Chapter
10
Bond Prices and Yield
Bodie, Kane, and Marcus
Essentials of Investments
12th Edition
© 2022 McGraw Hill. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw Hill.
10.1 Bond Characteristics
1
Bond.
• Security that obligates issuer to make payments to holder
over time.
Face Value ≡ Par Value.
• Payment to bondholder at maturity of bond.
Coupon Rate.
• Bond’s annual interest payment per dollar of par value.
Zero-Coupon Bond.
• Pays no coupons, sells at discount, pays par value at
maturity.
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Figure 10.1 Prices/Yields of U.S. Treasury Bonds
Maturity
Coupon
Bid
Ask
Change
Asked Yield
30-Jun-21
1.125
99.054
99.060
−0.008
1.714
15-Nov-22
1.625
100.004
100.010
−0.028
1.622
15-Nov-25
2.250
103.000
103.040
−0.042
1.715
15-Nov-27
2.250
103.162
103.172
−0.044
1.822
15-Nov-27
6.125
132.144
132.154
−0.076
1.793
15-Feb-31
5.375
135.176
135.196
−0.080
1.888
15-Nov-40
4.250
134.032
134.052
−0.100
2.214
15-Nov-49
2.375
101.096
101.116
−0.088
2.323
Source: Wall Street Journal Online, November 15, 2019
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10.1 Bond Characteristics
2
Treasury Bonds and Notes:
• Accrued interest and quoted bond prices.
• Quoted prices do not include interest accruing between payment
dates.
Accrued Interest (A.I.) =
Annual coupon payment Days since last coupon payment

2
Days separating coupon payments
Example: A bond (par value = $1,000) makes semi-annual payments
with a coupon rate of 6%. If 45 days have passed since the last coupon
payment, what is the accrued interest?
A.I . 
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 $30  $7.42
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4
Figure 10.2 Listing of Corporate Bonds
Most Active Investment Grade Bonds
Symbol
Coupon
Maturity
Moody’s®/
S$P
CVS HEALTH CORP
CVS4607885
5.050%
03/25/2048
Baa2/BBB
114.865
113.151
113.784
−1.2350
4.206514
BOEING CO
BA4866208
3.250%
02/01/2035
/A
104.678
103.634
104.242
−1.0690
2.899978
KEURIG DR PEPPER
INC
KDP4843943
3.551%
05/25/2021
/BBB
102.343
102.224
102.309
−0.0400
2.085152
BOEING CO
BA4866206
2.700%
02/01/2027
/A
102.812
101.717
101.842
−0.7960
2.417044
GROUP INC
MTU4657147
3.761%
07/26/2023
A1/
105.817
105.243
105.243
−0.3170
2.304181
ALTRIA GROUP INC
MO4403915
3.875%
09/16/2046
A3/BBB
91.051
89.224
90.692
0.021933
4.472984
HCA INC
HCA4843309
5.250%
06/15/2049
Baa3/BBB–
109.588
108.408
108.408
−1.6770
4.716027
Issuer Name
High
Low
Last
Change
Yield%
MITSUBISHI UFJ FINL
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10.1 Bond Characteristics
3
Corporate Bonds:
• Callable bonds.
• Call provisions on corporate bonds: May be repurchased by issuer
at specified call price during call period.
• Convertible bonds.
• Allow bondholder to exchange bond for specified number of
common stock shares.
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10.1 Bond Characteristics
4
Corporate Bonds:
• Puttable bonds.
• Holder may choose to exchange for par value or to extend for given
number of years.
• Floating-rate bonds.
• Coupon rates periodically reset according to specified market date.
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10.1 Bond Characteristics
5
Preferred Stock:
• Commonly pays fixed dividend.
• Floating-rate preferred stock becoming more popular.
• Dividends not normally tax-deductible.
• Corporations that purchase other corporations’ preferred stock are
taxed on only 30% of dividends received.
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10.1 Bond Characteristics
6
Other Domestic Issuers:
• State, local governments (municipal bonds).
• Federal Home Loan Bank Board.
• Government National Mortgage Association (Ginnie Mae).
• Federal National Mortgage Association (Fannie Mae).
• Federal Home Loan Mortgage Corporation (Freddie Mac) .
• Farm Credit agencies.
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10.1 Bond Characteristics
7
International Bonds:
• Foreign bonds.
• Issued by borrower in different country than where bond sold.
• Denominated in currency of market country.
• Eurobonds.
• Denominated in currency (usually that of issuing country) different
than that of market.
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10.1 Bond Characteristics
8
Innovation in the Bond Market:
• Maturity.
• Bonds conventionally issued with maturities up to 30 years.
• Recently some countries issued bonds 50 to 100 years.
• Inverse floaters.
• Coupon rate falls when interest rates rise.
• Asset-backed bonds.
• Income from specified assets used to service debt.
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10.1 Bond Characteristics
9
Innovation in the Bond Market:
• Pay-in-kind bonds.
• Issuers can pay interest in cash or additional bonds.
• Catastrophe bonds.
• Higher coupon rates to investors for taking on risk.
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10.1 Bond Characteristics
10
Innovation in the Bond Market:
• Indexed bonds.
• Payments tied to general price index or price of a particular
commodity.
• Treasury Inflation Protected Securities IPS): Par value of bond
increases with consumer price index.
(T
Nominal Return =
Real Return =
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Interest  Price Appreciation
Initial Price
1  Nominal Return
1
1  Inflation
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Table 10.1 TIPS, Principal and Interest Payments
Time
Inflation in Year
Just Ended
0
Par Value
Coupon
Payment
+
Principal
Repayment
=
Total
Payment
$1,000.00
1
2%
1,020.00
$40.80
0
$ 40.80
2
3
1,050.60
42.02
0
42.02
3
1
1,061.11
42.44
$1,061.11
1,103.55
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10.2 Bond Pricing
1
Bond value = Present value of coupons + Present
par value.
T
Coupon Par Value

t
T
(1

r
)
(1

r
)
t 1
Bond Value = 
• T = Maturity date.
• r = discount rate.
Bond Price = Coupon × Annuity Factor (r, t) + Par Value × PV Factor (r, T)
1  (1  r ) T
1
 Coupon 
 Par Value 
r
(1  r )T
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10.2 Bond Pricing
2
• Prices fall as market interest rate rises.
• Interest rate fluctuations are primary source of
bond market risk.
• Bonds with longer maturities more sensitive to
fluctuations in interest rate.
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Figure 10.3 Inverse Relationship between Bond Prices
and Yields
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Table 10.2 Bond Prices at Different Interest Rates
Bond Price at Given Market Interest Rate
Time to
Maturity
2%
4%
6%
8%
10%
1 year
$1,059.11
$1,038.83
$1,019.1 3
$1,000.00
$981.41
10 years
1,541.37
1,327.03
1,148.77
1,000.00
875.38
20 years
1,985.04
1,547.11
1,231.15
1,000.00
828.41
30 years
2,348.65
1,695.22
1,276.76
1,000.00
810.71
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10.2 Bond Pricing
3
Bond Pricing between Coupon Dates.
• Invoice price = Flat price + Accrued interest.
Bond Pricing in Excel.
• =PRICE (settlement date, maturity date, annual coupon
rate, yield to maturity, redemption value as percent of par
value, number of coupon payments per year).
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Spreadsheet 10.1 Valuing Bonds
Note: Spreadsheets available in Connect
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10.3 Bond Yields
1
Yield to Maturity.
• Discount rate that makes present value of bond’s
payments equal to price.
Current Yield.
• Annual coupon divided by bond price.
Premium Bonds.
• Bonds selling above par value.
Discount Bonds.
• Bonds selling below par value.
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Spreadsheet 10.2 Finding Yield to Maturity
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10.3 Bond Yields
2
Yield to Call:
• Calculated like yield to maturity.
• Time until call replaces time until maturity; call price
replaces par value.
• Premium bonds more likely to be called than discount
bonds.
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Figure 10.4 Bond Prices: Callable and Straight Debt
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10.3 Bond Yields
3
Realized compound return.
• Compound rate of return on bond with all coupons
reinvested until maturity.
Horizon analysis.
• Analysis of bond returns over multiyear horizon.
• Based on forecasts of bond’s YTM and investment options.
Reinvestment rate risk.
• Uncertainty surrounding cumulative future value of
reinvested coupon payments.
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Figure 10.5 Growth of Invested Funds
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10.4 Bond Prices Over Time
1
Yield to Maturity versus Holding Period Return.
• Yield to maturity
(YTM) measures
average rate of
return (RoR) if the
bond is held to
maturity.
© McGraw Hill
• Holding Period Return
(HPR) is the rate over
particular investment
period.
• HPR depends on
market price at the end
of the period.
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Figure 10.6 Price Paths of Coupon Bonds in Case of
Constant Market Interest Rates
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10.4 Bond Prices Over Time
2
Zero-Coupon Bonds and Treasury STRIPS.
• Zero-coupon bond.
• Carries no coupons.
• Provides all return in form of price appreciation.
• Separate Trading of Registered Interest and Principal of
Securities (STRIPS).
• Oversees creation of zero-coupon bonds from coupon-bearing
notes and bonds.
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10.4 Bond Prices Over Time
3
After-Tax Returns:
• Built-in price appreciation on original-issue discount bonds
constitutes implicit interest payment to holder.
• IRS calculates price appreciation schedule to determine
taxable interest income for built-in appreciation.
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Figure 10.7 Price of 30-Year Zero-Coupon Bond over
Time at Yield to Maturity of 10%
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10.5 Default Risk and Bond Pricing
1
Investment grade bond:
• Rated BBB and above by S&P or Baa and above by
Moody’s.
Speculative grade or junk bond.
• Rated BB or lower by S&P, Ba or lower by Moody’s, or
unrated.
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Figure 10.8 Bond Rating Classes
Bond Ratings
Very High Quality
Hight Quality
Speculative
Very Poor
Standard &
Poor’s
AAA AA
A BBB
BB B
CCC D
Moody’s
Aaa Aa
A Baa
Ba B
Caa C
At times both Moody’s and Standard & Poor’s use adjustments to these
ratings. S&P uses plus and minus signs: A+ is the strongest A rating and
A− the weakest. Moody’s uses a 1, 2, or 3 designation, with 1 indicating
the strongest.
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10.5 Default Risk and Bond Pricing
2
Determinants of Bond Safety:
• Coverage ratios.
• Company earnings to fixed costs.
• Leverage ratios.
• Debt to equity.
• Liquidity ratios.
• Current: Current assets to current liabilities.
• Quick: Assets excluding inventories to liabilities.
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10.5 Default Risk and Bond Pricing
3
Determinants of Bond Safety:
• Profitability ratios.
• Measures of RoR on assets or equity.
• Cash flow-to-debt ratio.
• Total cash flow to outstanding debt.
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Table 10.3 Financial Ratios and Default Risk
Aaa
Aa
A
Baa
Ba
B
C
EBITA/Assets (%)
12.3%
10.2%
10.8%
8.7%
8.5%
6.7%
4.1%
Operating profit margin (%)
25.4%
17.4%
14.9%
12.0%
11.5%
9.0%
4.6%
EBITA to interest coverage (multiple)
11.5
13.9
10.7
6.3
3.7
1.9
0.7
Debt/EBITDA (multiple)
1.9
1.8
2.3
2.9
3.7
5.2
8.1
Debt/(Debt + Equity) (%)
35.1%
31.0%
40.7%
46.4%
55.7%
65.8%
89.3%
Funds from operations/Total debt (%)
41.5%
43.4%
34.1%
27.1%
19.9%
11.7%
4.6%
Retained cash flow/net Debt (%)
31.4%
30.1%
27.3%
25.3%
19.7%
11.5%
5.1%
Note: EBITA is earnings before interest, taxes, and amortization.
Source: Moody’s Financial Metrics, Key Ratios by Rating and Industry
for Global Non-Financial Corporations, December 2013.
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10.5 Default Risk and Bond Pricing
4
Bond Indentures:
• Indenture.
• Defines contract between issuer and holder.
• Sinking fund.
• Indenture calling for issuer to periodically repurchase some
proportion of outstanding bonds before maturity.
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10.5 Default Risk and Bond Pricing
5
Bond Indentures:
• Subordination clause.
• Restrictions on additional borrowing stipulating senior bondholders
paid first in event of bankruptcy.
• Collateral.
• Specific asset pledged against possible default.
• Debenture.
• Bond not backed by specific collateral.
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10.5 Default Risk and Bond Pricing
6
Yield to Maturity and Default Risk.
• Stated yield is maximum possible yield to maturity of bond.
• Default premium.
• Increment to promised yield that compensates investor for default
risk.
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Figure 10.9 Callable Bond: Apple
Comment
Description of Bond
1. Interest of 3.45% will be payable on February 9 and August 9 of each
year. Thus, every 6 months each note will pay interest of (.0345/2) ×
$1,000 = $17.25.
ISSUE: Apple Inc. 3.45% Notes
2. Investors will be repaid the $1,000 face value in 2045.
DUE: February 9, 2045
3. Moody’s bond rating is Aa, the second-highest-quality rating.
RATING: Aa
4. A trustee is appointed to look after investors’ interest.
TRUSTEE: Issued under an indenture between Apple and The Bank
of New York Mellon Trust Company
5. The bonds are registered. The registrar keeps a record of who owns
the bonds.
REGISTERED: Issued in registered, book - entry form
6. The company is not obliged to repay any of the bonds on a regular
basis before maturity.
SINKING FUND: None
7. The company has the option to buy back the notes. The redemption
price is the greater of $1,000 or a price that is determined by the value
of an equivalent Treasury bond.
CALLABLE: In whole or in part at any time
8. The notes are senior debt, ranking equally with all Apple’s other
unsecured senior debt.
SENIORITY
9. The notes are not secured; that is, no assets have been set aside to
protect the noteholders in the event of default. However, if Apple sets
aside assets to protect any other bondholders, the notes will also be
secured by these assets. This is termed a negative pledge clause.
SECURITY: The notes are unsecured. However, “if Apple shall incur,
assume or guarantee any Debt, … it will secure … the debt
securities then outstanding equally and ratably with … such Debt.”
10. The principal amount of the issue was $2 billion. The notes were sold
at 99.11% of their principal value.
OFFERED: $2,000,000,000 at 99.11%
11. The book runners are the managing underwriters to the issue and
maintain the book of securities sold.
JOINT BOOK - RUNNING MANAGERS: Goldman, Sachs; Deutsche
Bank Securities
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Figure 10.10 Yield Spreads among Corporate Bonds
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10.5 Default Risk and Bond Pricing
Credit Default Swaps (CDS).
• Insurance policy on default risk of corporate bond or loan.
• Designed to allow lenders to buy protection against losses
on large loans.
• Later used to speculate on financial health of companies.
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Figure 10.11 Prices of CDS, Greece
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10.6 The Yield Curve
1
Yield Curve.
• Graph of yield to maturity as function of term to maturity.
Term Structure of Interest Rates.
• Relationship between yields to maturity and terms to
maturity across bonds.
Expectations Hypothesis.
• Yields to maturity determined solely by expectations of
future short-term interest rates.
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Figure 10.12 Treasury Yield Curve
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Figure 10.13 Returns to Two 2-Year Investment Strategies
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10.6 The Yield Curve
2
Forward Rate.
• Inferred short-term ROI for future period, makes expected
total return of long-term bond equal to that of rolling over
short-term bonds.
(1  yn ) n  (1  yn 1 ) n 1  (1  f n )
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10.6 The Yield Curve
3
Liquidity Preference Theory:
• Investors demand risk premium on long-term bonds.
• Liquidity premium.
• Extra expected return demanded by investors as compensation for
greater risk of long-term bonds.
• Spread between forward ROI and expected short sale.
f n  E ( rn )  Liquidity Premium
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Figure 10.14 Illustrative Yield Curves
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Figure 10.15 Term Spread: Yields on 10-Year versus 90day Treasuries
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© 2022 McGraw Hill. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw Hill. 51