Bond Prices and Yields
Chapter 14
McGraw-Hill/Irwin
Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
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14-3
14-4
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14-6
Bonds
Bonds are debt instruments (i.e. loans)
Government Bonds include:
US Treasury
Federal Agency
Municipal (Government bonds issued by
non Federal entities such as States and
Local Governments
Corporate Bonds – are private Bonds
14-7
Bond Markets
The U.S bond market has grown from $250 billion
in 1950 to $22 trillion in 2004
Amount Oustanding in 2004
$1,900
$3,900
$3,700
Municipal Bonds
Treasury Bonds
Corporate Bonds
Federal Agency Bonds
Mortgage-related debt
$5,300
Other
$4,500
$2,700
14-8
Bonds
Bonds typically make “interest only”
payments, and repay the amount
borrowed at maturity.
New bonds may be issue to repay an issue
that is maturing.
14-9
Par Value or Face Value
The Par or Face Value is the amount
that will be refunded at the maturity
date.
The par value is usually $1000
(especially for corporate bonds).
Assume $1000 par value unless
another value is provided.
14-10
Coupon Rate
The coupon rate is the annual rate of
interest (APR) paid on the bonds par
value. E.g. 6.125% or 6 1/8
Bond coupons historically were in 1/8%
increments, but that is becoming less
common
14-11
Bond Basics, II.
Two basic yield measures for a
bond are its coupon rate and its
current yield.
Annual coupon
Coupon rate 
Par value
Annual coupon
Current yield 
Bond price
14-12
Coupon Payment
The coupon payment is the periodic interest
payment made to bond holders.
CouponRate* FaceValue
CouponPm t
Num berOfPaym entsPerYear
Payments per year, P/YR, is the number of
coupon payments per year
P/YR = 2 for a typical (semiannual) bond
If P/YR not stated, assume P/YR=2
14-13
Bond Characteristics
Coupon rate
Zero coupon bond
Bond Equivalent Yield is the six month
yield on a bond, doubled
Accrued Interest
Indenture
14-14
A Quick Note on Bond Quotations, I.
We have seen how bond prices are quoted in
the financial press, and how to calculate bond
prices.
Note: If you buy a bond between coupon dates,
you will receive the next coupon payment
(and might have to pay taxes on it).
However, when you buy the bond between
coupon payments, you must compensate the
seller for any accrued interest.
14-15
A Quick Note on Bond Quotations, II.
The convention in bond price quotes is to
ignore accrued interest.
This results in what is commonly called a clean
price (i.e., a quoted price net of accrued interest).
Sometimes, this price is also known as a flat
price.
The price the buyer actually pays is called the
dirty price
This is because accrued interest is added to the
clean price.
Note: The price the buyer actually pays is
sometimes known as the full price, or invoice
price.
14-16
Pricing Example
If you purchase an 8% bond quoted at
98.156, 47 days after it last coupon (183
day coupon period), what price (ignoring
any commissions must you pay for this
bond?
Accrued Interest = $40 * (47/183) = 10.27
Purchase price = 981.56 + 10.27 =
991.83
14-17
Different Issuers of Bonds
U.S. Treasury
Notes and Bonds
Corporations
Municipalities
International Governments and Corporations
Innovative Bonds
Indexed Bonds
Floaters and Inverse Floaters
14-18
Provisions of Bonds
Secured or unsecured
Call provision
Convertible provision
Put provision (putable bonds)
Floating rate bonds
Sinking funds
14-19
Bond Pricing
PB  
T
t 1
Ct
 y
 1 
 2
t
ParValue

 y
 1 
 2
T
PB = Price of the bond
Ct = interest or coupon payments (an annuity)
T = number of periods to maturity
y = yield to maturity, or market discount rate
(or bond equivalent yield, which is the APR
for the bond
14-20
Price: 10-yr, 8% Coupon, Face = $1,000
Assume market rate = 6%
20
40
1000
P

t
20
(1.03)
t 1  1.03
 40
 1000
40

P  

20
20 
 0.03 0.03(1.03)  (1.03)
P  $1,148.77
Ct = 40 (Semi Annual)
Par = 1000
This bond is trading
T = 20 periods
at a premium. Why?
YTM = 6%
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Price: 10-yr, 8% Coupon, Face = $1,000
Assume market rate = 6% (Also called YTM)
Calculator Solution:
P/YR=2
PV(N=20, I/YR=6, PMT=40, FV=1000)
= - 1148.77
What if market rate = 10%?
PV(N=20, I/YR=10, PMT=40, FV=1000)=-875.38
Inverse relationship between Yield and Price!
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Bond Prices and Yields
Prices and Yields (required rates of
return) have an inverse relationship
When yields get very high the value of
the bond will be very low.
When yields approach zero, the value of
the bond approaches the sum of the
cash flows.
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Existing Bond Prices vs. YTM’s
Price
Yield
14-24
Yield to Maturity
Interest rate that makes the present
value of the bond’s payments equal to
its price.
Solve the bond formula for y
ParValue
C
t
PB  

T
t
(1 y / 2)
t 1 (1 y / 2)
T
14-25
Yield to Maturity Example
10 yr Maturity
Coupon Rate = 7%
Price = $950
Solve for r = semiannual rate
Multiply r by 2 to get YTM
35 1000
950  

T
t
(1 r )
t 1 (1 r )
20
r = 3.8635% YTM = 3.8635% * 2 = 7.727%
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Solving for YTM using Calculator
Data: Price = 950, Maturity=10 years,
Coupon Rate = 7.00%
I/YR on the HP10BII is an APR
P/YR=2
I/YR(N=20, PV=-950, PMT=35,FV=1000)
= 7.727
Press  EFF% = 7.876 (for EAY)
14-27
Yield Measures (Discount Bond Example)
Bond Equivalent Yield – is the APR, that
is the 6 month rate doubled
7.72% = 3.86% x 2
Effective Annual Yield
(1.0386)2 - 1 = 7.88%
Current Yield
Annual Interest / Market Price
$70 / $950 = 7.37 %
Coupon Rate = $70 / $1000 = 7.00%
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Relationship for Yield Measures
Consider the “denominator effect”
For Discount Bonds
YTM > Current Yield > Coupon Rate
For Premium Bonds
YTM < Current Yield < Coupon Rate
For Par Bonds
YTM = Current Yield = Coupon Rate
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Realized Yield versus YTM
The YTM measure the yield of an
investment while it is invested in the
bond
Investors may be interested in the
return on a portfolio and thus must
make reinvestment assumptions for the
coupon to assess the portfolio
If bonds are not held to maturity, one
may be interested in the Holding Period
Return
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Holding-Period Return: Single Period
HPR = [ C + ( Pt - Pt-1 )]
/ Pt-1
where
C = coupon payment
Pt = price today
Pt-1 = purchase price last period
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Holding-Period Return Example
Your purchase a 7.25% coupon bond with 25
years to maturity when the market rate is
6.135%. You sell it six months later when the
market rate is 5.891%. What is your hpr?
Step 1. Compute the purchase price
Step 2. Compute the current price
Step 3. Apply the hpr formula
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hpr: Multiperiod portolfio
Requires calculation of reinvestment
income
Solve for the Internal Rate of Return
using the following:
Future Value: sales price + future value of
coupons
Investment: purchase price
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Hpr example: Multiple period portfolio
You have a guaranteed account that
pays 5% EAR in which you will deposit
all coupon payments.
You purchase a 6.5% bond (14 years to
maturity, market rate 7.142) and hold it
for 2.5 years (now market rate is 6.314).
What EAR do you earn on your portfolio
(bond plus guaranteed account)?
Answer: Follow the CF’s
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Taxation of Zero Coupon Bonds
Although zero coupon bonds pay no
coupon, the IRS requires one pay taxes
on the imputed interest each year
(assumes “constant yield method”)
The imputed interest each year is just
the path of capital gains over time
Example. Buy a ten year zero for $500.
What is the (approx) YTM?
What is you taxable interest for the first
three years?
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Note: Your actual tax situation depends how
long you hold this bond, and whether you sell
if for a gain or loss relative to it imputed price
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Taxation of Original Issue Discount Bonds
Bonds issued with very low coupons,
will realize capital gains over time. The
IRS will impute interest on such bond.
Assume a 15-year annual coupon bond
has a 3% coupon when the market
interest rate is 6%. You sell this bond
one year from now when the market
rate is 7%. What is you before and after
tax hpr if you ordinary tax rate is 28%,
and your capital gains rate is 15%?
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14-38
Default Risk and Ratings
Rating companies
Moody’s Investor Service
Standard & Poor’s
Duff and Phelps
Fitch
Rating Categories
Investment grade (AAA – BBB, or Aaa – Baa)
Speculative grade
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Factors Used by Rating Companies
Coverage ratios
Leverage ratios
Liquidity ratios
Profitability ratios
Cash flow to debt
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Protection Against Default
Sinking funds
Subordination of future debt
Dividend restrictions
Collateral
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