Declassify their boards of directors
Student 601
M3-1.pdf
Slide 1
6-1
Key Concepts and Skills
• Know the important bond features and bond types
• Understand:
– Bond values and why they fluctuate
– Bond ratings and what they mean
– The impact of inflation on interest rates
– The term structure of interest rates and the determinants of bond yields
When a corporation (or government) wishes to borrow money from the public on a long-term basis, it
usually does so by issuing, or selling, debt securities that are generically called bonds. In this Module, we
learn the various features of corporate bonds and some of the terminology associated with bonds. We then
discuss the cash flows associated with a bond and how bonds can be valued using our discounted cash flow
procedure.
Slide 2
6-2
Bond Definitions
• Bond
– Debt contract
– Interest-only loan
• Par value (face value) ~ $1,000
• Coupon rate
• Coupon payment
• Maturity date
• Yield to maturity
A bond is normally an interest-only loan, meaning that the borrower will pay the interest every period, but
none of the principal will be repaid until the end of the loan. The amount that will be repaid at the end of
the loan is called the bond's face value or par value. As in our example, this par value is usually $1,000
for corporate bonds. The annual coupon divided by the face value is called the coupon rate. The number
of years until the face value is paid is called the bond's time to maturity. To determine the value of a bond
at a particular point in time, we need to know the number of periods remaining until maturity, the face value,
the coupon, and the market interest rate for bonds with similar features. This interest rate required in the
market on a bond is called the bond's yield to maturity (YTM). Yield to maturity, required return, and
market rate are used interchangeably.
Coupon payment = Coupon rate X Par value
Note: Although the majority of corporate bonds have a $1,000 face value, there are an increasing number
of “baby bonds” outstanding, i.e., bonds with face values less than $1,000. The use of the term “baby bond”
goes back at least as far as 1970, when it was used in connection with AT&T’s announcement of the intent
to issue bonds with low face values. It was also used in describing Merrill Lynch’s 1983 program to issue
bonds with $25 face values. More recently, the term has come to mean bonds issued in lieu of interest
payments by firms unable to make the payments in cash. Baby bonds issued under these circumstances are
also called “PIK” (payment-in-kind) bonds, or “bunny” bonds, because they tend to proliferate in LBO
circumstances.
Slide 3
6-3
Bond Value
• Bond Value = PV of coupons + PV of par
• Bond Value = PV of annuity + PV of lump sum
• As interest rates increase, present values decrease.
• So, as interest rates increase, bond prices decrease
and vice versa.
The cash flows from a bond are the coupons and the face value. The value of a bond (market price) is the
present value of the expected cash flows discounted at the market rate of interest. Yield to maturity (YTM)
– the required market rate or return, or rate that makes the discounted cash flows from a bond equal to the
bond’s market price
As time passes, interest rates change in the marketplace. The cash flows from a bond, however, stay the
same. As a result, the value of the bond will fluctuate. When interest rates rise, the present value of the
bond's remaining cash flows declines, and the bond is worth less. When interest rates fall, the bond is
worth more.
Slide 4
6-4
The Bond-Pricing Equation
t
t
YTM)(1
F
YTM
YTM)(1
1 1-
C ValueBond +
+
+ =
PV(Annuity) PV(lump sum)
C = Coupon payment; F = Face value
Slide 5
6-5
Valuing a Discount Bond with Annual Coupons
• Consider a bond with a coupon rate of 10% and annual coupons. The par value is $1,000, and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond?
7-5
Slide 6
6-6
Valuing a Discount Bond with Annual Coupons
• Coupon rate = 10%
• Annual coupons
• Par = $1,000
• Maturity = 5 years
• YTM = 11%
5
5
)11.1(
1000
11.0
)11.1(
1 1
100B +
−
=
Using the formula:
B = PV(annuity) + PV(lump sum)
B = 369.59 + 593.45 = 963.04
Using the calculator:
5 N
11 I/Y
100 PMT
1000 FV
CPT PV = -963.04
Note: When YTM > Coupon rate Price < Par = “Discount Bond”
Remember the sign convention on the calculator. The easy way to remember it with bonds is we pay the
PV (-) so that we can receive the PMT (+) and the FV(+).
Discount bond – a bond that sells for less than its par value. This is the case when the YTM is greater than
the coupon rate.
The coupon rate and the face value are fixed by the bond indenture when the bond is issued (except for
floating-rate bonds). Therefore, the expected cash flows don’t change during the life of the bond. However,
the bond price will change as interest rates change and as the bond approaches maturity.
Slide 7
6-7
Valuing a Premium Bond with Annual Coupons
• Suppose you are reviewing a bond that has a 10% annual coupon and a face value of $1000. There are 20 years to maturity, and the yield to maturity is 8%. What is the price of this bond?
7-7
Slide 8
6-8
Valuing a Premium Bond with Annual Coupons
• Coupon rate = 10%
• Annual coupons
• Par = $1,000
• Maturity = 20 years
• YTM = 8%
20
20
)08.1(
1000
08.0
)08.1(
1 1
100 +
−
=B
Using the formula:
B = PV(annuity) + PV(lump sum)
B = 981.81 + 214.55 = 1196.36
Note: When YTM < Coupon rate Price > Par = “Premium Bond”
Using the calculator:
20 N
8 I/Y
100 PMT
1000 FV
CPT PV = -1196.36
Premium bond – a bond that sells for more than its par value. This is the case when the YTM is less than
the coupon rate.
Slide 9
6-9
Graphical Relationship Between Price and Yield-to-maturity
600
700
800
900
1000
1100
1200
1300
1400
1500
0% 2% 4% 6% 8% 10% 12% 14%
B o
n d
P ri
c e
Yield-to-maturity
Negative relation between Bond Price (PV) and YTM (I/Y).
Slide 10
6-10
Bond Prices: Relationship Between Coupon and Yield
• If YTM = coupon rate, then par value = bond price
• If YTM > coupon rate, then par value > bond price
▪ Why? The discount provides yield above coupon rate.
▪ Price below par value, called a discount bond
• If YTM < coupon rate, then par value < bond price
▪ Why? Higher coupon rate causes value above par.
▪ Price above par value, called a premium bond
There are the purely mechanical reasons for these results. We know that present values decrease as rates
increase. Therefore, if we increase our yield above the coupon, the present value (price) must decrease
below par. On the other hand, if we decrease our yield below the coupon, the present value (price) must
increase above par.
Slide 11
6-11
The Bond-Pricing Equation Adjusted for Semi-annual Coupons
2t
2t
YTM/2)(1
F
YTM/2
YTM/2)(1
1 -1
2
C ValueBond
+ +
+ =
C = Annual coupon payment C/2 = Semi-annual coupon
YTM = Annual YTM (as an APR) YTM/2 = Semi-annual YTM
t = Years to maturity 2t = Number of 6-month
periods to maturity
In practice, bonds issued in the United States usually make coupon payments twice a year
Slide 12
6-12
Example
• If an ordinary bond has a coupon rate of
14 percent, then the owner will get a total
of $140 per year, but this $140 will come in
two payments of $70 each. The yield to
maturity is quoted at 16 percent. The bond
matures in seven years.
• How many coupon payments are there?
• What is the semiannual coupon payment?
• What is the semiannual yield?
• What is the bond price?
Slide 13
6-13
Semiannual Bonds
• Coupon rate = 14% - Semiannual
• YTM = 16% (APR)
• Maturity = 7 years – Number of coupon payments? (2t or N)
• 14 = 2 x 7 years
– Semiannual coupon payment? (C/2 or PMT)
• $70 = (14% x 1000)/2
– Semiannual yield? (YTM/2 or I/Y)
• 8% = 16%/2
Note: Bond yields are quoted like APRs; the quoted rate is equal to the actual rate per period multiplied by
the number of periods.
Coupon rate = 14%, semiannual coupons
YTM = 16%
Maturity = 7 years
Par value = $1,000
Slide 14
6-14
Example 7.1
• Semiannual coupon = $70
• Semiannual yield = 8%
• Periods to maturity = 14
• Bond value =
• 70[1 – 1/(1.08)14] / .08 + 1000 / (1.08)14 = 917.56
( ) ( )2t
2t
2 YTM1
F
2 YTM
2 YTM1
1 -1
2 C Value Bond
+ +
+ =
14
14
)08.1(
1000
08.0
)08.1(
1 1
70B +
−
=
Using the calculator:
14 N
8 I/Y
70 PMT
1000 FV
CPT PV = -917.56
Slide 15
6-15
Interest Rate Risk
• Price Risk ▪ Change in price due to changes in interest rates
▪ Long-term bonds have more price risk than short-term bonds.
▪ Low coupon rate bonds have more price risk than high coupon rate bonds.
• Reinvestment Rate Risk ▪ Uncertainty concerning rates at which cash flows can be reinvested
▪ Short-term bonds have more reinvestment rate risk than long-term bonds.
▪ High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds.
The risk that arises for bond owners from fluctuating interest rates is called interest rate risk. How much
interest rate risk a bond has depends on how sensitive its price is to interest rate changes. This sensitivity
directly depends on two things: the time to maturity and the coupon rate. As we will see momentarily, you
should keep the following in mind when looking at a bond:
All other things being equal, the longer the time to maturity, the greater the interest rate risk.
All other things being equal, the lower the coupon rate, the greater the interest rate risk.
If we compared a 10-year bond to a 1-year bond, we would see that the 10-year bond has much greater
interest rate risk. However, if you were to compare a 20-year bond to a 30-year bond, you would find that
the 30-year bond has somewhat greater interest rate risk because it has a longer maturity, but the difference
in the risk would be fairly small.
The value of a bond depends on the present value of its coupons. As a result, all other things being equal,
its value will fluctuate more as interest rates change. Put another way, the bond with the higher coupon has
a larger cash flow early in its life, so its value is less sensitive to changes in the discount rate.
Bonds are usually not issued with maturities longer than 30 years. However, low interest rates have led to
the issuance of bonds with much longer maturities. In the 1990s, Walt Disney issued “Sleeping Beauty”
bonds with a 100-year maturity. This company wanted to lock in the historically low interest rates for a
long time.
One potentially undesirable feature of high-coupon bonds is the required reinvestment of coupons at the
computed yield-to-maturity if one is to actually earn that yield. Those who purchased bonds in the early
1980s (when even high-grade corporate bonds had coupons over 11%) found, to their dismay, that interest
payments could not be reinvested at similar rates a few years later without taking greater risk. A good
example of the trade-off between interest rate risk and reinvestment risk is the purchase of a zero-coupon
bond – one eliminates reinvestment risk but maximizes interest-rate risk.
Slide 16
6-16
Figure 7.2
Slide 17
6-17
• Yield to Maturity (YTM) is the rate implied by the current bond price.
• Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity.
• If you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV the opposite sign.)
Computing Yield to Maturity
Slide 18
6-18
YTM with Annual Coupons
Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09. – Will the yield be more or less than 10%?
15 N
928.09 PV (enter as a negative)
1000 FV
100 PMT
CPT I/Y = 11% Result = YTM
The YTM is more than the coupon since the price is less than par.
Slide 19
6-19
YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate and
semiannual coupons, has a face value of
$1000, 20 years to maturity and is selling for
$1197.93.
– Is the YTM more or less than 10%?
– What is the semiannual coupon payment?
– How many periods are there?
Slide 20
6-20
YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,197.93.
40 N
1197.93 PV (negative)
1000 FV
50 PMT
CPT PV 4% (= ½ YTM)
YTM = 4%*2 = 8%
NOTE: Solving a semi-
annual payer for YTM
results in a 6-month yield.
The calculator & Excel
solve what you enter.
The 4% value is the 6-month interest rate. YTM is an annual rate.
Slide 21
6-21
The Bond Indenture “Deed of Trust”
Contract between issuing company and bondholders includes:
– Basic terms of the bonds
– Total amount of bonds issued
– Secured versus Unsecured
– Sinking fund provisions
– Call provisions
• Deferred call
• Call premium
– Details of protective covenants
The bond indenture is the written legal agreement between the corporation (the borrower) and its creditors.
It can run several hundred pages.
• Sinking fund—an account managed by the bond trustee for early redemption. Reduces risk of default, but bondholders may not receive all of expected coupons.
• Call provision—allows company to “call” or repurchase part or all of issue.
• Call premium—amount by which the call price exceeds the par value.
• Deferred call—firm cannot call bonds for a designated period.
• Protective covenants – indenture conditions that limit the actions of firms.
Slide 22
6-22
The Bond Indenture
Many of these features will be detailed in the bond indenture.
Slide 23
6-23
Bond Classifications
• Registered vs. Bearer Bonds
• Security ▪ Collateral – secured by financial securities
▪ Mortgage – secured by real property, normally land or buildings
▪ Debentures – unsecured
▪ Notes – unsecured debt with original maturity less than 10 years
• Seniority – Senior versus Junior, Subordinated
Corporate bonds are usually in registered form: company has a registrar who will record the ownership of
each bond and record any changes in ownership. The company will pay the interest and principal directly
to the owner of record. The bond could be in bearer form.: A bond issued without record of the owner's
name; payment is made to whomever holds the bond. This means that the certificate is the basic evidence
of ownership, and the corporation will “pay the bearer.” Ownership is not otherwise recorded, and, as with
a registered bond with attached coupons, the holder of the bond certificate detaches the coupons and sends
them to the company to receive payment. There are two drawbacks to bearer bonds. First, they are difficult
to recover if they are lost or stolen. But they are now much less common (in the United States) than
registered bonds.
Debt securities are classified according to the collateral and mortgages used to protect the bondholder.
Collateral is a general term that frequently means securities (for example, bonds and stocks). A debenture
is an unsecured bond, for which no specific pledge of property is made. This is standard terminology in the
US – but it may not transfer to other countries. For example, debentures are secured debt in the United
Kingdom.
Note: Since bearer bonds are not registered with the corporation, it is easier for bondholders to receive
interest payments without reporting them on their income tax returns. In an attempt to eliminate this
potential for tax evasion, all bonds issued in the US after July 1983 must be in registered form. It is still
legal to offer bearer bonds in some other nations, however. Some foreign bonds are popular among
international investors particularly due to their bearer status.
Seniority In general terms, seniority indicates preference in position over other lenders, and debts are
sometimes labeled as senior or junior to indicate seniority.
Seniority—order of precedence of claims in the event of bankruptcy. Senior debt is paid first. Junior or
subordinated debt is lower in priority.
In the event of default, holders of subordinated debt must give preference to other specified creditors.
Slide 24
6-24
Bond Characteristics and Required Returns
• Coupon rate
– (risk characteristics of the bond when issued)
– Usually ≈ yield at issue
• Which bonds will have the higher coupon, all else equal? – Secured debt versus a debenture
– Subordinated debenture versus senior debt
– A bond with a sinking fund versus one without
– A callable bond versus a non-callable bond
Higher coupons:
Debenture—secured debt is less risky because the income from the security is used to pay it off first.
Subordinated debenture—will be paid after the senior debt.
Bond without sinking fund—company has to come up with substantial cash at maturity to retire debt, and
this is riskier than systematic retirement of debt through time.
Callable bond—call potential is unattractive to investors. Debt is usually purchased with the expectation of
receiving periodic coupon payments for many years. If a bond is called before maturity, the coupon stream
stops. Bondholders bear the risk of the bond being called early, usually when rates are lower. They don’t
receive all of the expected coupons and they have to reinvest at lower rates.
Slide 25
6-25
Bond Ratings – Investment Quality
Investment grade
• High Grade
– Moody’s Aaa and S&P AAA – capacity to pay is extremely strong
– Moody’s Aa and S&P AA – capacity to pay is very strong
• Medium Grade
– Moody’s A and S&P A – capacity to pay is strong, but
more susceptible to changes in circumstances
– Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay
Debt ratings are an assessment of the credit worthiness of the corporate issuer. Bond ratings are important
to a firm because a higher rating indicates lower default risk and translates into a lower coupon rate
Firms typically pay rating agencies to have a bond issue rated. The major rating agencies are Moody’s,
Standard & Poor’s, and Fitch. The rating categories of the three agencies are similar, dividing bonds into
two main groups: investment grade and speculative grade.
Investment-grade bonds have the lowest degree of default risk (rated at least BBB by S&P or Baa by
Moody's).
The question sometimes arises as to why a potential issuer would be willing to pay rating agencies tens of
thousands of dollars in order to receive a rating, especially given the possibility that the resulting rating
could be less favorable than expected.
Slide 26
6-26
Bond Ratings - Speculative
speculative grade
• Low Grade
– Moody’s Ba, B, Caa and Ca
– S&P BB, B, CCC, CC
– Considered speculative with respect to capacity to pay. The “B” ratings are the lowest degree of speculation.
• Very Low Grade
– Moody’s C and S&P C – income bonds with no interest being paid
– Moody’s D and S&P D – in default with principal and interest in arrears
Speculative grade bonds are also called “junk” bonds.
A bond's credit rating can change as the issuer's financial strength. Bonds that drop into junk territory from
above are called “fallen angels.”
Slide 27
6-27
• Treasury Securities ▪ Federal government debt
▪ T-bills – pure discount bonds with original maturity of one year or less
▪ T-notes – coupon debt with original maturity between one and ten years
▪ T-bonds – coupon debt with original maturity greater than ten years
• Municipal Securities ▪ Debt of state and local governments
▪ Varying degrees of default risk, rated similar to corporate debt
▪ Interest received is tax-exempt at the federal level.
Government Bonds
Long-term debt instruments issued by a governmental entity. Treasury bonds are bonds issued by a federal
government; a state or local government issues municipal bonds (munis).
Municipal securities (munis) - varying degrees of default risk, and, in fact, they are rated much like
corporate issues. Also, they are almost always callable. The most intriguing thing about munis is that their
coupons are exempt from federal income taxes (though not necessarily state income taxes), which makes
them very attractive to high-income, high–tax bracket investors.
Slide 28
6-28
Example A taxable bond has a yield of 8% and a
municipal bond has a yield of 6%
• If you are in a 40% tax bracket, which bond do you prefer?
▪ 8%(1 - .4) = 4.8%
▪ The after-tax return on the corporate bond is 4.8%, compared to a 6% return on the municipal
• At what tax rate would you be indifferent between the two bonds?
▪ 8%(1 – T) = 6%
▪ T = 25%
You should be willing to accept a lower stated yield on municipals because you do not have to pay taxes
on the interest received. Why are you willing to accept a lower rate of interest? It may be helpful to take
the example and illustrate the indifference point using dollars instead of just percentages. The discount you
are willing to accept depends on your tax bracket.
Consider a taxable bond with a yield of 8% and a tax-exempt municipal bond with a yield of 6%.
Suppose you own one $1,000 bond in each and both bonds are selling at par. You receive $80 per year
from the corporate and $60 per year from the municipal. How much do you have after taxes if you are in
the 40% tax bracket? Corporate: 80 – 80(.4) = 48; Municipal = 60
Why should the federal government exempt munis from taxation? It provides an incentive for local
governments to raise capital on their own.
Slide 29
6-29
Treasury Quotations
Figure 6.3 shows a portion of the daily Treasury note and bond listings from The Wall Street Journal online.
The only difference between a Treasury note and a Treasury bond is that notes have 10 years or less to
maturity at the time of issuance. The entry that begins “05/15/2030” is highlighted. Reading from left to
right, the “05/15/2030” tells us that the bond's maturity is May 15, 2030. The 6.250 is the bond's coupon
rate. Treasury bonds all make semiannual payments and have a face value of $1,000, so this bond will pay
$31.25 per six months until it matures.
The difference between the two prices is called the bid-ask spread (or just “spread”), and it represents the
dealer's profit. The bid price, or what a dealer is willing to pay for the bond, on the 05/15/2030 bond is
150.7188. With a $1,000 face value, this quote represents $1,507.188. The asked price, or the price at which
the dealer is willing to sell the bond, is 150.7500, or $1,507.500. The next number quoted is the change in
the asked price from the previous day, measured as a percentage of face value, so this issue's asked price
rose by .8906 percent, or $8.906, in value from the previous day. Finally, the last number reported is the
yield to maturity, based on the asked price. Notice that this is a premium bond because it sells for more than
its face value.
Slide 30
6-30
Zero Coupon Bonds
• Make no periodic interest payments (coupon rate = 0%)
• Entire yield-to-maturity comes from the difference between the purchase price and the par value (capital gains)
• Cannot sell for more than par value
• Sometimes called zeroes, or deep discount bonds
• Treasury Bills and U.S. Savings bonds are good examples of zeroes
A bond that pays no coupons at all must be offered at a price that is much lower than its stated value. Such
bonds are called zero coupon bonds, or just zeroes. Zero-coupon bonds are bonds that are offered at deep
discounts because there are no periodic coupon payments.
Slide 31
6-31
Floating Rate Bonds
• Coupon rate floats depending on some index value
• Examples – adjustable rate mortgages and inflation-linked Treasuries
• Less price risk with floating rate bonds
– Coupon floats, so is less likely to differ substantially from the yield-to-maturity
• Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor”
The conventional bonds we have talked about in this module have fixed-dollar obligations because the
coupon rate is set as a fixed percentage of the par value. Similarly, the principal is set equal to the par value.
With floating-rate bonds (floaters), the coupon payments are adjustable. Adjustments are tied to an interest
rate index such as the Treasury bill interest rate or the 30-year Treasury bond rate.
The coupon rate has a floor and a ceiling, meaning that the coupon is subject to a minimum and a maximum.
The coupon rate is said to be “capped,” and the upper and lower rates are sometimes called the collar.
Whereas there is less price risk, there is greater reinvestment (or refinancing) risk.
Slide 32
6-32
Other Bond Types
• Structured notes
based on stocks, bonds, commodities, or currencies
• Convertible bonds can be swapped for a fixed number of shares of stock
anytime before maturity at the holder's option
• Put bonds force the issuer to buy the bond back at a stated price
• Catastrophe bonds
• Income bonds
Structured notes are bonds that are based on stocks, bonds, commodities, or currencies. One particular type
of structured note has a return based on a stock market index. At expiration, if the stock index has declined,
the bond returns the principal. However, if the stock index has increased, the bond will return a portion of
the stock index return, say 80 percent. Another type of structured note will return twice the stock index
return, but with the potential for loss of principal.
Convertible bonds – bonds can be converted into shares of common stock at the bondholders discretion
Lower required return.
Put bond – bondholder can force the company to buy the bond back prior to maturity Lower required return.
Catastrophe bonds – issued by property and casualty companies. Pay interest and principal as usual unless
claims reach a certain threshold for a single disaster. At that point, bondholders may lose all remaining
payments. Higher required return
Income bonds – coupon payments depend on level of corporate income. If earnings are not enough to cover
the interest payment, it is not owed. Higher required return
There are many other types of provisions that can be added to a bond and many bonds have several
provisions – it is important to recognize how these provisions affect required returns
Slide 33
6-33
Bond Markets
• Primarily over-the-counter transactions with dealers connected electronically
• Extremely large number of bond issues, but generally low daily volume in single issues
• Getting up-to-date prices difficult, particularly on small company or municipal issues
• Treasury securities are an exception
There is no particular place where buying and selling occur. Instead, dealers around the country (and around
the world) stand ready to buy and sell. The various dealers are connected electronically.
Because the bond market is almost entirely OTC, it has historically had little or no transparency. A financial
market is transparent if it is possible to easily observe its prices and trading volume. On the New York
Stock Exchange, for example, it is possible to see the price and quantity for every single transaction. In
contrast, in the bond market, it is often not possible to observe either. Transactions are privately negotiated
between parties, and there is little or no centralized reporting of transactions.
Bonds are bought and sold in enormous quantities every day. You may be surprised to learn that the trading
volume in bonds on a typical day is many, many times larger than the trading volume in stocks
What is the largest securities market in the world? Most people would guess the New York Stock Exchange.
In fact, the largest securities market in the world in terms of trading volume is the U.S. Treasury market.
One reason the bond markets are so big is that the number of bond issues far exceeds the number of stock
issues. There are two reasons for this. First, a corporation would typically have only one common stock
issue outstanding. However, a single large corporation could easily have a dozen or more note and bond
issues outstanding. Beyond this, federal, state, and local borrowing is simply enormous. For example, even
a small city would usually have a wide variety of notes and bonds outstanding,
Although the total volume of trading in bonds far exceeds that in stocks, only a very small fraction of the
total bond issues that exist actually trade on a given day. This fact, combined with the lack of transparency
in the bond market, means that getting up-to-date prices on individual bonds is often difficult or impossible,
particularly for smaller corporate or municipal issues. Instead, a variety of sources of estimated prices exist
and are very commonly used.
Slide 34
6-34
• Sukuk are bonds that have been created to meet a demand for assets that comply with Shariah, or Islamic law.
• Shariah does not permit the charging or paying of interest.
• Sukuk are typically bought and held to maturity, and they are extremely illiquid.
Sukuk
Bonds issued to comply with Sharia, or Islamic law, which does not permit charging or paying interest.
The bonds typically confer partial ownership of some aspect of the firm to the bondholder.
Slide 35
6-35
• Bond quotes are available online.
• One good site is FINRA’s Market Data Center (http://finra-markets.morningstar.com/BondCenter/Default.jsp).
• Go to the site, choose a company, enter it in the Issuer Name bar, choose Corporate, and see what you can find!
Work the Web Example
Slide 36
6-36
Quoted Price vs. Invoice Price
• Quoted bond prices = “clean” price
– Net of accrued interest
• Invoice Price = “dirty” or “full” price
– Price actually paid
– Includes accrued interest
• Accrued Interest
– Interest earned since last coupon payment is owed to bond seller at time of sale
If you buy a bond between coupon payment dates, the price you pay is usually more than the price you are
quoted. The reason is that standard convention in the bond market is to quote prices net of “accrued interest,”
meaning that accrued interest is deducted to arrive at the quoted price. This quoted price is called the clean
price.
The price you actually pay, however, includes the accrued interest. This price is the dirty price, also known
as the “full” or “invoice” price.
Example: Suppose the last coupon was paid 50 days ago and there are 182 days in the current coupon period.
If the semiannual coupon payment is $40, then the accrued interest would be (50 ⁄ 182) × 40 = $10.99. This
amount would be added to the quoted price to determine the “dirty price.”
Suppose you buy a bond with a 12 percent annual coupon, payable semiannually. You actually pay $1,080
for this bond, so $1,080 is the dirty, or invoice, price. Further, on the day you buy it, the next coupon is due
in four months, so you are between coupon dates. Notice that the next coupon will be $60. The accrued
interest on a bond is calculated by taking the fraction of the coupon period that has passed, in this case two
months out of six, and multiplying this fraction by the next coupon, $60. So, the accrued interest in this
example is 2/6 × $60 = $20. The bond's quoted price (i.e., its clean price) would be $1,080 − 20 = $1,060.
Bond prices are traditionally quoted “clean” or without accrued interest. If a bond is purchased (or sold)
between coupon payment dates, then any interest earned since the last coupon payment is due to the holder
(seller) of the bond.
At the time of the exchange, accrued interest is computed and added to the quoted price to arrive at the
“invoice price,” also called the “full” or “dirty” price.
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Clean vs. Dirty Prices
• Clean price: quoted price
• Dirty price: price actually paid = quoted price plus accrued interest
• Example: Consider a T-bond with a 4% semiannual yield and a clean price of $1,282.50: ▪ Number of days since last coupon = 61
▪ Number of days in the coupon period = 184
▪ Accrued interest = (61/184)(.04*1000) = $13.26
▪ Dirty price = $1,282.50 + $13.26 = $1,295.76
• So, you would actually pay $ 1,295.76 for the bond
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Assuming that the November maturity is November 15, then the coupon dates would be November 15
and May 15. Therefore, July 15 would be 16 + 30 + 15 = 61 days since the last coupon
The number of days in the coupon period would be 16 + 30 + 31 + 31 + 30 + 31 + 15 = 184
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Inflation and Interest Rates
• Real rate of interest
=Change in purchasing power
• Nominal rate of interest
= Quoted rate of interest,
= Change in purchasing power and inflation
• The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation
So far, we haven't considered the role of inflation in our various discussions of interest rates, yields, and
returns. Because this is an important consideration, we consider the impact of inflation next.
In examining interest rates, or any other financial market rates such as discount rates, bond yields, rates of
return, and required returns, it is often necessary to distinguish between real rates and nominal rates.
Nominal rates are called “nominal” because they have not been adjusted for inflation. Real rates are rates
that have been adjusted for inflation.
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The Fisher Effect
The Fisher Effect defines the relationship
between real rates, nominal rates and
inflation
(1 + R) = (1 + r)(1 + h)
R = nominal rate (Quoted rate)
r = real rate
h = expected inflation rate
Approximation: R ≈ r + h
The Fisher Effect is a theoretical relationship between nominal returns, real returns, and the expected
inflation rate. Let R be the nominal rate, r the real rate, and h the expected inflation rate.
The approximation works pretty well with “normal” real rates of interest and expected inflation. If the
expected inflation rate is high, then there can be a substantial difference.
It is important to note that financial rates, such as interest rates, discount rates, and rates of return, are almost
always quoted in nominal terms.
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Example
If we require a 10% real return and we
expect inflation to be 8%, what is the
nominal rate?
▪ R = (1.1)(1.08) – 1 = .188 = 18.8%
▪ Approximation: R = 10% + 8% = 18%
▪ Because the real return and expected inflation
are relatively high, there is significant
difference between the actual Fisher Effect
and the approximation.
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• Term structure is the relationship between time to maturity and yields, all else equal.
• It is important to recognize that we pull out the effect of default risk, different coupons, etc.
• Yield curve – graphical representation of the term structure
▪ Normal – upward-sloping; long-term yields are higher than short- term yields
▪ Inverted – downward-sloping; long-term yields are lower than short-term yields
Term Structure of Interest Rates
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Figure 7.6 – Upward-Sloping Yield Curve
Term structure of interest rates – relationship between nominal interest rates on default-free, pure discount
bonds and maturity
Inflation premium – portion of the nominal rate that is compensation for expected inflation
Interest rate risk premium – reward for bearing interest rate risk
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Figure 7.6 – Downward-Sloping Yield Curve
Term structure of interest rates – relationship between nominal interest rates on default-free, pure discount
bonds and maturity
Inflation premium – portion of the nominal rate that is compensation for expected inflation
Interest rate risk premium – reward for bearing interest rate risk
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Figure 7.7
Current yield curve https://www.bloomberg.com/markets/rates-bonds/government-bonds/us
Bloomberg to get the current Treasury yield curve
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Factors Affecting Bond Yields
• Real rate of interest
• Expected future inflation premium
• Interest rate risk premium
• Default risk premium – bond ratings
• Taxability premium – municipal versus taxable
• Liquidity premium – bonds that have more frequent trading will generally have lower required returns
• Maturity premium – longer term bonds will tend to have higher required returns. Anything else that affects the risk of the cash flows to the bondholders will affect the required returns
If we combine all of the things we have discussed regarding bond yields, we find that bond yields represent
the combined effect of no fewer than six things. The first is the real rate of interest. On top of the real rate
are five premiums representing compensation for (1) expected future inflation, (2) interest rate risk, (3)
default risk, (4) taxability, and (5) lack of liquidity. As a result, determining the appropriate yield on a bond
requires careful analysis of each of these effects.
• Treasury yield curve – plot of yields on Treasury notes and bonds relative to maturity
• Default risk premium – the portion of a nominal rate that represents compensation for the possibility of default
• Taxability premium – the portion of a nominal rate that represents compensation for unfavorable tax status
• Liquidity premium – the portion of a nominal rate that represents compensation for lack of liquidity
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• What is the price of a $1,000 par value bond with a 6% coupon rate paid semiannually, if the bond is priced to yield 5% and it has 9 years to maturity?
• What would be the price of the bond if the yield rose to 7%.
• What is the current yield on the bond if the YTM is 7%?
Comprehensive Problem
5% YTM: 18 N; 2.5 I/Y; 30 PMT; 1,000 FV; CPT PV = 1,071.77
7% YTM: 18 N; 3.5 I/Y; 30 PMT; 1,000 FV; CPT PV = 934.05
Current yield = 60/934.05 = 6.42%
