Chapter 4 Valuing Bonds
Chapter Overview
1. Why would an investor be willing to receive a dividend in chocolate? Why or why not? Why
was this unique bond issue successful? Relate this to the relevant cash flows for such a
2. Under what circumstances would there be a financial interest in an issuer refinancing a bond?
4-2 Bond Prices and Interest Rates
4-4 Bond Markets
1. Smart Practices Video. This quotes Todd Richter, managing director, Bank of America
Securities, concerning the factors that drive value.
3. Smart Ideas Video. Annette Poulsen talks about bond covenants, and the tradeoff between
flexibility for the corporation and flexibility for the bondholder.
5. Smart Solutions. A step-by-step solution to problem 4-19, a municipal bond problem.
Lecture Guide
4-1 Valuation Basics
The instructor should point out the recurring theme throughout this textbook, that there is a link
4-1a The Fundamental Valuation Model
The fundamental valuation model takes the time value of money techniques and applies them to the
4-2 Bond Pricees and Interest Rates
4-2a Bond Vocabulary
Make of note of bond terminology for students and the fact that different terms can be used to
4-2b The Basic Equation (Assuming Annual Interest)
In a bond problem, you could be given either the coupon interest rate the percent yearly interest
paid by the bond, or you could be given the dollar amount of interest paid by the bond. If you are
given a coupon interest percent, you can compute the dollar interest by multiplying the face value
of the bond by the coupon interest rate. This represents the C in the equation and is the cash flow
in the previous chapter. Note also that yield to maturity is determined after bond prices – what the
market will pay – are known. Yield to maturity is what an investor would earn if he bought the
bond and held it until it matured. It is difficult to calculate yield to maturity without a financial
calculator. Using the formula means solving for r using trial and error, a very time-consuming
process.
Suppose a $1,000 face value bond is selling for $1,100. The bond has 10 years left to maturity.
The bond has an 8% coupon rate. Using the approximation formula, the YTM is:
80 + (1000 – 1100)/10 = 70/1050 = 6.7%
(1000 + 1100)/2
Solving for YTM using a financial calculator, the solution is:
(1000 + 200)/2
Calculating YTM using a financial calculator yields:
N = 10
PMT = 80
FV = 1,000
This is true for when you are comparing two identical bonds with differing interest rates. If two
bonds have the same risk and maturity characteristics, and one carries a coupon rate of 10% and the
other a coupon rate of 12%, the 12% bond will be more valuable, and will sell for a higher price.
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Now suppose you own the 10% bond. A year later, interest rates increase to 12%. Now a new
4-2c Semi-Annual Compounding
In bond calculations, note that price (PV) must be negative while coupon payment (PMT)
and face value (FV) are positive. Mathematically, the inputs in a calculator would still give you the
same answer if you inputted a positive number for price and negative numbers for face value
4-2d Bond Prices and Interest Rates
Bonds may be premium or discount bonds at various times after the bond is issued.
However, as the bond approaches maturity, it will once again converge toward the par value it had
at issue.
Note that longer-term bonds are more sensitive to changes in the interest rate than are shorter-
term bonds, and that lower-coupon bonds are more sensitive to interest rate changes than are higher
coupon bonds. The former is true because a changed discount rate affects cash flows over a longer
period of time in a longer-term bond. When the coupon rate is lower, a given change in interest
rates represents a larger percentage change in the current coupon rate.
A bond is the sum of the discounted value of the coupon interest payments plus the discounted
principal repayment. Note also that as a bond approaches maturity, the discounted value of the
principal amount becomes a larger and larger proportion of the bond’s value.
Figure 4-2 The Relationship Between Bond Prices and Required Returns for Bonds with
Differing Times to Maturity but the Same 6% Coupon Rate
Interest Rate Risks: (Including Inflation and Issuer Risk)
Price fluctuations will not affect an investor who wishes to hold a bond to maturity. However,
an investor should not simply hold a bond to maturity to avoid loss of principal. Investors should
be looking at alternative investments that could offer higher returns. It could be worthwhile to sell
a bond when it is high priced if it is possible to reinvest at an even higher rate.
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A bond’s risk includes the risk that interest rates will change and reinvestment rate risk, the
risk of reinvesting your intermediate cash flows (coupon payments) and principal repayment. A
short-term bond carries more reinvestment rate risk for the investor – the investor will receive
interest and principal cash flows and must decide how to reinvest those funds. A long-term bond
carries more interest rate risk, the risk that interest rates will change after the bond is purchased and
adversely impact the bond’s price.
Ask students which kind of risk is more important, interest rate risk or reinvestment rate risk?
For a long term or short-term investor? Most students will agree that long-term investors face
4.3 Types of Bonds
Bonds have primary and secondary markets, just as stocks do. However, in general bonds are less
4-3a Bonds by Issuer
Corporate bonds are issued by large companies who need money to finance new investments.
Most corporate bonds have a par value of $1,000 and pay interest semi-annually. The corporate
4-3b Bonds by Features
This section can also be related to the risk-return relationship. Which is riskier, floating
rate or fixed rate debt? The answer depends on the point of view you take. Floating rate debt is
Table 4.1 Zero-Coupon Bond Prices and Taxable Income
4-4 Bond Markets
The bond market is much larger than the stock market in terms of dollar volume of
4-4a Bond Price Quotations
Bond prices, like stock prices have different bid and ask prices. The difference, or spread,
is the transaction cost of making the trade. Bond traders take a fee for bringing together buyers and
sellers.
Figure 4.5 Price Quotes for Most Active Investment-Grade Bonds
Have the students follow the listing for the most active bonds and identify the most active
of the group.
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Corporate Bond Quotations
In Table 4.5, or any bond listing, note that bond prices are quoted as if a $100 bond were being
traded (even though bonds trade in denominations of at least $1,000). This means that the price is
4-4b Bond Ratings
Note that some bonds are junk bonds at issue, when a poorly rated entity issues the bonds. Some
investment grade bonds become junk bonds, called fallen angels, if the firm’s credit rating drops
Figure 4.2 Bond Ratings
Table 4.3 The Relationship Between Bond Ratings and Spreads at Different Maturities at a
Given Point in Time
4-5 Term Structure of Interest Rates
4-5a The Yield Curve
Bond yields vary with maturity. The relationship between time to maturity and yield
to maturity for bonds of equal risk is referred to as the term structure of interest rates.
Figure 4-6 Yield Curves for U.S. Government Bonds
Look at what the current term structure of interest rates is. As noted in a footnote of the text,
4-5b Using the Yield Curve to Forecast Interest Rates
4-5c The Liquidity Preference and Preferred Habitat Theories
4-5d Conclusion
Note that like any asset bonds are the discounted sum of their cash flows. The risk-return
relationship is very important. Coupon rate reflect the risk of the firm and reflect the features of
Chapter 4 Resource Articles
“Widows and Orphans Beware: Treasuries Might Not Be So Safe”, Wall Street Journal, September
18, 2002. As the stock market declined, many investors turned to bonds. As bond prices rise,
yields are driven down. The yield on the benchmark 10-year Treasury note is less than 4%, the
Enrichment Exercises
1. Quiz students with easy (no calculation) concept questions. For example, suppose you wish to
value a 10 year bond, with a face value of $1,000 and a coupon rate of 10%. R is equal to
10%. What is the value of the bond? While you can show students the calculations, point out
2. Demonstrating the changes in yield curve over time is very impressive in a classroom. If you
have internet access in your classroom, go to http://www.smartmoney.com/bonds and click on
Living Yield Curve. If you cannot do this in the classroom, ask students to go to this web site
on their own and compare today’s yield curve with past yield curves. Could they have used the
shape of the yield curve to predict the current downturn in the market? What was the yield
curve like in 2000 at the peak of the stock market? What changes have taken place since then?
Answers to Concept Review Questions
1. Managers need to understand how bonds and stocks are priced because (1) firms regularly
issue stocks and bonds to raise money for investment (2) understanding how securities are
2. Holding future cash flows constant, the asset’s price falls if risk rises because those future cash
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4. According to Equation 4.1, the price of the land would depend on the cash flow generated by
5. The coupon rate equals the annual coupon payment divided by par value. The coupon yield
equals the annual coupon payment divided by the bond’s market price.
7. “Interest rate risk” refers to the possibility that a bond’s price will change because the market’s
8. The cash flows (bond yields) of ordinary bonds are contractually fixed. Thus, an increase in
9. The federal government, state and local governments, and corporations are the main bond
issuers in the United States.
10. A pure discount bond makes no coupon payments, while an ordinary bond selling at a discount
11. The option to convert bonds into common stock benefits bondholders. Once the stock price
rises high enough, the value of the bonds starts to behave like the stock’s value—the prices
13. The dollar price of a corporate bond quoted as 97.84%, with a $1,000 par value, is $978.40.
14. The yield spread on corporate bonds versus Treasury bond must always be positive due to risk.
Corporate bonds are riskier, so they must offer higher yields than Treasury bonds do. This
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15. The height of the yield curve depends on inflation because investors are aware that inflation
16. TIPS provide protection against inflation. Because TIPS coupon payments rise with inflation,
the coupon rate on TIPS is effectively fixed in real terms rather than in nominal terms. An
Answers to Self-Test Problems
ST4-1. A 5-year bond pays interest annually. Its par value is $1,000 and its coupon rate equals 7%.
If the market’s required return on the bond is 8 percent, what is the bond’s market price?
ST4-2. A bond that matures in 2 years makes semiannual interest payments. Its par value is
$1,000, its coupon rate equals 4%, and the bond’s market price is $1,019.27. What is the
bond’s yield to maturity?
A: The YTM is the value of r that solves this equation.
An alternative approach to this problem uses the Excel function, =IRR. This function
requires that you input the price of the bond as a negative value, followed by the positive
cash flows that the bond promises.
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A
1 -1,019.27
2 20
3 20
4 20
5 20
Now in an empty cell type the function, = IRR(A1:A5), and Excel will return the value
ST4-3. Two bonds offer a 5% coupon rate, paid annually, and sell at par ($1,000). One bond
A: Because the bonds currently sell at par, the coupon rate and the YTM must be equal at 5%.
If the YTM drops to 4%, both bonds will sell at a premium, but the price of the ten-year
bond will increase more than the price of the two-year bond.
ST4-4. The nominal rate of interest is 5% and the expected inflation rate is 2%.
a. What is the approximate real rate of return? What is the exact real rate?
b. Repeat part (a) but assume that you are in a country experiencing hyperinflation, so the
nominal interest rate is 90% and the expected inflation rate is 80%.