Chapter 07 – Interest Rates and Bond Valuation
Chapter 7
INTEREST RATES AND BOND VALUATION
CHAPTER WEB SITES
Section Web Address
7.1 bonds.yahoo.com
personal.fidelity.com
money.cnn.com/markets/bondcenter
www.bankrate.com
investorguide.com
7.2 www.investinginbonds.com
www.finra.org/marketdata
www.sifma.org
www.sec.gov
7.3 www.standardandpoors.com
www.moodys.com
www.fitchinv.com
www.publicdebt.treas.gov
www.brillig.com/debt_clock
www.ny.frb.org
7.4 money.cnn.com
emma.msrb.org
7.5 cxa.marketwatch.com/finra/MarketData/Default.aspx
www.finra.org
http://www.stls.frb.org/fred/files
7.7 www.bloomberg.com/markets
www.smartmoney.com
CHAPTER ORGANIZATION
7.1 Bonds and Bond Valuation
Bond Features and Prices
Bond Values and Yields
Interest Rate Risk
Finding the Yield to Maturity: More Trial and Error
7.2 More about Bond Features
Is It Debt or Equity?
Long-Term Debt: The Basics
The Indenture
7.3 Bond Ratings
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Chapter 07 – Interest Rates and Bond Valuation
7.4 Some Different Types of Bonds
Government Bonds
Zero Coupon Bonds
Floating-Rate Bonds
Other Types of Bonds
Sukuk
7.5 Bond Markets
How Bonds are Bought and Sold
Bond Price Reporting
A Note about Bond Price Quotes
7.6 Inflation and Interest Rates
Real versus Nominal Rates
The Fisher Effect
Inflation and Present Values
7.7 Determinants of Bond Yields
The Term Structure of Interest Rates
Bond Yields and the Yield Curve: Putting It All Together
Conclusion
7.8 Summary and Conclusions
ANNOTATED CHAPTER OUTLINE
1. Bonds and Bond Valuation
A. Bond Features and Prices
Bonds – long-term IOUs, usually interest-only loans (interest is
paid by the borrower every period with the principal repaid at the
end of the loan).
Coupons – the regular interest payments (if fixed amount – level
coupon).
Face or par value – principal, amount repaid at the end of the loan
Coupon rate – coupon quoted as a percent of face value
Maturity – time until face value is paid, usually given in years
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Chapter 07 – Interest Rates and Bond Valuation
B. Bond Values and Yields
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.
Real World Tip: Not all bond interest is paid in cash. Isle of Arran
Distillers Ltd., a UK firm, offered investors the chance to purchase
bonds for approximately $675; the bonds gave investors the right
to receive ten cases of the firm’s products: malt whiskeys. The
reason? According to Harold Currie, the company’s chairman,
“The idea of the bond is to create a customer base from the
beginning. The whiskey will not be available in shops and will be
exclusive to the bondholders.”
Example: Suppose Wilhite, Co. issues $1,000 par bonds with 20
years to maturity. The annual coupon is $110. Similar bonds have a
yield to maturity of 11%.
Bond value = PV of coupons + PV of face value
Bond value = 110[1 – 1/(1.11)20] / .11 + 1,000 / (1.11)20
Bond value = 875.97 + 124.03 = $1,000
or N = 20; I/Y = 11; PMT = 110; FV = 1,000; CPT PV = -1,000
Since the coupon rate and the yield are the same, the price should
equal face value.
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.
Example: Suppose the YTM on bonds similar to that of Wilhite
Co. (see the previous example) is 13% instead of 11%. What is the
bond price?
Bond price = 110[1 – 1/(1.13)20] / .13 + 1,000/(1.13)20
Bond price = 772.72 + 86.78 = 859.50
or N = 20; I/Y = 13; PMT = 110; FV = 1,000; CPT PV = -859.50
The difference between this price, 859.50, and the par value of
$1000 is $140.50. This is equal to the present value of the
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Chapter 07 – Interest Rates and Bond Valuation
difference between bonds with coupon rates of 13% ($130) and
Wilhite’s coupon: PMT = 20; N = 20; I/Y = 13; CPT PV = -140.50.
Real-World Tip: It is unfortunate that many students fail to grasp
the fact that the Yield to Maturity concept links three things: a
purely mathematical artifact (the computed YTM), an economic
concept (the relationship between value and return in market
equilibrium), and a real-world observation (the fact that bond
values move up and down in response to financial events). Without
the underlying economics, neither the YTM nor observed bond
price changes mean much.
Lecture Tip: You should stress the issue that 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.
Lecture Tip: You may wish to further explore the loss in value of
$115 in the example in the book. You should remind the class that
when the 8% bond was issued, bonds of similar risk and
maturity were yielding 8%. The coupon rate was set so that the
bond would sell at par value; therefore, the coupons were set at
$80 per year.
One year later, the ten-year bond has nine years remaining to
maturity. However, bonds of similar risk and nine years to maturity
are being issued to yield 10%, so they have coupons of $100 per
year. The bond we are looking at only pays $80 per year.
Consequently, the old bond will sell for less than $1,000. The
mathematical reason for that is discussed in the text. However,
many students can intuitively grasp that you wouldn’t be willing to
pay as much for a bond that only pays $80 per year for 9 years as
you would for a bond that pays $100 per year for 9 years.
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.
Example: Consider the Wilhite bond in the previous examples.
Suppose that the yield on bonds of similar risk and maturity is 9%
instead of 11%. What will the bonds sell for?
Bond value = 110[1 – 1/(1.09)20] / .09 + 1,000/(1.09)20
Bond value = 1,004.14 + 178.43 = $1,182.57
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Chapter 07 – Interest Rates and Bond Valuation
General Expression for the value of a bond:
Bond value = present value of coupons + present value of par
Bond value = C[1 – 1/(1+r)t] / r + FV / (1+r)t
Semiannual coupons – coupons are paid twice a year. Everything is
quoted on an annual basis so you divide the annual coupon and the
yield by two and multiply the number of years by 2.
Example: A $1,000 bond with an 8% coupon rate, with coupons
paid semiannually, is maturing in 10 years. If the quoted YTM is
10%, what is the bond price?
Bond value = 40[1 – 1/(1.05)20] / .05 + 1,000 / (1.05)20
Bond value = 498.49 + 376.89 = $875.38
C. Interest Rate Risk
Interest rate risk – changes in bond prices due to fluctuating
interest rates.
All else equal, the longer the time to maturity, the greater the
interest rate risk.
All else equal, the lower the coupon rate, the greater the interest
rate risk.
Real-World Tip: In 1998, newscasters frequently referred to rates
reaching historic lows. As a refresher, the lowest rate in 1998 on
10-year Treasuries (monthly, annualized returns for the constant
maturity index) was 4.53%. Rates increased after that point and
then fell to a low of 3.33% in June of 2003 and rebounded some to
4.10% in October of 2004 (still below the “historic lows” in
1998!)
But, even this is nowhere near historic lows. Going back to 1953,
the rate on 10-year Treasuries was under 4% (and often under
3%) for most of the 1950s and early 1960s. The lowest rate during
that time was 2.29% in April of 1954. However, people have short-
term memories. Rates started to rise in 1963 and topped out over
15% in 1981. In fact, rates were greater than 10% from 1980 –
1985. So, is 4.5% low or high? As Einstein would say – it’s all
relative.
Reference: www.federalreserve.gov/releases
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Chapter 07 – Interest Rates and Bond Valuation
Real-World Tip: Upon learning the concept of interest rate risk,
students sometimes conclude that bonds with low interest-rate risk
(i.e. high coupon bonds) are necessarily “safer” than otherwise
identical bonds with lower coupons. In reality, the contrary may be
true: increasing interest rate volatility over the last two decades
has greatly increased the importance of interest rate risk in bond
valuation. The days when bonds represented a “widows and
orphans” investment are long gone.
You may wish to point out that 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.
D. Finding the Yield to Maturity: More Trial and Error
It is a trial and error process to find the YTM via the general
formula above. Knowing if a bond sells at a discount (YTM >
coupon rate) or premium (YTM < coupon rate) is a help, but using
a financial calculator is by far the quickest, easiest, and most
accurate method.
Lecture Tip: Students should understand that finding the yield to
maturity is a tedious process of trial and error. It may help to pose
a hypothetical situation in which a 10-year, 10% coupon bond
sells for $1,100. Ask whether paying a higher price than $1,000
would yield an investor more or less than 10%. Hopefully, the
students will recognize that if they pay $1,000 for the right to
receive $100 per year, the bond would yield 10%. Thus a starting
point in determining the YTM would be 9%. And if the same bond
is selling for $1,200, one might want to try 8% as a starting point,
since we would be paying a higher price and earning a lower
yield.
Lecture Tip: You may wish to discuss the components of required
returns for bonds in a fashion analogous to the stock return
discussion in the next chapter. As with common stocks, the required
return on a bond can be decomposed into current income and
capital gains components. The yield-to-maturity (YTM) equals the
current yield plus the capital gains yield.
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Chapter 07 – Interest Rates and Bond Valuation
Consider the premium bond described in Example 7.2. The bond
has $1,000 face value, $30 semiannual coupons, and 5 years to
maturity. When the required return on bonds of similar risk is
4.2%, the market value of the bond is $1,080.42. But what if one
purchases this bond and sells it a year later at the going price?
Assume no change in market rates. The current income portion of
the bondholder’s return equals the interest received divided by the
initial outlay; current yield = 60 / 1,080.42 = .0553 = 5.53%.
The capital gains yield equals the change in bond price divided by
the initial outlay. Given no change in market rates, the “one-year-
later” price must be $1,065.65. Therefore, the capital gains yield
is (1,065.65 – 1,080.42) / 1,080.42 = -.0137 = -1.37%. Summing,
the YTM = 5.55% – 1.37% = 4.18% (slight difference due to
rounding). In other words, buying a premium bond and holding it
to maturity ensures capital losses over the life of the bond;
however, the higher-than-market coupon will exactly offset the
losses. The opposite is true for discount bonds.
2. More on Bond Features
A. Is It Debt or Equity?
In general, debt securities are characterized by the following
attributes:
-Creditors (or lenders or bondholders) generally have no voting
rights.
-Payment of interest on debt is a tax-deductible business expense.
-Unpaid debt is a liability, so default subjects the firm to legal
action by its creditors.
It is sometimes difficult to tell whether a hybrid security is debt or
equity. The distinction is important for many reasons, not the least
of which is that (a) the IRS takes a keen interest in the firm’s
financing expenses in order to be sure that nondeductible expenses
are not deducted and (b) investors are concerned with the strength
of their claims on firm cash flows.
B. Long-Term Debt: The Basics
Major forms are public and private placement.
Long-term debt – loosely, bonds with a maturity of one year or
more.
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Chapter 07 – Interest Rates and Bond Valuation
Short-term debt – less than a year to maturity, also called unfunded
debt.
Bond – strictly speaking, secured debt; but used to describe all
long-term debt.
C. The Indenture
Indenture – written agreement between issuer and creditors
detailing terms of borrowing. (Also, deed of trust.) The indenture
includes the following provisions:
-Bond terms
-The total face amount of bonds issued
-A description of any property used as security
-The repayment arrangements
-Any call provisions
-Any protective covenants
Terms of a bond – face value, par value, and form
Registered form – ownership is recorded, payment made
directly to owner
Bearer form – payment is made to holder (bearer) of bond
Lecture Tip: 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.
Security – debt classified by collateral and mortgage
Collateral – strictly speaking, pledged securities
Mortgage securities – secured by mortgage on real property
Debenture – an unsecured debt with 10 or more years to
maturity
Note – a debenture with 10 years or less maturity
Seniority – order of precedence of claims
Subordinated debenture – of lower priority than senior debt
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Chapter 07 – Interest Rates and Bond Valuation
Repayment – early repayment in some form is typical
Sinking fund – an account managed by the bond trustee for
early redemption
Call provision – allows company to “call” or repurchase part or all
of an issue
Call premium – amount by which the call price exceeds the par
value
Deferred call – firm cannot call bonds for a designated period
Call protected – the description of a bond during the period it
can’t be called
Protective covenants – indenture conditions that limit the actions
of firms
Negative covenant – “thou shalt not” sell major assets, etc.
Positive covenant – “thou shalt” keep working capital at or
above $X, etc.
Lecture Tip: Domestically issued bearer bonds will become
obsolete in the near future. 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.
Lecture Tip: Ask the class to consider the difference in yield for a
secured bond versus a debenture. Since a secured bond offers
additional protection in bankruptcy, it should have a lower
required return (lower yield). It is a good idea to ask students this
question for each bond characteristic. It encourages them to think
about the risk-return tradeoff.
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