maturity
and
the belief that the Federal government will never default on its securities. Therefore,
it
serves as the building block for interest rates because other securities have longer
maturities or some default risk, or both, and the Treasury bill rate is the starting point
for
the rate these securities must offer.
2-28. No, because bond ratings are relative measures of risk, not absolute measures. While
a
triple A rating is an indicator of very high quality, a security with such a rating could
still
default.
2-29. Agree. A marginal tax rate is assumed for the municipal. The TEY must be
calculated to put the municipal bond yield on a before tax basis, making it comparable to
other bond
yields.
ANSWERS TO END-OF-CHAPTER PROBLEMS
2-1.
tax
Taxable equivalent yield = tax-exempt municipal yield
1.0 – marginal tax rate
The taxable equivalent yield for a tax-exempt yield of 7.5%, for an investor in a 25%
bracket, is
Taxable equivalent yield = .075 / [1-.25]
= 10%
2-2. According to the problem, the corporate bond yields .08 (1-.15) = 6.8% after tax>
6.5%, so choose the corporate bond. or
The municipal bond has a taxable equivalent yield of .065 / [1 – .15] = 7.65%< 8%, so
choose the corporate bond.
2-3.
First, calculate the effective state rate as:
Marginal state rate x (1 โ marginal federal rate)
.06 x (1 – .15) = 5.1%
Next, calculate the combined effective fed/st tax rate as:
Combined rate = effective state rate + federal rate
= .0510 + .15 = .201
Finally, solve the combined TEY equation using this new combined rate:
Combined TEY = .055 / ( 1 – .201) = .0688 = 6.88%.
CFA
2-4.
Quoted Price
98 1/16
102 7/8
109 9/16
86 11/32
Price per $1 par
value (rounded)
0.9806
1.0288
1.0956
0.8634
Par value
Dollar price
$1,000
$5,000
$10,000
$100,000
980.625
5,143.75
10,956.25
86,343.75
CFA
2-5.
a. Below par value since the coupon rate is less than the yield required by the market.
b. Below par value since the coupon rate is less than the yield required by the market.
c. Below par value since the coupon rate is less than the yield required by the market.
d. Above par value since the coupon rate is greater than the yield required by the market.
e. Par value since the coupon rate is equal to the yield required by the market.
a.
b.
c.
d.
e.
Issue
Coupon rate
A
B
C
D
E
7 ยผ%
8 3/8 %
0%
5 7/8%
4 ยฝ%
Required yield
by the market
7.25%
7.15%
6.20%
5.00%
4.50%
Price
Par
Above par
Below par
Above par
Par
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