Part 3
Valuation of Securities
Chapters in This Part
Chapter 6 Interest Rates and Bond Valuation
Chapter 7 Stock Valuation
Integrative Case 3: Encore International
Chapter 6
Interest Rates and Bond Valuation
Instructor’s Resources
Chapter Overview
This chapter introduces interest-rate and bond-market fundamentals, beginning with the distinction between
nominal and real interest rates and the role of expected inflation in linking the two. Risk premia are added to
highlight components of the nominal return on a risky security, namely the (i) real risk-free rate, (ii) expected
inflation rate, and (iii) risk premium on the security. Next, the discussion turns to the relationship between the
nominal interest rate on a bond and its term to maturity—formally referred to as the term structure of interest
rates and represented pictorially by the yield curve. The exposition notes the general upward slope of the yield
curve—that is, that long-term interest rates tend to exceed short-term rates—and offers three explanations: (a)
expectations about future short-term rates, (ii) general investor preference for short-term, liquid debt, and (iii)
segmentation of short- and long-term debt markets. The focus then moves to bond-market institutions with a
catalogue of the major types of issues along with their legal issues, risk characteristics, and indenture provisions.
The role of rating agencies is also emphasized. The chapter concludes by presenting the basic model for bond
valuation as a special case of the general model for valuing assets (i.e., value is simply the present value of
expected cash flows from the asset). Examples are provided of the impact of variation in coupon/principal
payments, timing of coupon/principal payments, and required rates of return on the market price of a bond. The
final topic is yield to maturity—explained as nothing more than the interest rate equating the present value of a
bond’s remaining coupons and principal payments with its market price.
Suggested Answers to Opener-in-Review
Assume the bonds Aston Martin issued in 2017 pay interest semiannually.
a. How much cash would a bondholder receive every 6 months if the bonds have a coupon rate of 5.75%?
The bonds pay 5.75%2 or 0.02875 semiannually. Although not stated explicitly in the problem, par value of
b. When Austin Martin issued the bonds, maturity was 20 years, and the required return was 6% per year.
What was the market price? Did the bond sell at par, at a premium, or at a discount? Why?
Market price of the bond (given 40 semiannual coupon payments of $28.75, a $1,000 principal payment at
the market rate rises above the coupon rate, bond price falls until yield-to-maturity equals the market rate.
c. Given your answer to part b, what was the current yield of Aston Martin bonds when they were first issued?
Suppose the bonds are now worth $1,075 each. What is the current yield on the bonds now?
Current yield = Bond’s annual interest payment Current price
As established in part b, bond price at issuance was $971.11, and annual interest is $57.50, so current yield
d. The chapter opener also mentions Aston Martin bonds issued in 2011 with a 10.25% coupon rate. Assume
these bonds paid interest annually, carried a par value of $1,000, and matured in eight years. One year
after issue, price was 39% below par value. What was yield to maturity (YTM)?
YTM is the discount rated that equates present value of the seven remaining annual coupon payments of
Note: Market price must be entered as a negative number.
Answers to Review Questions
6-1 The real rate of interest measures the return on an investment, not in dollars, but in terms of how much the
investment increases one’s purchasing power. The nominal rate of interest is the actual rate of interest
In words, demanders and suppliers of loanable funds care about the real interest rate –the cost of
6-2 The term structure of interest rates is the relationship between nominal rate of return and time to maturity
for bonds with similar risk. The yield curve is a pictorial representation of this relationship.
6-3. Under the expectations theory of the term structure, the slope of the yield curve for bonds with similar risk
should reflect expectations about future short-term interest rates on those securities.
a. Downward sloping: Investors expect short-term interest rates to fall.
6-4. a. Under the expectations theory of the term structure of interest rates, the shape of the yield
b. The liquidity-preference theory assumes investors prefer short- to long-term debt instruments because
short-term debt is more liquid and less risky (i.e., suffer lower capital losses when interest rates rise).
c. The market-segmentation theory assumes the market for short- and long-term debt instruments is
distinct, with demand and supply determining the interest rate in each market. Under the market-
6-5 Prior discussion noted the nominal rate of interest (r) approximately equals the real rate (r*) plus expected
inflation (i)—ignoring risk. Broadening to encompass risky debt instruments:
Contractual provisions: The risk provisions in the indenture will be invoked and materially affecting
the bond’s attractiveness (like the firm calling the bonds when interest rates fall).
6-6 Most corporate bonds are issued in $1,000 denominations with maturities of 10 to 30 years. The stated
interest rate represents the percentage of the bond’s par value to be paid annually, though most bonds pay
6-7 A bond indenture is a complex legal document specifying rights of bondholders and duties of the issuing
firm. Indentures generally contain standard debt provisions and restrictive covenants. Standard debt
provisions specify generally acceptable record-keeping and business practices for the issuer and typically
6-8. Borrowing long term costs more than borrowing short term. On top of the base risk-free Treasury rate, the
(flotation/administrative costs can be spread over more bonds), and (iii) default risk is higher.
6-9 A bond with a conversion feature gives holders the option of converting the bond into a certain number of
a certain number of shares of common stock at a specified price.
6-10 Current yield equals a bond’s annual interest payment divided by its current market price. Bonds prices are
quoted as a percentage of par value; for example, a quote of 98.621 means the bond price is 98.621 percent
6-11 Eurobonds are issued by international borrowers in countries with currencies other than that in which the
the host currency—such as a yen-denominated bond issued in Japan by a French firm.
6-12 A financial manager should understand valuation because, on her firm’s behalf, she will (i) issue bonds
6-13. The three inputs in asset valuation are (i) Cash flows—cash received from asset ownership, (ii) Timing—
discount cash flows (i.e., higher risk implies a discount rate).
6-14 The valuation process applies to assets providing cash flows of any size (constant, mixed stream, and lump
sum) over any time period (intermittent, annual, semiannual, etc.).
6-15 The value of any asset is the present value of all cash flows expected from the asset; value depends on the
cash flows, their timing, and required rate of return. Formally:
V0 =
6-16 The basic valuation equation for a bond paying annual interest is:
B0 = + + + … + + = +
For annual interest, n is the number of years and r the annual rate of return. For semiannual interest, n is
the number of years × 2, and r is annual required rate of return 2.
6-17 A bond sells at a discount when required return exceeds the coupon rate and at a premium when the
6-18 If required return on a bond is constant until maturity and different from the coupon interest rate, bond
price will approach par value as maturity approaches (or par value plus the final interest payment).
6-19 Other things equal, the longer a bond’s maturity, the more responsive its price is to changes in market
interest rates. Risk-averse investors, therefore, prefer bonds with a short time to maturity. Long-term
6-20 Yield-to-maturity (YTM) is the compound annual rate of return investors would earn by purchasing a bond
at the current market price (which, after issue, does not necessary equal par value) and holding to maturity.
=rate(remaining periods,coupon payments per period,-current market price,principal,0)
Note: Bond price must be entered as a negative number. Also, the command produces interest rate per
6-23 Answers will vary because “givens” are algorithmically generated in MyFinanceLab.
Suggested Answer to Focus on Practice Box:
“I-Bonds Adjust for Inflation”
What effect does the inflation-adjusted interest rate have on the price of an I-bond, compared with similar bonds
offering no inflation protection?
I-bonds offer inflation insurance. Specifically, the I-bond interest rate includes (i) a fixed rate that remains
constant over the life of the bond and (ii) an adjustable rate that equals the inflation rate (at a short lag). If
Suggested Answer to Focus on Ethics Box:
Can Bond Ratings Be Trusted?
What ethical issues could arise because companies or governments issuing debt (rather than investors) pay
NRSROs to rate those instruments?
Rating agencies (National Recognized Statistical Ratings Organizations or NRSROs) want to keep issuers happy
Why do you think NRSROs inflated ratings for new complex MBSs but not traditional corporate bonds in the
run-up to the Great Recession?
An NRSRO cannot ignore issuer financial condition and award any rating it wishes. Investors/firms value
ratings because of the rater’s reputation for sound, independent analysis. In the run-up to the Great Recession,
Answers to Warm-Up Exercises
E6-1 Finding the real rate of interest (LG 1)
Answer: If r* real interest rate, r the nominal interest rate (risk free), and i expected inflation, then:
Note: Expected inflation is well under 1%, so the approximation is close.
E6-2 Yield curve (LG 1)
Answer: a.
b. Consider two options for a 10-year investment, purchasing: (i) a 10-year bond paying 4.51% or
(ii) a 5-year bond paying 3.7% and another 5-year bond in 5 years. Under the expectations
Simple, intuitive math yields a close approximation. Ignoring compounding, the 10-year return
c. Using the logic from part (b), the return on purchasing a 3-year bond today must equal the return
on purchasing a 2-year bond today and a 1-year bond in two years. So,
d. Yield curves may have an upward slope for several reasons other than expectations of rising interest
rates. According to the liquidity-preference theory, investors prefer short- to long-term debt
because short-term debt is more liquid and less subject to capital losses when interest rates rise.
E6-3 Calculating inflation expectation (LG 1)
Answer: The inflation expectation for a specific maturity is approximately the difference between the nominal
yield and real interest rate at that maturity (i.e., in the Table below we use Equation 6.1a):
Maturity Yield Real Interest Rate Inflation Expectation
3 months 1.41% 0.80% 0.61%
6 months 1.71 0.80 0.91
E6-4 Real returns (LG 1)
Answer: A T-bill will yield a negative real return if its nominal return falls below the inflation rate. More
precisely, let r* be the real interest rate, r the nominal interest rate, and i the expected inflation rate,
so:
In words, if the nominal rate on T bills falls below 3.3%, the real return will be negative. To earn a
E6-5 Calculating risk premium (LG 1)
Answer: Let rj be the nominal rate of interest on security j, RF the risk-free rate, and RPj the risk premium on
security j; then rj = RF + RPj. Or alternatively, RPj= rj – RF. So:
Security Nominal interest rate Risk premium
AAA 5.12% 5.12% 4.51% 0.61%
E6-6 The basic valuation model (LG 4)
Answer: Find the present value of the cash-flow stream for each asset by discounting expected cash flows with
the required return:
Asset 1:PV $300 0.09 $3,333.33
E6-7 Calculating present value of a bond when required return exceeds the coupon rate
(LG 4)
Answer: The value of a bond is the present value of its future cash flows, discounted at the required rate of
return. Let C represent dollar coupon payments per period, M the dollar face value or principal to be
returned on maturity, n the number of periods until maturity, and r the required rate of return.
Bond value (also market price) is below face value because the coupon rate (6%) is less than the
required rate of return. Bond value may also be obtained in Excel using the PV command and the
Note: Dollar coupon payment must be a negative number. Also, the final entry before the right
parenthesis indicates whether payments occur at beginning (1) or end of period (0).
E6-8 Bond valuations using required rates of return (LG5)
Answer: a. Specific student answers will vary but the following general relationships will
hold:
When required rate of return exceeds coupon rate, bond sells at a discount.
b. Student answers will vary but should be consistent with their answers to part (a).