CU Floating Rate And Mortgage Bonds Discussion

1st assignment is:

Answer the following questions:

1. What are Floating Rate Bonds? What are the characteristics? Discuss.

2. Discuss Mortgage Bonds & Debentures.

3. Discuss Bond Ratings Criteria. Also what is the importance of Bond Ratings?

REFERENCES ARE MANDATORY.

2nd assignment is:

Write  a brief summary of the important concepts learned from the file below.

Chapter 7
Chapter 7. Bonds and Their Valuation
John Clark/Shutterstock.com
Introduction
Sizing Up Risk in the Bond Market
Many people view Treasury securities as a lackluster but ultrasafe investment. From a
default standpoint, Treasuries are indeed our safest investments, but their prices can still
decline in any given year if interest rates increase. This is especially true for long-term
Treasury bonds, which lost nearly 15% in 2009. However, bonds can also perform well when
rates drop, as they have in many recent years. Indeed, Treasury bonds earned a return of
over 27% in 2011, and they outgained stocks in 9 of the 20 years between 2000 and 2019.
Not all bonds are alike, and they don’t always move in the same direction. For example,
corporate bonds are often callable, and issuers can default on them, whereas Treasury
bonds are not exposed to these risks. To compensate investors for these additional risks,
corporate bonds typically have higher yields. When the economy is strong, corporate bonds
generally produce higher returns than Treasuries because their promised returns are higher,
and most make their promised payments because few go into default. However, when the
economy weakens, concerns about defaults rise, which lead to declines in corporate bond
prices. Furthermore, at any point in time, there are widespread differences among corporate
bonds. For example, in April 2020, outstanding bonds issued by Johnson & Johnson, with an
AAA credit rating, maturing in 2033, were trading at a yield to maturity of 1.902%. At the
same point in time, bonds issued by Genworth Financial Inc., with a B credit rating, maturing
in 2034, were trading at a yield to maturity of 8.033%.
A 2009 article in The Wall Street Journal highlighted the concerns that bond investors faced
in the aftermath of the financial crisis. Much of this advice continues to be relevant in
today’s environment. The article offers what it refers to as “five key pointers”:
Watch Out for Defaults. Investors should be wary of low-rated corporate bonds on the edge
of default. The article cautions investors about increased default risk in the municipal market
as state and local governments struggle to balance their budgets.
Limit Your Rate Risk. Rates are likely to increase over time as the economy continues to
recover. As we see in this chapter, increasing interest rates reduce the value of bonds, and
this effect is particularly important for investors of long-term bonds. For this reason, The
Wall Street Journal writer suggests that some bond investors may want to gradually shift
away from longer-maturity bonds.
Consider a Passive Strategy. This advice is directed specifically to investors in bond mutual
funds. Rather than investing in actively managed funds, where the portfolio manager is
constantly moving in and out of different bonds, the author suggests that investors invest in
index funds or exchange-traded funds (ETFs) that track a broad index of bonds.
Have an Inflation Hedge. Many analysts worry that down the road, higher government
spending and a relaxed monetary policy will ultimately lead to higher levels of inflation. As
we will see in this chapter, one way to hedge against rising inflation is to invest in Treasury
securities that are indexed to inflation.
Don’t Try to Time the Market. As we have seen in recent years, bond prices can move quickly
and dramatically, which makes it difficult to effectively bet on where the market is heading
next. Rather than trying to time the next move in the market, the article urges investors to
adopt a more steady long-term strategy when it comes to bonds.
Although these pointers are relevant in today’s market, in many ways the advice is timeless.
In the face of similar risks in 2001, a BusinessWeek article gave investors the following
similar advice, which is still applicable today:
Take the same diversified approach to bonds as you do with stocks. Blend in U.S.
government, corporate—both high-quality and high-yield—and perhaps even some foreign
government debt. If you’re investing taxable dollars, consider tax-exempt municipal bonds.
And it doesn’t hurt to layer in some inflation-indexed bonds.
Sources: Michael A. Pollack, “The New Bond Equation,” The Wall Street Journal (wsj.com),
August 3, 2009; Scott Patterson, “Ahead of the Tape: Junk Yields Flashing Back to ’01 Slump,”
The Wall Street Journal, January 30, 2008, p. C1; Roger G. Ibbotson, Stocks, Bonds, Bills, and
Inflation: 2020 Yearbook (Chicago, IL: Duff & Phelps, 2020); Susan Scherreik, “Getting the
Most Bang Out of Your Bonds,” BusinessWeek (businessweek.com), November 12, 2001; and
FINRA (finra-markets.morningstar.com/BondCenter/), April 8, 2020.
Putting Things in Perspective
In previous chapters, we noted that companies raise capital in two main forms: debt and
equity. In this chapter, we examine the characteristics of bonds and discuss the various
factors that influence bond prices. In Chapter 9, we will turn our attention to stocks and their
valuation.
If you skim through The Wall Street Journal, you will see references to a wide variety of
bonds. This variety may seem confusing, but in actuality, only a few characteristics
distinguish the various types of bonds.
When you finish this chapter, you should be able to do the following:
Identify the different features of corporate and government bonds.
Discuss how bond prices are determined in the market, what the relationship is between
interest rates and bond prices, and how a bond’s price changes over time as it approaches
maturity.
Calculate a bond’s yield to maturity and yield to call if it is callable, and determine the “true”
yield.
Explain the different types of risk that bond investors and issuers face, and discuss how a
bond’s terms and collateral can be changed to affect its interest rate.
7-1. Who Issues Bonds?
A bond is a long-term contract under which a borrower agrees to make payments of interest
and principal on specific dates to the holders of the bond. Bonds are issued by corporations
and government agencies that are looking for long-term debt capital. For example, on
January 4, 2021, Allied Food Products borrowed $170 million by issuing $170 million of
bonds. For convenience, we assume that Allied sold 170,000 individual bonds for $1,000
each. Actually, it could have sold one $170 million bond, 17 bonds each with a $10 million
face value, or any other combination that totaled $170 million. In any event, Allied received
the $170 million, and in exchange, it promised to make annual interest payments and to
repay the $170 million on a specified maturity date.
Until the 1970s, most bonds were beautifully engraved pieces of paper and their key terms,
including their face values, were spelled out on the bonds. Today, though, virtually all bonds
are represented by electronic data stored in secure computers, much like the “money” in a
bank checking account.
Bonds are grouped in several ways. One grouping is based on the issuer: the U.S. Treasury,
corporations, state and local governments, and foreigners. Each bond differs with respect to
risk and consequently its expected return.
Treasury bonds, generally called Treasuries and sometimes referred to as government bonds,
are issued by the federal government. It is reasonable to assume that the U.S. government
will make good on its promised payments, so Treasuries have no default risk. However, these
bonds’ prices do decline when interest rates rise; so they are not completely riskless.
Corporate bonds are issued by business firms. Unlike Treasuries, corporates are exposed to
default risk—if the issuing company gets into trouble, it may be unable to make the
promised interest and principal payments and bondholders may suffer losses. Corporate
bonds have different levels of default risk depending on the issuing company’s
characteristics and the terms of the specific bond. Default risk is often referred to as “credit
risk,” and as we saw in Chapter 6, the larger this risk, the higher the interest rate investors
demand.
Municipal bonds, or munis, are bonds issued by state and local governments. Like
corporates, munis are exposed to some default risk, but they have one major advantage
over all other bonds: As we discussed in Chapter 3, the interest earned on most munis is
exempt from federal taxes and from state taxes if the holder is a resident of the issuing state.
Consequently, the market interest rate on a muni is considerably lower than on a corporate
bond of equivalent risk.
Foreign bonds are issued by a foreign government or a foreign corporation. All foreign
corporate bonds are exposed to default risk, as are some foreign government bonds. Indeed,
recently, concerns have risen about possible defaults in many countries, including Argentina,
Greece, Ireland, Italy, Portugal, and Spain. In fact, in November 2017, Venezuela defaulted
on its debts. An additional risk exists when the bonds are denominated in a currency other
than that of the investor’s home currency. Consider, for example, a U.S. investor who
purchases a corporate bond denominated in Japanese yen. At some point, the investor will
want to close out his investment and convert the yen back to U.S. dollars. If the Japanese
yen unexpectedly falls relative to the dollar, the investor will have fewer dollars than he
originally expected to receive. Consequently, the investor could still lose money even if the
bond does not default.
SelfTest
What is a bond?
What are the four main issuers of bonds?
Why are U.S. Treasury bonds not completely riskless?
In addition to default risk, what key risk do investors in foreign bonds face? Explain.
7-2. Key Characteristics of Bonds
An excellent website on bonds is finra-markets.morningstar.com/BondCenter/. It provides
extensive information about the bond market, and allows you to quickly search for a
particular bond or to perform an advanced search based on select criteria.
Although all bonds have some common characteristics, different types of bonds can have
different contractual features. For example, most corporate bonds have provisions that allow
the issuer to pay them off early (“call” features), but the specific call provisions vary widely
among different bonds. Similarly, some bonds are backed by specific assets that must be
turned over to the bondholders if the issuer defaults, while other bonds have no such
collateral backup. Differences in contractual provisions (and in the fundamental underlying
financial strength of the companies backing the bonds) lead to differences in bonds’ risks,
prices, and expected returns. To understand bonds, it is essential that you understand the
following terms.
7-2A. Par Value
The par value is the stated face value of the bond; for illustrative purposes, we generally
assume a par value of $1,000, although any multiple of $1,000 (e.g., $10,000 or $10 million)
can be used. The par value generally represents the amount of money the firm borrows and
promises to repay on the maturity date.
7-2B. Coupon Interest Rate
Allied Food Products’s bonds require the company to pay a fixed number of dollars of
interest each year. This payment, generally referred to as the coupon payment, is set at the
time the bond is issued and remains in force during the bond’s life. Typically, at the time a
bond is issued, its coupon payment is set at a level that will induce investors to buy the bond
at or near its par value. Most of the examples and problems throughout this text focus on
bonds with fixed coupon rates.
When this annual coupon payment is divided by the par value, the result is the coupon
interest rate. For example, Allied’s bonds have a $1,000 par value, and they pay $80 in
interest each year. The bond’s coupon payment is $80, so its coupon interest rate is
$
80
/
$
1,000
=
8
%
. In this regard, the $80 is the annual income that an investor receives when he or she
invests in the bond.
Allied’s bonds are fixed-rate bonds because the coupon rate is fixed for the life of the bond.
In some cases, however, a bond’s coupon payment is allowed to vary over time. These
floating-rate bonds work as follows: The coupon rate is set for an initial period, often 6
months, after which it is adjusted every 6 months based on some open market rate. For
example, the bond’s rate may be adjusted so as to equal the 10-year Treasury bond rate plus
a “spread” of 1.5 percentage points. Other provisions can be included in corporate bonds.
For example, some can be converted at the holders’ option into fixed-rate debt, and some
floaters have upper limits (caps) and lower limits (floors) on how high or low the rate can go.
Some bonds pay no coupons at all but are offered at a discount below their par values and
hence provide capital appreciation rather than interest income. These securities are called
zero coupon bonds (zeros). Other bonds pay some coupon interest, but not enough to
induce investors to buy them at par. In general, any bond originally offered at a price
significantly below its par value is called an original issue discount (OID) bond. Some of the
details associated with issuing or investing in zero coupon bonds are discussed in more detail
in Web Appendix 7A.
7-2C. Maturity Date
Bonds generally have a specified maturity date on which the par value must be repaid.
Allied’s bonds, which were issued on January 4, 2021, will mature on January 3, 2036; thus,
they had a 15-year maturity at the time they were issued. Most bonds have an original
maturity (the maturity at the time the bond is issued) ranging from 10 to 40 years, but any
maturity is legally permissible. Of course, the effective maturity of a bond declines each year
after it has been issued. Thus, Allied’s bonds had a 15-year original maturity. But in 2022, a
year later, they will have a 14-year maturity; a year after that, they will have a 13-year
maturity; and so on.
7-2D. Call Provisions
Many corporate and municipal bonds contain a call provision that gives the issuer the right
to call the bonds for redemption. The call provision generally states that the issuer must pay
the bondholders an amount greater than the par value if they are called. The additional sum,
which is termed a call premium, is often equal to 1 year’s interest. For example, the call
premium on a 10-year bond with a 10% annual coupon and a par value of $1,000 might be
$100, which means that the issuer would have to pay investors $1,100 (the par value plus
the call premium) if it wanted to call the bonds. In most cases, the provisions in the bond
contract are set so that the call premium declines over time as the bonds approach maturity.
Also, although some bonds are immediately callable, in most cases, bonds are often not
callable until several years after issue, generally 5 to 10 years. This is known as a deferred
call, and such bonds are said to have call protection.
Companies are not likely to call bonds unless interest rates have declined significantly since
the bonds were issued. Suppose a company sold bonds when interest rates were relatively
high. Provided the issue is callable, the company could sell a new issue of low-yielding
securities if and when interest rates drop, use the proceeds of the new issue to retire the
high-rate issue, and thus reduce its interest expense. This process is called a refunding
operation. Thus, the call privilege is valuable to the firm but detrimental to long-term
investors, who will need to reinvest the funds they receive at the new and lower rates.
Accordingly, the interest rate on a new issue of callable bonds will exceed that on the
company’s new noncallable bonds. For example, on April 30, 2021, Pacific Timber Company
sold a bond issue yielding 6% that was callable immediately. On the same day, Northwest
Milling Company sold an issue with similar risk and maturity that yielded only 5.5%, but its
bonds were noncallable for 10 years. Investors were willing to accept a 0.5% lower coupon
interest rate on Northwest’s bonds for the assurance that the 5.5% interest rate would be
earned for at least 10 years. Pacific, on the other hand, had to incur a 0.5% higher annual
interest rate for the option of calling the bonds in the event of a decline in rates.
Note that the refunding operation is similar to a homeowner refinancing his or her home
mortgage after a decline in interest rates. Consider, for example, a homeowner with an
outstanding mortgage at 7%. If mortgage rates fall to 4%, the homeowner will probably find
it beneficial to refinance the mortgage. There may be some fees involved in the refinancing,
but the lower rate may be more than enough to offset those fees. The analysis required is
essentially the same for homeowners and corporations.
7-2E. Sinking Funds
Some bonds include a sinking fund provision that facilitates the orderly retirement of the
bond issue. Years ago firms were required to deposit money with a trustee that invested the
funds and then used the accumulated sum to retire the bonds when they matured. Today,
though, sinking fund provisions require the issuer to buy back a specified percentage of the
issue each year. A failure to meet the sinking fund requirement constitutes a default, which
may throw the company into bankruptcy. Therefore, a sinking fund is a mandatory payment.
Suppose a company issued $100 million of 20-year bonds and it is required to call 5% of the
issue, or $5 million of bonds, each year. In most cases, the issuer can handle the sinking fund
requirement in either of two ways:
It can call in for redemption, at par value, the required $5 million of bonds. The bonds are
numbered serially, and those called for redemption would be determined by a lottery
administered by the trustee.
The company can buy the required number of bonds on the open market.
The firm will choose the least-cost method. If interest rates have fallen since the bond was
issued, the bond will sell for more than its par value. In this case, the firm will use the call
option. However, if interest rates have risen, the bonds will sell at a price below par, and so
the firm can and will buy $5 million par value of bonds in the open market for less than $5
million. Note that a call for sinking fund purposes is generally different from a refunding call
because most sinking fund calls require no call premium. However, only a small percentage
of the issue is normally callable in a given year.
Although sinking funds are designed to protect investors by ensuring that the bonds are
retired in an orderly fashion, these funds work to the detriment of bondholders if the bond’s
coupon rate is higher than the current market rate. For example, suppose the bond has a
10% coupon, but similar bonds now yield only 7.5%. A sinking fund call at par would require
a long-term investor to give up a bond that pays $100 of interest and then to reinvest in a
bond that pays only $75 per year. This is an obvious disadvantage to those bondholders
whose bonds are called. On balance, however, bonds that have a sinking fund are regarded
as being safer than those without such a provision; so at the time they are issued, sinking
fund bonds have lower coupon rates than otherwise similar bonds without sinking funds.
7-2F. Other Features
Several other types of bonds are used sufficiently often to warrant mention. First,
convertible bonds are bonds that are exchangeable into shares of common stock at a fixed
price at the option of the bondholder. Convertibles offer investors the chance for capital
gains if the stock price increases, but that feature enables the issuing company to set a lower
coupon rate than on nonconvertible debt with similar credit risk. Bonds issued with warrants
are similar to convertibles, but instead of giving the investor an option to exchange the
bonds for stock, warrants give the holder an option to buy stock for a stated price, thereby
providing a capital gain if the stock’s price rises. Because of this factor, bonds issued with
warrants, like convertibles, carry lower coupon rates than otherwise similar nonconvertible
bonds.
While callable bonds give the issuer the right to retire the debt prior to maturity, putable
bonds allow investors to require the company to pay in advance. If interest rates rise,
investors will put the bonds back to the company and reinvest in higher coupon bonds. Yet
another type of bond is the income bond, which pays interest only if the issuer has earned
enough money to pay the interest. Thus, income bonds cannot bankrupt a company;
however, from an investor’s standpoint, they are riskier than “regular” bonds. Yet another
bond is the indexed, or purchasing power, bond. The interest rate is based on an inflation
index such as the consumer price index (CPI), so the interest paid rises automatically when
the inflation rate rises, thus protecting bondholders against inflation. As we mentioned in
Chapter 6, the U.S. Treasury is the main issuer of indexed bonds.
SelfTest
Define floating-rate bonds, zero coupon bonds, callable bonds, putable bonds, income
bonds, convertible bonds, and inflation-indexed bonds (TIPS).
Which is riskier to an investor, other things held constant—a callable bond or a putable
bond? Explain.
In general, how is the rate on a floating-rate bond determined?
What are the two ways sinking funds can be handled? Which alternative will be used if
interest rates have risen? If interest rates have fallen?
7-3. Bond Valuation
Resource
Students can download the Excel chapter models from the textbook’s student companion
site on cengage.com. Once downloaded onto your computer, retrieve the Chapter 7 Excel
model and follow along as you read this chapter.
The value of any financial asset—a stock, a bond, a lease, or even a physical asset such as an
apartment building or a piece of machinery—is the present value of the cash flows the asset
is expected to produce. The cash flows for a standard coupon bearing bond, like those of
Allied Food, consist of interest payments during the bond’s 15-year life plus the amount
borrowed (generally the par value) when the bond matures. In the case of a floating-rate
bond, the interest payments vary over time. For zero coupon bonds, there are no interest
payments, so the only cash flow is the face amount when the bond matures. For a “regular”
bond with a fixed coupon, like Allied’s, here is the situation:
Details
Where:
r
d
=
the market rate of interest on the bond, 8%. This is the discount rate used to calculate the
present value of the cash flows, which is also the bond’s price. In Chapter 6, we discussed in
detail the various factors that determine market interest rates. Note that
r
d
is not the coupon interest rate. However,
r
d
is equal to the coupon rate at times, especially the day the bond is issued; when the two
rates are equal, as in this case, the bond sells at par.
N
=
the number of years before the bond
matures
=
15
. N declines over time after the bond has been issued, so a bond that had a maturity of 15
years when it was issued (original
maturity
=
15
) will have
N
=
14
after 1 year,
N
=
13
after 2 years, and so forth. At this point, we assume that the bond pays interest once a year,
or annually; so N is measured in years. Later on we will analyze semiannual payment bonds,
which pay interest every 6 months.
INT
=
dollars of interest paid each
year
=
Coupon rate
×
Par value
=
0.08
(
$
1,000
)
=
$
80
. In calculator terminology,
INT
=
PMT
=
80
. If the bond had been a semiannual payment bond, the payment would have been $40
every 6 months. The payment would have been zero if Allied had issued zero coupon bonds,
and it would have varied over time if the bond had been a “floater.”
M
=
the par, or maturity, value of the
bond
=
$
1,000
. This amount must be paid at maturity. Back in the 1970s and before, when paper bonds
with paper coupons were used, most bonds had a $1,000 value. Now with computer-entry
bonds, the par amount purchased can vary, but in the text we use $1,000 for simplicity.
We can now redraw the time line to show the numerical values for all variables except the
bond’s value (and price, assuming an equilibrium exists),
V
B
:
Details
The following general equation can be solved to find the value of any bond:
7.1
Bond’s value
=
V
B
=
INT
(
1
+
r
d
)
1
+
INT
(
1
+
r
d
)
2
+
…
+
INT
(
1
+
r
d
)
N
+
M
(
1
+
r
d
)
N
=
∑
t
=
1
N
INT
(
1
+
r
d
)
t
+
M
(
1
+
r
d
)
N
Inserting values for the Allied bond, we have:
V
B
=
∑
t
=
1
15
$
80
(
1.08
)
t
+
$
1,000
(
1.08
)
15
The cash flows consist of an annuity of N years plus a lump sum payment at the end of Year
N, and this fact is reflected in Equation 7.1.
We could simply discount each cash flow back to the present and sum those PVs to find the
bond’s value; see Figure 7.1 for an example. However, this procedure is not very efficient,
especially when the bond has many years to maturity. Therefore, we use a financial
calculator to solve the problem. Here is the setup:
Details
Simply input
N
=
15
,
r
d
=
I
/
YR
=
8
,
INT
=
PMT
=
80
, and
M
=
FV
=
1000
; then press the PV key to find the bond’s value, $1,000. Because the PV is an outflow to the
investor, it is shown with a negative sign. The calculator is programmed to solve Equation
7.1. It finds the PV of an annuity of $80 per year for 15 years discounted at 8%; then it finds
the PV of the $1,000 maturity value; then it adds those two PVs to find the bond’s value. In
this Allied example, the bond is selling at a price equal to its par value.
Whenever the bond’s market, or going, rate,
r
d
, is equal to its coupon rate, a fixed-rate bond will sell at its par value. Normally, the coupon
rate is set at the going rate in the market the day a bond is issued, causing it to sell at par
initially.
The coupon rate remains fixed after the bond is issued, but interest rates in the market move
up and down. Looking at Equation 7.1, we see that an increase in the market interest rate
(
r
d
)
causes the price of an outstanding bond to fall, whereas a decrease in the rate causes the
bond’s price to rise. For example, if the market interest rate on Allied’s bond increased to
12% immediately after it was issued, we would recalculate the price with the new market
interest rate as follows:
Details
The bond’s price would fall to $727.57, well below par, as a result of the increase in interest
rates. Whenever the going rate of interest rises above the coupon rate, a fixed-rate bond’s
price will fall below its par value; this type of bond is called a discount bond.
Figure 7.1 Time Line for Allied Food Products’ Bonds, 8% Interest Rate
Details
On the other hand, bond prices rise when market interest rates fall. For example, if the
market interest rate on Allied’s bond decreased to 4% immediately after it was issued, we
would once again recalculate its price as follows:
Details
In this case, the price rises to $1,444.74. In general, whenever the going interest rate falls
below the coupon rate, a fixed-rate bond’s price will rise above its par value; this type of
bond is called a premium bond.
To summarize, here is the situation:
r
d
=
coupon rate, fixed-rate bond sells at par; hence, it is a par bond.
r
d
>
coupon rate, fixed-rate bond sells below par; hence, it is a discount bond.
r
d
< coupon rate, fixed-rate bond sells above par; hence, it is a premium bond. Quick Question Question A friend of yours just invested in an outstanding bond with a 5% annual coupon and a remaining maturity of 10 years. The bond has a par value of $1,000, and the market interest rate is currently 7%. How much did your friend pay for the bond? Is it a par, premium, or discount bond? Answer Using a financial calculator, we can determine that your friend paid $859.53 for the bond. Details Using Excel’s PV function, we solve for the bond’s value as follows: Details Here we find that the bond’s value is equal to $859.53. Because the bond’s coupon rate (5%) is less than the current market interest rate (7%), the bond is a discount bond—reflecting that interest rates have increased since this bond was originally issued. SelfTest A bond that matures in 8 years has a par value of $1,000 and an annual coupon payment of $70; its market interest rate is 9%. What is its price? ($889.30) A bond that matures in 12 years has a par value of $1,000 and an annual coupon rate of 10%; the market interest rate is 8%. What is its price? ($1,150.72) Which of those two bonds is a discount bond, and which is a premium bond? Explain. 7-4. Bond Yields If you examine the bond market table of The Wall Street Journal or a price sheet put out by a bond dealer, you will typically see information regarding each bond’s maturity date, price, and coupon interest rate. You will also see a reported yield. Unlike the coupon interest rate, which is fixed, the bond’s yield varies from day to day, depending on current market conditions. To be most useful, the bond’s yield should give us an estimate of the rate of return we would earn if we purchased the bond today and held it over its remaining life. If the bond is not callable, its remaining life is its years to maturity. If it is callable, its remaining life is the years to maturity if it is not called or the years to the call if it is called. In the following sections, we explain how to calculate those two possible yields and which one is likely to be earned by an investor. 7-4A. Yield to Maturity Suppose you were offered a 14-year, 8% annual coupon, $1,000 par value bond at a price of $1,422.52. What rate of interest would you earn on your investment if you bought the bond, held it to maturity, and received the promised interest payments and maturity value? This rate is called the bond’s yield to maturity (YTM), and it is the interest rate generally discussed by investors when they talk about rates of return and the rate reported by The Wall Street Journal and other publications. To find the YTM, all you need to do is solve Equation 7.1 for r d as follows: V B = INT ( 1 + r d ) 1 + INT ( 1 + r d ) 2 + … + INT ( 1 + r d ) N + � ( 1 + r d ) N $ 1,422.52 = $ 80 ( 1 + r d ) 1 + … + $ 80 ( 1 + r d ) 14 + $ 1,000 ( 1 + r d ) 14 You can substitute values for r d until you find a value that “works” and force the sum of the PVs in the equation to equal $1,422.52. However, finding r d = YTM by trial and error would be a tedious, time-consuming process. However, as you might guess, the calculation is easy with a financial calculator. Here is the setup: Simply enter N = 14 , PV = 1422.52 , PMT = 80 , and FV = 1000 ; then press the I/YR key. The answer, 4%, will appear. Quick Question Question You have just purchased an outstanding 15-year bond with a par value of $1,000 for $1,145.68. Its annual coupon payment is $75. What is the bond’s yield to maturity? Answer Using a financial calculator, we can determine that the bond’s YTM is 6%. Details Using Excel’s RATE function, we solve for the bond’s YTM as follows: Details Here we find the bond’s YTM is equal to 6%. Because the bond’s coupon rate ( $ 75 / $ 1,000 = 7.5 % ) is greater than its YTM 6%, the bond is a premium bond—indicating that interest rates have declined since the bond was originally issued. The yield to maturity can also be viewed as the bond’s promised rate of return, which is the return that investors will receive if all of the promised payments are made. However, the yield to maturity equals the expected rate of return only when (1) the probability of default is zero and (2) the bond cannot be called. If there is some default risk or the bond may be called, there is some chance that the promised payments to maturity will not be received, in which case the calculated yield to maturity will exceed the expected return. Note also that a bond’s calculated yield to maturity changes whenever interest rates in the economy change, which is almost daily. An investor who purchases a bond and holds it until it matures will receive the YTM that existed on the purchase date, but the bond’s calculated YTM will change frequently between the purchase date and the maturity date. 7-4B. Yield to Call If you purchase a bond that is callable and the company calls it, you do not have the option of holding it to maturity. Therefore, the yield to maturity would not be earned. For example, if Allied’s 8% coupon bonds were callable and if interest rates fell from 8% to 4%, the company could call in the 8% bonds, replace them with 4% bonds, and save $ 80 $ 40 = $ 40 interest per bond per year. This would be beneficial to the company, but not to its bondholders. If current interest rates are well below an outstanding bond’s coupon rate, a callable bond is likely to be called, and investors will estimate its most likely rate of return as the yield to call (YTC) rather than the yield to maturity. To calculate the YTC, we modify Equation 7.1, using years to call as N and the call price rather than the maturity value as the ending payment. Here’s the modified equation: 7.2 Price of bond = ∑ t = 1 N INT ( 1 + r d ) t + Call price ( 1 + r d ) N Here N is the number of years until the company can call the bond, call price is the price the company must pay in order to call the bond (it is often set equal to the par value plus 1 year’s interest), and r d is the YTC. To illustrate, suppose Allied’s bonds had a deferred call provision that permitted the company, if it desired, to call them 10 years after their issue date at a price of $1,080. Suppose further that interest rates had fallen and that 1 year after issuance the going interest rate had declined, causing their price to rise to $1,422.52. Here is the time line and the setup for finding the bonds’ YTC with a financial calculator: Details Details The YTC is 3.28%—this is the return you would earn if you bought an Allied bond at a price of $1,422.52 and it was called 9 years from today. (It could not be called until 10 years after issuance because of its deferred call provision. One year has gone by, so there are 9 years left until the first call date.) A company is more likely to call its bonds if they are able to replace their current highcoupon debt with less expensive financing. Broadly speaking, a bond is more likely to be called if its price is above par—because a price above par means that the going market interest rate (the yield to maturity) is less than the coupon rate. So, do you think Allied will call its 8% bonds when they become callable? Allied’s action will depend on what the going interest rate is when they become callable. If the going rate remains at r d = 4 % , Allied could save 8 % 4 % = 4 % , or $40 per bond per year; so it would call the 8% bonds and replace them with a new 4% issue. There would be some cost to the company to refund the bonds, but because the interest savings would most likely be worth the cost, Allied would probably refund them. Therefore, you should expect to earn the YTC = 3.28 % rather than the YTM = 4 % if you purchased the bond under the indicated conditions. Quick Question Question You have just purchased an outstanding 15-year bond with a par value of $1,000 for $1,145.68. Its annual coupon payment is $75. We calculated the YTM of this bond (6%) in the Quick Question. Now, assume that this bond is callable in 7 years at a price of $1,075. What is the bond’s YTC? If the yield curve remains flat at its current level during this time period, would you expect to earn the YTM or YTC? Answer Using a financial calculator, we can determine that the bond’s YTC is 5.81%. Details Using Excel’s RATE function, we solve for the bond’s YTC as follows: Details Here we find the bond’s YTC is equal to 5.81%. This bond sells at a premium, so interest rates have declined since the bond was originally issued. If the yield curve remained flat at this current level during the next 7 years, you would expect the firm to call the bond and issue bonds at the lower 6% interest rate, assuming the cost of doing so was lower than the $ 75 $ 60 = $ 15 savings per bond. In the balance of this chapter, we assume that bonds are not callable unless otherwise noted. However, some of the end-of-chapter problems deal with yield to call. SelfTest Explain the difference between yield to maturity (YTM) and yield to call (YTC). Halley Enterprises’s bonds currently sell for $975. They have a 7-year maturity, an annual coupon of $90, and a par value of $1,000. What is their yield to maturity? (9.51%) The Henderson Company’s bonds currently sell for $1,275. They pay a $120 annual coupon, have a 20-year maturity, and a par value of $1,000, but they can be called in 5 years at $1,120. What are their YTM and their YTC, and if the yield curve remained flat, which rate would investors expect to earn? (8.99%, 7.31%, YTC) 7-5. Changes in Bond Values over Time When a coupon bond is issued, the coupon is generally set at a level that causes the bond’s market price to equal its par value. If a lower coupon were set, investors would not be willing to pay $1,000 for the bond, but if a higher coupon were set, investors would clamor for it and bid its price up over $1,000. Investment bankers can judge quite precisely the coupon rate that will cause a bond to sell at its $1,000 par value. A bond that has just been issued is known as a new issue. Once it has been issued, it is an outstanding bond, also called a seasoned issue. Newly issued bonds generally sell at prices very close to par, but the prices of outstanding bonds can vary widely from par. Except for floating-rate bonds, coupon payments are constant; so when economic conditions change, a bond with an $80 coupon that sold at its $1,000 par value when it was issued will sell for more or less than $1,000 thereafter. Among its outstanding bonds, Allied currently has three equally risky issues that will mature in 15 years: Allied’s just-issued 15-year bonds have an 8% annual coupon. They were issued at par, which means that the market interest rate on their issue date was also 8%. Because the coupon rate equals the market interest rate, these bonds are trading at par, or $1,000. Five years ago Allied issued 20-year bonds with a 5% annual coupon. These bonds currently have 15 years remaining until maturity. They were originally issued at par, which means that 5 years ago the market interest rate was 5%. Currently, this bond’s coupon rate is less than the 8% market rate, so they sell at a discount. Using a financial calculator or spreadsheet, we can quickly find that they have a price of $743.22. (Set N = 15 , I / YR = 8 , PMT = 50 , and FV = 1000 , and solve for the PV to calculate the price.) Ten years ago Allied issued 25-year bonds with an 11% annual coupon. These bonds currently have 15 years remaining until maturity. They were originally issued at par, which means that 10 years ago the market interest rate must have been 11%. Because their coupon rate is greater than the current market rate, they sell at a premium. Using a financial calculator or spreadsheet, we can find that their price is $1,256.78. (Set N = 15 , I / YR = 8 , PMT = 110 , and FV = 1000 , and solve for the PV to determine the price.) Each of these three bonds has a 15-year maturity, each has the same credit risk, and thus each has the same market interest rate, 8%. However, the bonds have different prices because of their different coupon rates. Now let’s consider what would happen to the prices of these three bonds over the 15 years until they mature, assuming that market interest rates remain constant at 8% and Allied does not default on its payments. Table 7.1 demonstrates how the prices of each of these bonds will change over time if market interest rates remain at 8%. One year from now each bond will have a maturity of 14 years—that is, N = 14 . With a financial calculator, override N = 15 with N = 14 , and press the PV key; that gives you the value of each bond 1 year from now. Continuing, set N = 13 , N = 12 , and so forth, to see how the prices change over time. Table 7.1 also shows the current yield (which is the coupon interest divided by the bond’s price), the capital gains yield, and the total return over time. For any given year, the capital gains yield is calculated as the bond’s annual change in price divided by the beginning-ofyear price. For example, if a bond was selling for $1,000 at the beginning of the year and $1,035 at the end of the year, its capital gains yield for the year would be $ 35 / $ 1,000 = 3.5 % . (If the bond was selling at a premium, its price would decline over time. Then the capital gains yield would be negative, but it would be offset by a high current yield.) A bond’s total return is equal to the current yield plus the capital gains yield. In the absence of default risk and assuming market equilibrium, the total return is also equal to YTM and the market interest rate, which in our example is 8%. Table 7.1 Calculation of Current Yields, Capital Gains Yields, and Total Returns for 5%, 8%, and 11% Coupon Bonds When the Market Rate Remains Constant at 8% Details Figure 7.2 plots the three bonds’ predicted prices as calculated in Table 7.1. Notice that the bonds have very different price paths over time but that at maturity all three will sell at their par value of $1,000. Here are some points about the prices of the bonds over time: The price of the 8% coupon bond trading at par will remain at $1,000 if the market interest rate remains at 8%. Therefore, its current yield will remain at 8%, and its capital gains yield will be zero each year. The 5% bond trades at a discount; however, at maturity, it must sell at par because that is the amount the company will pay its bondholders. Therefore, its price must rise over time. The 11% coupon bond trades at a premium. However, its price must be equal to its par value at maturity; so the price must decline over time. Figure 7.2 Time Paths of 5%, 8%, and 11% Coupon Bonds When the Market Rate Remains Constant at 8% Details Although the prices of the 5% and 11% coupon bonds move in opposite directions over time, each bond provides investors with the same total return, 8%, which is also the total return on the 8% coupon par value bond. The discount bond has a low coupon rate (and therefore a low current yield), but it provides a capital gain each year. In contrast, the premium bond has a high current yield, but it has an expected capital loss each year. SelfTest What is meant by the terms new issue and seasoned issue? Last year a firm issued 20-year, 8% annual coupon bonds at a par value of $1,000. Suppose that 1 year later the going market interest rate drops to 6%. What is the new price of the bonds, assuming they now have 19 years to maturity? ($1,223.16) Suppose that 1 year after issue, the going market interest rate is 10% (rather than 6%). What would the price have been? ($832.70) Why do the prices of fixed-rate bonds fall if expectations for inflation rise? 7-6. Bonds with Semiannual Coupons Although some bonds pay interest annually, the vast majority actually make payments semiannually. To evaluate semiannual bonds, we must modify the valuation model (Equation 7.1) as follows: Divide the annual coupon interest payment by 2 to determine the dollars of interest paid each 6 months. Multiply the years to maturity, N, by 2 to determine the number of semiannual periods. Divide the nominal (quoted) interest rate, r d , by 2 to determine the periodic (semiannual) interest rate. On a time line, there would be twice as many payments, but each would be half as large as with an annual payment bond. Making the indicated changes results in the following equation for finding a semiannual bond’s value: 7.1a V B = ∑ t = 1 2 N INT / 2 ( 1 + r d / 2 ) t + M ( 1 + r d / 2 ) 2 N To illustrate, assume that Allied Food’s 15-year bonds, as discussed in Section 7-3, pay $40 of interest each 6 months rather than $80 at the end of each year. Thus, each interest payment is only half as large but there are twice as many of them. We would describe the coupon rate as “8% with semiannual payments.” When the going (nominal) rate is r d = 4 % with semiannual compounding, the value of a 15-year, 8% semiannual coupon bond that pays $40 interest every 6 months is found as follows: Details Enter N = 30 , r d I / YR = 2 , PMT = 40 , and FV = 1000 ; then press the PV key to obtain the bond’s value, $1,447.93. The value with semiannual interest payments is slightly larger than $1,444.74, the value when interest is paid annually as we calculated in Section 7-3. This higher value occurs because each interest payment is received somewhat faster under semiannual compounding. Alternatively, when we know the price of a semiannual bond, we can easily back out the bond’s nominal yield to maturity. In the previous example, if you were told that a 15-year bond with an 8% semiannual coupon was selling for $1,447.93, you could solve for the bond’s periodic interest rate as follows: Details In this case, enter N = 30 , PV = 1447.93 , PMT = 40 , and FV = 1000 ; then press the I/YR key to obtain the interest rate per semiannual period, 2%. Multiplying by 2, we calculate the bond’s nominal yield to maturity to be 4%. Quick Question Question You have just purchased an outstanding noncallable, 15-year bond with a par value of $1,000. Assume that this bond pays interest of 7.5%, with semiannual compounding. If the going (nominal) annual rate is 6%, what price did you pay for this bond? How does the price compare to the price of the annual coupon bond? Answer Using a financial calculator, we can determine that the bond’s price is $1,147.00. Details Using Excel’s PV function, we solve for the semiannual bond’s price as follows: Details Here we find that the bond’s value is equal to $1,147.00. In the Quick Question we calculated the YTM on this annual bond whose price was $1,145.68. Notice that the semiannual bond’s price is $ 1,147.00 $ 1,145.68 = $ 1.32 greater due to the interest payments being received semiannually rather than on an annual basis. SelfTest Describe how the annual payment bond valuation formula is changed to evaluate semiannual coupon bonds, and write the revised formula. Hartwell Corporation’s bonds have a 20-year maturity, an 8% semiannual coupon, and a face value of $1,000. The going nominal annual interest rate ( r d ) is 7%. What is the bond’s price? ($1,106.78) 7-7. Assessing a Bond’s Riskiness In this section, we identify and explain the two key factors that impact a bond’s riskiness. Once those factors are identified, we differentiate between them and discuss how you can minimize these risks. 7-7A. Price Risk As we saw in Chapter 6, interest rates fluctuate over time, and when they rise, the value of outstanding bonds decline. This risk of a decline in bond values due to an increase in interest rates is called price risk (or interest rate risk). To illustrate, refer back to Allied’s bonds; assume once more that they have an 8% annual coupon, and assume that you bought one of these bonds at its par value, $1,000. Shortly after your purchase, the going interest rate rises from 8% to 12%. As we saw in Section 7-3, this interest rate increase would cause the bond’s price to fall from $1,000 to $727.57, so you would have a loss of $272.43 on the bond. Because interest rates can and do rise, rising rates cause losses to bondholders; people or firms who invest in bonds are exposed to risk from increasing interest rates. Price risk is higher on bonds that have long maturities than on bonds that will mature in the near future. This follows because the longer the maturity, the longer before the bond will be paid off and the bondholder can replace it with another bond with a higher coupon. This point can be demonstrated by showing how the value of a 1-year bond with an 8% annual coupon fluctuates with changes in r d and then comparing those changes with changes on a 15-year bond. The 1-year bond’s values at different interest rates are shown here: Value of a 1-year bond at: Details You would obtain the first value with a financial calculator by entering N = 1 , I / YR = 4 , PMT = 80 , and FV = 1000 and then pressing PV to get $1,038.46. With all the data still in your calculator, enter I / YR = 8 to override the old I / YR = 4 , and press PV to find the bond’s value at an 8% rate; it drops to $1,000. Then enter I / YR = 12 , and press the PV key to find the last bond value, $964.29. The effects of increasing rates on the 15-year bond value as found earlier in Section 7-3 can be compared with the just-calculated effects for the 1-year bond. This comparison is shown in Figure 7.3, where we show bond prices at several rates and then plot those prices on the graph. Compared to the 1-year bond, the 15-year bond is far more sensitive to changes in rates. At an 8% interest rate, both the 15-year and 1-year bonds are valued at $1,000. When rates rise to 12%, the 15-year bond falls to $727.57, but the 1-year bond falls only to $964.29. The price decline for the 1-year bond is only 3.57%, while that for the 15-year bond is 27.24%. Figure 7.3 Values of Long- and Short-Term 8% Annual Coupon Bonds at Different Market Interest Rates Details Note: Bond values were calculated using a financial calculator assuming annual, or once a year, compounding. For bonds with similar coupons, this differential interest rate sensitivity always holds true— the longer a bond’s maturity, the more its price changes in response to a given change in interest rates. Thus, even if the risk of default on two bonds is exactly the same, the one with the longer maturity is typically exposed to more risk from a rise in interest rates. The logical explanation for this difference in price risk is simple. Suppose you bought a 15year bond that yielded 8%, or $80 a year. Now suppose interest rates on comparable-risk bonds rose to 12%. You would be stuck receiving only $80 of interest for the next 15 years. On the other hand, had you bought a 1-year bond, you would have earned a low return for only 1 year. At the end of the year, you would have received your $1,000 back; then you could have reinvested it and earned 12%, or $120 per year, for the next 14 years. 7-7B. Reinvestment Risk As we saw in the preceding section, an increase in interest rates hurts bondholders because it leads to a decline in the current value of a bond portfolio. But can a decrease in interest rates also hurt bondholders? The answer is yes because if interest rates fall, long-term investors will suffer a reduction in income. For example, consider a retiree who has a bond portfolio and lives off the income it produces. The bonds in the portfolio, on average, have coupon rates of 8%. Now suppose interest rates decline to 4%. Many of the bonds will mature or be called; as this occurs, the bondholder will have to replace 8% bonds with 4% bonds. Thus, the retiree will suffer a reduction of income. The risk of an income decline due to a drop in interest rates is called reinvestment risk, and its importance has been demonstrated to all bondholders in recent years as a result of the sharp drop in rates since the mid-1980s. Reinvestment risk is obviously high on callable bonds. It is also high on short-term bonds because the shorter the bond’s maturity, the fewer the years before the relatively high old coupon bonds will be replaced with the new low-coupon issues. Thus, retirees whose primary holdings are short-term bonds or other debt securities will be hurt badly by a decline in rates, but holders of noncallable long-term bonds will continue to enjoy the old high rates. 7-7C. Comparing Price Risk and Reinvestment Risk Note that price risk relates to the current market value of the bond portfolio, while reinvestment risk relates to the income the portfolio produces. If you hold long-term bonds, you will face significant price risk because the value of your portfolio will decline if interest rates rise, but you will not face much reinvestment risk because your income will be stable. On the other hand, if you hold short-term bonds, you will not be exposed to much price risk, but you will be exposed to significant reinvestment risk. Table 7.2 summarizes how a bond’s maturity and coupon rate affect its price risk and reinvestment risk. For example, a longterm zero coupon bond will have a very high level of price risk and relatively little reinvestment risk. In contrast, a short-term bond with a high coupon rate will have low price risk but considerable reinvestment risk. Table 7.2 Comparing Price Risk and Reinvestment Risk Bond Level of Price Risk Level of Reinvestment Risk Longer-maturity bonds High Low Higher-coupon bonds Low High Which type of risk is “more relevant” to a given investor depends on how long the investor plans to hold the bonds—this is often referred to as his or her investment horizon. To illustrate, consider an investor who has a relatively short 1-year investment horizon—say, the investor plans to go to graduate school a year from now and needs money for tuition and expenses. Reinvestment risk is of minimal concern to this investor because there is little time to reinvest. The investor could eliminate price risk by buying a 1-year Treasury security because he would be assured of receiving the face value of the bond 1 year from now (the investment horizon). However, if this investor were to buy a long-term Treasury security, he would bear a considerable amount of price risk because, as we have seen, long-term bond prices decline when interest rates rise. Consequently, investors with shorter investment horizons should view long-term bonds as being more risky than short-term bonds. By contrast, the reinvestment risk inherent in short-term bonds is especially relevant to investors with longer investment horizons. Consider a retiree who is living on income from her portfolio. If this investor buys 1-year bonds, she will have to “roll them over” every year, and if rates fall, her income in subsequent years will likewise decline. A younger couple saving for their retirement or their children’s college costs, for example, would be affected similarly because if they buy short-term bonds, they too will have to roll over their portfolio at possibly much lower rates. Because of the uncertainty today about the rates that will be earned on these reinvested cash flows, long-term investors should be especially concerned about the reinvestment risk inherent in short-term bonds. To account for the effects related to both a bond’s maturity and coupon, many analysts focus on a measure called duration. A bond’s duration is the weighted average of the time it takes to receive each of the bond’s cash flows. It follows that a zero coupon bond whose only cash flow is paid at maturity has a duration equal to its maturity. On the other hand, a coupon bond will have a duration that is less than its maturity. You can use Excel’s DURATION function to calculate a bond’s duration. We discuss duration in greater detail in Web Appendix 7B. One way to manage both price and reinvestment risk is to buy a zero coupon Treasury bond with a duration equal to the investor’s investment horizon. A very simple way to do this is to buy a zero coupon bond with a maturity that matches the investment horizon. For example, assume your investment horizon is 10 years. If you buy a 10-year zero, you will receive a guaranteed payment in 10 years equal to the bond’s face value. Moreover, as there are no coupons to reinvest, there is no reinvestment risk. This explains why investors with specific goals often invest in zero coupon bonds. Recall from Chapter 6 that maturity risk premiums are generally positive. Moreover, a positive maturity risk premium implies that investors, on average, regard longer-term bonds as being riskier than shorter-term bonds. That, in turn, suggests that the average investor is more concerned with price risk. Still, it is appropriate for each investor to consider his or her own situation, to recognize the risks inherent in bonds with different maturities, and to construct a portfolio that deals best with the investor’s most relevant risk. SelfTest Differentiate between price risk and reinvestment risk. To which type of risk are holders of long-term bonds more exposed? Short-term bondholders? What type of security can be used to minimize both price risk and reinvestment risk for an investor with a fixed investment horizon? Does this security protect the real payoff? Explain. 7-8. Default Risk Potential default is another important risk that bondholders face. If the issuer defaults, investors will receive less than the promised return. Recall from Chapter 6 that the quoted interest rate includes a default risk premium—the higher the probability of default, the higher the premium and thus the yield to maturity. Default risk on Treasuries is zero, but this risk is substantial for lower-grade corporate and municipal bonds. To illustrate, suppose two bonds have the same promised cash flows—their coupon rates, maturities, liquidity, and inflation exposures are identical—but one has more default risk than the other. Investors will naturally pay more for the one with less chance of default. As a result, bonds with higher default risk have higher market rates: r d = r * + IP + DRP + LP + MRP . If a bond’s default risk changes, r d and thus the price will be affected. Thus, if the default risk on Allied’s bonds increases, their price will fall and the yield to maturity ( YTM = r d ) will increase. 7-8A. Various Types of Corporate Bonds Default risk is influenced by the financial strength of the issuer and the terms of the bond contract, including whether collateral has been pledged to secure the bond. The characteristics of some key types of bonds are described in this section. Mortgage Bonds Under a mortgage bond, the corporation pledges specific assets as security for the bond. To illustrate, in 2021, Billingham Corporation needed $10 million to build a regional distribution center. Bonds in the amount of $4 million, secured by a first mortgage on the property, were issued. (The remaining $6 million was financed with equity capital.) If Billingham defaults on the bonds, the bondholders can foreclose on the property and sell it to satisfy their claims. If Billingham had chosen to, it could have issued second mortgage bonds secured by the same $10 million of assets. In the event of liquidation, the holders of the second mortgage bonds would have a claim against the property, but only after the first mortgage bondholders had been paid in full. Thus, second mortgages are sometimes called junior mortgages because they are junior in priority to the claims of senior mortgages, or first mortgage bonds. All mortgage bonds are subject to an indenture, which is a legal document that spells out in detail the rights of the bondholders and the corporation. The indentures of many major corporations were written 20, 30, 40, or more years ago. These indentures are generally “open ended,” meaning that new bonds can be issued from time to time under the same indenture. However, the amount of new bonds that can be issued is usually limited to a specified percentage of the firm’s total “bondable property,” which generally includes all land, plant, and equipment. And, of course, the coupon interest rate on newly issued bonds changes over time, along with the market rate on the older bonds. Debentures A debenture is an unsecured bond, and as such, it provides no specific collateral as security for the obligation. Therefore, debenture holders are general creditors whose claims are protected by property not otherwise pledged. In practice, the use of debentures depends on the nature of the firm’s assets and on its general credit strength. Extremely strong companies such as General Electric and ExxonMobil can use debentures because they do not need to put up property as security for their debt. Debentures are also issued by weak companies that have already pledged most of their assets as collateral for mortgage loans. In this case, the debentures are quite risky, and that risk will be reflected in their interest rates. A 2020 study by Benmelech, Kumar, and Rajan documents a dramatic decline in the use of secured financing over the past century. While 98.5% of debt issued in 1900 was secured, this proportion has fallen to around 15% in recent years. The authors suggest that bondholders have become more confident that their claims will be honored in bankruptcy even without having the additional security protection, and this increased confidence has made them more willing to invest in unsecured debt. At the same time, issuers often prefer unsecured debt because they want to preserve the option to issue secured debt later if times become tough. Consistent with this view, they also find that the proportion of secured financing does typically increase during economic downturns. Subordinated Debentures The term subordinate means “below” or “inferior to,” and in the event of bankruptcy, subordinated debt has a claim on assets only after senior debt has been paid in full. Subordinated debentures may be subordinated to designated notes payable (usually bank loans) or to all other debt. In the event of liquidation or reorganization, holders of subordinated debentures receive nothing until all senior debt, as named in the debentures’ indenture, has been paid. Precisely how subordination works and how it strengthens the position of senior debtholders are explained in detail in Web Appendix 7C. 7-8B. Bond Ratings Since the early 1900s, bonds have been assigned quality ratings that reflect their probability of going into default. The three major rating agencies are Moody’s Investors Service (Moody’s), Standard & Poor’s Corporation (S&P), and Fitch Investors Service. Moody’s and S&P’s rating designations are shown in Table 7.3. The triple-A and double-A bonds are extremely safe. Single-A and triple-B bonds are also strong enough to be called investmentgrade bonds, and they are the lowest-rated bonds that many banks and other institutional investors are permitted by law to hold. Double-B and lower bonds are speculative-grade bonds (junk bonds), and they have a significant probability of going into default. Table 7.3 Bond Ratings, Default Risk, and Yields Consistent with these arguments, Table 7.3 shows that lower-rated bonds generally have higher default rates. These numbers are based on an underlying sample of bonds rated by Fitch Ratings over the past several years. For example, 0.46% of A-rated bonds defaulted within the first 5 years of being issued, whereas 36.19% of C-rated bonds defaulted within 5 years. The numbers in this table also illustrate that (as expected) lower-rated bonds have higher yields and their issuing companies have higher debt ratios. Bond Rating Criteria The framework used by rating agencies examines both qualitative and quantitative factors. Quantitative factors relate to financial risk—examining a firm’s financial ratios, such as those discussed in Chapter 4. Published ratios are, of course, historical—they show the firm’s condition in the past, whereas bond investors are more interested in the firm’s condition in the future. Qualitative factors considered include an analysis of a firm’s business risk, such as its competitiveness within its industry and the quality of its management. Determinants of bond ratings include the following: Financial Ratios. All of the ratios are potentially important, but those related to financial risk are key. The rating agencies’ analysts perform a financial analysis along the lines discussed in Chapter 4 and forecast future ratios along the lines described in Chapter 17. Qualitative Factors: Bond Contract Terms. Every bond is covered by a contract, often called an indenture, between the issuer and the bondholders. The indenture spells out all the terms related to the bond. Included in the indenture are the maturity, the coupon interest rate, a statement of whether the bond is secured by a mortgage on specific assets, any sinking fund provisions, and a statement of whether the bond is guaranteed by some other party with a high credit ranking. Other provisions might include restrictive covenants such as requirements that the firm not let its debt ratio exceed a stated level and that it keep its times-interest-earned ratio at or above a given level. Some bond indentures are hundreds of pages long, while others are quite short and cover just the terms of the loan. Miscellaneous Qualitative Factors. Included here are issues like the sensitivity of the firm’s earnings to the strength of the economy, the way it is affected by inflation, a statement of whether it is having or likely to have labor problems, the extent of its international operations (including the stability of the countries in which it operates), potential environmental problems, and potential antitrust problems. Today the most important factor is exposure to subprime loans, including the difficulty to determine the extent of this exposure as a result of the complexity of the assets backed by such loans. We see that bond ratings are determined by a great many factors, some quantitative and some qualitative (or subjective). Also, the rating process is dynamic—at times, one factor is of primary importance; at other times, some other factor is key. Table 7.4 provides a summary of the criteria a rating agency examines when rating a company’s bonds. Panel a shows how business and financial risk determine the “anchor” for establishing the underlying bond rating. Panel b further illustrates how this anchor is combined with a comprehensive set of other factors to determine the issuer’s final credit rating. Table 7.4 Bond Rating Criteria Details Source: “Corporate Ratings Methodology,” Standard & Poor’s Ratings Services (McGraw-Hill Financial), April 2014. Importance of Bond Ratings Bond ratings are important to both firms and investors. First, because a bond’s rating is an indicator of its default risk, the rating has a direct, measurable influence on the bond’s interest rate and the firm’s cost of debt. Second, most bonds are purchased by institutional investors rather than individuals, and many institutions are restricted to investment-grade securities. Thus, if a firm’s bonds fall below BBB, it will have a difficult time selling new bonds because many potential purchasers will not be allowed to buy them. As a result of their higher risk and more restricted market, lower-grade bonds have higher required rates of return, r d , than high-grade bonds. Figure 7.4 illustrates this point. In each of the years shown on the graph, U.S. government bonds have had the lowest yields, AAA bonds have been next, and BBB bonds have had the highest yields. The figure also shows that the gaps between yields on the three types of bonds vary over time, indicating that the cost differentials, or yield spreads, fluctuate from year to year. There was a dramatic increase in the yield spreads between corporate and Treasury securities in the aftermath of the recent financial crisis. In the years after the crisis, these spreads narrowed as investors slowly once again became more willing to hold riskier securities. This point is highlighted in Figure 7.5, which gives the yields on the three types of bonds and the yield spreads for AAA and BBB bonds over Treasuries in January 2009 and January 2020. Note first from Figure 7.5 that the risk-free rate, or vertical axis intercept, was lower in January 2020 than it was in January 2009. Second, the slope of the line decreased. Finally, it is worth noting that in the months following January 2020, these spreads once again started to increase due to economic concerns related to the coronavirus pandemic. Figure 7.4 Yields on Selected Long-Term Bonds, 1994–2020 Details Source: FRED Economic Data, Federal Reserve Bank of St. Louis, fred.stlouisfed.org. Figure 7.5 Relationship between Bond Ratings and Bond Yields, 2009 and 2020 Details Source: FRED Economic Data, Federal Reserve Bank of St. Louis, fred.stlouisfed.org. Changes in Ratings Changes in a firm’s bond rating affect its ability to borrow funds and its cost of that capital. Rating agencies review outstanding bonds on a periodic basis, occasionally upgrading or downgrading a bond as a result of its issuer’s changed circumstances. For example, on April 11, 2018, Moody’s upgraded the debt rating of Netflix from B1 to Ba3. Moody’s cited expectations for continuing subscriber and revenue growth as reasons for the upgrade. On the other hand, on March 27, 2018, Moody’s downgraded Tesla’s credit rating from B2 to B3. Moody’s cited the shortfall in Tesla’s Model 3 production and a tight financial situation as reasons for the downgrade. Table 7.3 provides data on the percentage of downgrades and upgrades within each rating category for 2019. As you can see, with the exception of the AAA-rated bonds, the percentage of downgrades in 2019 exceeded the percentage of upgrades at each bond rating. Over the long run, rating agencies have done a reasonably good job of measuring the average credit risk of bonds and of changing ratings whenever there is a significant change in credit quality. However, it is important to understand that ratings do not adjust immediately to changes in credit quality, and in some cases, there can be a considerable lag between a change in credit quality and a change in rating. For example, Enron’s bonds still carried an investment-grade rating on a Friday in December 2001, but the company declared bankruptcy 2 days later, on Sunday. More recently, the rating agencies have come under considerable fire for significantly underestimating the risks of many of the securities that were backed by subprime mortgages. Many worry that rating agencies don’t have the proper incentives to measure risk because they are paid by the issuing firms. In response to these concerns, the Dodd-Frank Act, which was enacted in 2010, directed the SEC to put in place stronger oversight of the rating agencies. The exact nature of this oversight remains a work in progress. 7-8C. Bankruptcy and Reorganization When a business becomes insolvent, it doesn’t have enough cash to meet its interest and principal payments. A decision must then be made whether to dissolve the firm through liquidation or to permit it to reorganize and thus continue to operate. These issues are addressed in Chapters 7 and 11 of the federal bankruptcy statutes, and the final decision is made by a federal bankruptcy court judge. The decision to force a firm to liquidate versus permitting it to reorganize depends on whether the value of the reorganized business is likely to be greater than the value of its assets if they were sold off piecemeal. In a reorganization, the firm’s creditors negotiate with management on the terms of a potential reorganization. The reorganization plan may call for restructuring the debt, in which case the interest rate may be reduced; the term to maturity, lengthened; or some of the debt may be exchanged for equity. The point of the restructuring is to reduce the financial charges to a level that is supportable by the firm’s projected cash flows. Of course, the common stockholders also have to “take a haircut”—they generally see their position diluted as a result of additional shares being given to debtholders in exchange for accepting a reduced amount of debt principal and interest. A trustee may be appointed by the court to oversee the reorganization, but the existing management generally is allowed to retain control. Liquidation occurs if the company is deemed to be worth more “dead” than “alive.” If the bankruptcy court orders a liquidation, assets are auctioned off and the cash obtained is distributed as specified in Chapter 7 of the Bankruptcy Act. Web Appendix 7C provides an illustration of how a firm’s assets are distributed after liquidation. For now, this is what you need to know: (1) The federal bankruptcy statutes govern reorganization and liquidation. (2) Bankruptcies occur frequently. (3) A priority of the specified claims must be followed when the assets of a liquidated firm are distributed. (4) Bondholders’ treatment depends on the terms of the bond. (5) Stockholders generally receive little in reorganizations and nothing in liquidations because the assets are usually worth less than the amount of debt outstanding. SelfTest Differentiate between mortgage bonds and debentures. Name the major rating agencies, and list some factors that affect bond ratings. Why are bond ratings important to firms and investors? Do bond ratings adjust immediately to changes in credit quality? Explain. Differentiate between Chapter 7 liquidations and Chapter 11 reorganizations. In general, when should each be used? 7-9. Bond Markets Corporate bonds are traded primarily in the over-the-counter (OTC) market. Most bonds are owned by and traded among large financial institutions (e.g., life insurance companies, mutual funds, hedge funds, and pension funds, all of which deal in very large blocks of securities), and it is relatively easy for over-the-counter bond dealers to arrange the transfer of large blocks of bonds among the relatively few holders of the bonds. It would be more difficult to conduct similar operations in the stock market among the literally millions of large and small stockholders, so a higher percentage of stock trades occur on the exchanges. Accrued Interest and the Pricing of Coupon Bonds In this chapter, we have demonstrated the various factors that influence bond prices. But in practice, how much you are willing to pay for a bond also depends on when the next coupon payment is due. Clearly, all else equal, you would be willing to pay more for a bond the day before a coupon is paid, than you would the day after it has been paid. So, if you purchase a bond between coupon payments, you also have to pay what is called accrued interest. Accrued interest represents the amount of interest that has accumulated between coupon payments, and it can be calculated as follows: Accrued interest = Coupon payment × Number of days since the last coupon payment Number of days in the coupon period Let’s consider, for example, a corporate bond that was issued on April 30, 2020. The bond has an 8% semiannual coupon and a par value of $1,000—which means six months later, on October 30, 2020, the bond will pay its first $40 coupon, and on April 30, 2021, it will pay its second $40 coupon. If you buy the bond on July 19, 2021 (79 days since the bond’s last coupon payment on April 30), you will have to pay the seller $17.56 in accrued interest: Accrued interest = $ 40 × ( 79 / 180 ) = $ 17.56 In most cases, bonds are quoted net of accrued interest—in what is often referred to as a clean price. The actual invoice price you pay (often referred to as the dirty price) is the clean price plus accrued interest. In the case of the preceding bond, let’s assume that the bond’s nominal yield to maturity is the same as it was when the bond was issued (8%), which means that excluding accrued interest the bond continues to trade at par. It follows that: Clean price ( quoted price ) = $ 1,000 Accrued interest = $ 17.56 Dirty price ( invoice price ) = Clean price + Accrued interest = $ 1,017.56 You can also use the Accrued Interest function in Excel (ACCRINT) to easily calculate a bond’s accrued interest. As a final point, in the examples we use in the text, when we refer to a bond’s price we are referring to the bond’s quoted, or clean, price. But you should keep in mind that if you buy or sell a bond, the actual price paid or received is the dirty price, which includes accrued interest. A number of leading business publications and websites routinely report key developments in the Treasury, corporate, and municipal bond markets. For example, The Wall Street Journal provides a list of bonds whose yield spreads (relative to Treasury securities) widened and narrowed the most in the previous day. Table 7.5 reprints a portion of this data for a given day in April 2020. The table also reports the company’s previous day’s stock performance, which enables an investor to easily see how recent news has affected both the company’s stock price and the interest rate on its debt. As part of its reported data, The Wall Street Journal also includes interesting data regarding a number of bond indices and a snapshot of government bond rates in different countries. Other helpful sources include the bond sections of Bloomberg.com and Finra-markets.morningstar.com. Table 7.5 The Wall Street Journal Corporate Debt Section, April 8, 2020 Details Sources: MarketAxess Corporate Bond Ticker; WSJ Market Data Group; Corporate Debt Section, The Wall Street Journal (wsj.com), April 9, 2020, p. B8. SelfTest Why do most bond trades occur in the over-the-counter (OTC) market? How is accrued interest calculated? What is meant by the terms clean price and dirty price?