5-1
CHAPTER 5
Bonds and Their Valuation
 Bonds: Facts and Motivations
 Bond valuation
 Finding price and yield
 Yield-to-maturity: Details
 A relationship between price and yield
 Premium, discount, and par bonds
 Assessing risk
 Default risk, interest rate risk, and
reinvestment rate risk
 Bond ratings
 Types of bonds
 Bond contract terms and bankruptcy process
5-2
Top Five Largest U.S. Corporate
Bond Financings, as of July 1999
Issuer
Ford Motor Co.
AT&T
RJR Holdings
WorldCom
Sprint
Date
July 1999
Mar 1999
May 1989
Aug 1998
Nov 1998
Amount
$8.6 billion
$8.0 billion
$6.1 billion
$6.1 billion
$5.0 billion
5-3
Advantage of Debt over Equity
Interest expense is tax-deductible
but dividend is not.
Avoid earning/ownership dilution
Avoid a high flotation cost for
issuing stock.
Flotation cost = Underwriting fee,
Fee to investment banker
5-4
Example of Tax Saving with Debt
 Income Statement
Revenue
−COGS
Profit Margin
− Op. Cost
Firm w/o Debt
EBIT
$5
−Int. Exp
0
EBT
5
−Tax (30%)
1.5
Net Income
3.5
Firm w/ Debt
$5
1
4
1.2
2.8
 30 cents savings for every dollar of interest
expense
5-5
Who Issue a Bond?
 Domestically,
 Treasury bill, note, or bond: Issued by federal
government, Called “risk-free” securities, about $4
trillion market
 Municipal bond: “munis”
 Corporate bond: our focus, about $5 trillion market
 Internationally,
 Euro bond (Dollar-denominated bonds sold in
Germany by GM)
 Foreign bond: “Yankee” bond (dollar-denominated
bond sold in U.S. by non-U.S. issuer), “Samurai”
bond (Yen bonds sold in Japan by a non-Japanese
borrower), etc
5-6
5-7
Bond Pricing: Cash Flow
AMD
(Issuer, Seller, or
Borrower)
Coupons at
t=1,2, …. T
Investor
(Buyer, Lender)
Face Value at T
Price?
Main Question: How much would be the fair price a buyer is
willing to pay for this bond?
5-8
Elements of Bond Pricing
1. Par value (par): Face amount. paid at maturity.
Assume $1,000.
2. Coupon interest rate (C or INT): Stated interest rate
on the bond certificate. Multiply by par value to get
dollars of interest to be paid. Generally fixed.
3. Maturity (N): Years until bond must be repaid.
Declines over time.
4. Yield-to-Maturity (YTM, rd): The current market
interest rate that is used to discount the future
coupon payments and face amount. Or, the required
rate of return to be earned from other bonds with
same level of risk.
5-9
Financial Asset Valuation
0
1
2
r
...
Value
PV =
n
CF1
CF1
1+ r 
1
+
CF2
CF2
1+ r 
2
+ ... +
CFn
CFn
1+ r 
n
.
The value of any financial asset (e.g., a bond, a stock, a loan,
etc) is simply the present value of the cash flows the asset is
expected to produce.
5 - 10
An AMD Bond
AMD Bond
10% Coupon
$1,000 Par
5-year Maturity
 Suppose AMD issues a
bond with a par value of
$1,000 at a coupon rate of
10% for five years. That
is, AMD promises to pay
you $100 at the end of
each of 5 years and
$1,000 at the end of 5th
year. Suppose the
current market interest
rate is 10%. How much
would you pay for a bond
now?
5 - 11
The Value of AMD bonds
0
1
2
r=10%
Present
Value
5
...
100
100
1,100
=$1,000*10%
100
100
100
1, 000
PV 

 ...... 

1
2
5
(1  10%) (1  10%)
(1  10%) (1  10%)5
 90.91 + 82.64 + ...... + 62.09 + 620.92
 $1000
5 - 12
The bond consists of a 10-year, 10%
annuity of $100/year plus a $1,000 lump
sum at t = 10:
PV annuity
= $ 614.46
PV maturity value =
385.54
Value of bond
= $1,000.00
INPUTS
OUTPUT
10
N
10
I/YR
PV
-1,000
100
PMT
1000
FV
5 - 13
What if a price is given?: What’s the YTM
on a 10-year, 9% annual coupon, $1,000
par value bond that sells for $887?
0
rd=?
1
887
10
...
90
PV1
.
.
.
PV10
PVM
9
90
90
1,000
Find rd that “works”!
5 - 14
Find rd
VB 
INT
... +
1 +
1 + r d 
90
887 
1 +
1 + r d 
INPUTS
OUTPUT
10
N
... +
I/YR
10.91
INT
1 + r d 
N
+
M
1 + r d 
N
90
1,000
10 +
10
1+ r d  1 + r d 
−887
PV
90
PMT
Watch out a negative sign on PV.
1000
FV
5 - 15
Semiannual Bonds
1. Multiply years by 2 to get periods = 2n.
2. Divide nominal rate by 2 to get periodic
rate = rd/2.
3. Divide annual INT by 2 to get PMT =
INT/2.
INPUTS
OUTPUT
2n
N
rd/2
I/YR
OK
PV
INT/2
PMT
OK
FV
5 - 16
Find the value of 10-year, 10% coupon,
semiannual bond if rd = 13%.
2(10)
INPUTS
20
N
OUTPUT
13/2
6.5
I/YR
PV
-834.72
N  Multiply by 2
YTM  Divide by 2
INT  Divide by 2
100/2
50
PMT
1000
FV
5 - 17
What if a price is given with semiannual
coupons?: What’s the YTM on a 10-year, 9%
semiannual coupon, $1,000 par value bond
that sells for $887?
0
rd=?
1
...
45
PV1
.
.
.
PV10
PVM
887
9
45
20
In 6 mth
periods
45
1,000
Find rd that “works”!
5 - 18
Find rd for Semiannual Bonds
45
887 
1 +
1 + r d 
INPUTS
OUTPUT
20
N
... +
45
1,000
20 +
20
1+ r d  1 + r d 
-887
45
I/YR
PV
PMT
5.44 x2 =10.88
Watch out a negative sign on PV.
Don’t forget multiplying 5.44 by 2.
1000
FV
5 - 19
We are dealing with two rates:
Coupon rate and YTM
 Coupon rate = A stated interest rate on the
bond at the time of issuance, Usually fixed.
Can be used to compute periodic cash flows
to investors. Easier to understand.
5 - 20
We are dealing with two rates:
Coupon rate and YTM
 Yield-to-maturity
 The compounded rate of return earned on a
bond held to maturity if an investor re-invests
all the coupon payments until maturity.
 Usually, same as the current market interest
rate for a similar investment. Also known as
the opportunity cost of capital, i.e., the rate
that could be earned on alternative
investments of equal risk.
 The discount rate that equates a bond’s price
with the present value of its future cash flows.
5 - 21
YTM: Example
 2−year @ 10% annual coupon bonds, YTM = 15% 
Price = $918.71
 Now, assume that an investor re-invest first coupon
income (t = 1) at 15% for one year.
 Then, total cash inflows upon maturity in year 2 is
equal to
 100*1.15 = 115 plus
 100 plus
 1,000
 = 1215
 Find I that makes a PV of 918.75 equal to FV of 1215
when N = 2
 N = 2, PV = −918.75 , PMT = 0, FV= 1,215  I = 15%
5 - 22
YTM is a function of many factors!
rd = (r* + DRP) + IP + Others.
rd
= Required rate of return on a
debt security.
r*
= Real risk-free rate. T-bond
rate if no inflation; 1% to 4%.
DRP
= Default risk premium.
IP
= Inflation premium.
Others = Liquidity premium and/or
Maturity risk premium.
5 - 23
Graphical Relationship Between Price
and Yield-to-Maturity
1500
1400
1300
Price
1200
1100
1000
900
800
700
600
0%
2%
4%
6%
8%
10%
12%
14%
Yield
Price and Yield move in an opposite direction!
5 - 24
Any explanation?
5 - 25
5 - 26
5 - 27
What would happen if expected
inflation rose by 3%, causing rd = 13%?
INPUTS
OUTPUT
10
N
13
I/YR
PV
-837.21
100
PMT
1000
FV
When rd rises, above the coupon rate,
the bond’s value falls below par, so it
sells at a discount.
5 - 28
What would happen if inflation fell, and
rd declined to 7%?
INPUTS
OUTPUT
10
N
7
I/YR
PV
-1,210.71
100
PMT
1000
FV
If coupon rate > rd, price rises above
par, and bond sells at a premium.
5 - 29
Premium, Discount, Par Bonds
If coupon rate < rd, bond sells at a
discount. (Price < Par)
If coupon rate = rd, bond sells at its
par value. (Price = Par)
If coupon rate > rd, bond sells at a
premium. (Price > Par)
If rd rises, price falls - very important.
Price = par at maturity.
5 - 30
Examples: Premium, Discount, and
Par Bond
Example 1: Find the value of 10%, 10-year, $1,000 par
value annual bond. Assume YTM = 10%.
Example 2: Find the value of 10%, 10-year, $1,000 par
value annual bond. Assume YTM = 13%.
Example 3: Find the value of 10%, 10-year, $1,000 par
value annual bond. Assume YTM = 7%.
Now plot three bonds. Put price on the y-axis and yield on
the x-axis.
5 - 31
Definitions
Annual
coupon
pmt
Current yield =
Current price
Change
in
price
Capital gains yield =
Beginning price
Exp total
Exp
Exp cap
= YTM =
+
return
Curr yld
gains yld
5 - 32
Find current yield and capital gains
yield for a 8%, 10-year bond when the
bond sells for $827.97 and YTM =
10.91%.
$80
Current yield =$827.97
= 0.0966 = 9.66%.
5 - 33
YTM = Current yield + Capital gains yield.
Cap gains yield = YTM - Current yield
= 10.91% - 9.66%
= 1.25%.
Could also find values in Years 0 and 1,
get difference, and divide by value in
Year 1. Same answer.
5 - 34
Premium and Discount Bonds
All 10-year
Bonds
Premium
C = 15%
YTM = 10.91%
Discount
C = 8%
YTM = 10.91%
Current
Yield
12.08%
9.66%
Capital Gain ─1.17%
or Loss
Yield
1.25%
5 - 35
Change in price of a bond over time:
Suppose the bond was issued 20
years ago and now has 10 years to
maturity. What would happen to its
value over time if the required rate
of return remained at 10%, or at
13%, or at 7%?
5 - 36
Bond Value ($)
1,372
1,211
rd = 7%.
rd = 10%.
1,000
M
837
rd = 13%.
775
30
25
20
15
10
5
0
Years remaining to Maturity
5 - 37
The value of a premium bond would
decrease to $1,000.
The value of a discount bond would
increase to $1,000.
A par bond stays at $1,000 if rd
remains constant.
At maturity, the value of any bond
must equal its par value. Any
economic rationale?
5 - 38
Changes in Bond Price over Time:
Reality
5 - 39
Three Risks in the Bond Market
Default risk: A seller may not pay me
coupons and principal.
Interest rate risk: A volatile interest
movement may depress the value of
my bonds. (also called price risk)
Reinvestment risk: I may be forced to
re-invest my coupon payments at a
lower interest rate.
5 - 40
Bond Ratings Provide One Measure
of Default Risk
Investment Grade
Junk Bonds
Moody’s Aaa
Aa
A
Baa
Ba
B
S&P
AA
A
BBB
BB
B CCC D
AAA
Caa
C
5 - 41
Importance of Bond Ratings
A rating is an indicator of default risk
A lower rating means difficulty in
selling new bonds as the company
needs new financing.
A lower rating means a higher interest
expense in the future funding.
A downgrades may have negative
impact on equity prices.
5 - 42
Bond Rating and Market Interest Rates
Rating
Interest Rate
Spread over Long
Bond Rate
AAA
7.20%
0.20%
AA
7.50
0.50
A
8.00
1.00
BBB
8.50
1.50
BB
9.00
2.00
B
10.25
3.25
CCC
12.00
5.00
CC
13.00
6.00
C
14.50
7.50
Source: Applied Corporate Finance by Aswath Damodaran, 1997
5 - 43
What’s interest rate (or price) risk?
Does a 1-year or 10-year 10% bond
have more risk?
Interest rate risk: Rising rd causes
bond’s price to fall.
rd
1-year Change 10-year Change
5%
$1,048
$1,386
10%
1,000
4.8%
15%
956
4.4%
1,000
38.6%
749
25.1%
5 - 44
Value
1,500
10-year
1-year
1,000
500
kd
0
0%
5%
10%
15%
5 - 45
What is reinvestment rate risk?
The risk that CFs will have to be
reinvested in the future at lower
rates, reducing income.
5 - 46
Buying a short-term bond and rolling over 9
years in a declining interest rate environment
0
1
0
r=10%
1100
1
r=7%
9
...
1070
70
Or, Buying a long-term, 10-year bond in a
declining interest rate environment
0
1
2
r=7%
r=10%
100
=$1,000*10%
10
...
100
1,100
5 - 47
Long-term bonds: High interest rate
risk, low reinvestment rate risk.
Short-term bonds: Low interest rate
risk, high reinvestment rate risk.
Nothing is riskless!
5 - 48
True or False: “All 10-year bonds have
the same price and reinvestment rate
risk.”
False! Low coupon bonds have less
reinvestment rate risk but more price
risk than high coupon bonds.
If two bonds with different coupon rates
have the same maturity, then the value
of the one with the lower coupon is
proportionately more dependent on the
value amount to be received at maturity.
5 - 49
Summary: Risks in Bond Trading
LongTerm
Bond
ShortTerm
Bond
HighLowCoupon Coupon
Bond
Bond
Interest Higher
Rate
Risk
Lower
Lower
Higher
Reinves Lower
tment
Risk
Higher
Higher
Lower
5 - 50
Other Types of Bonds
 Treasury Bond: Issued by the federal
government
 Callable bond: The seller has an option to
buy back their bonds from bond investors.
 Convertible bond: The seller grant
bondholders the right to exchange each bond
for a designated number of common stock
shares of the issuing firm.
 Zero-coupon bonds: “zeros” or “deep
discount” bonds
 Floating-rate bonds
5 - 51
Callable Bond
Callable bond: A 10-year, 10% annual
coupon,$1,000 par value bond is selling
for $1,134.20 with an 8% yield to maturity.
It can be called after 5 years at $1,050.
What’s the bond’s nominal yield to
call (YTC)?
INPUTS
OUTPUT
5
N
I/YR
7.54%
-1134.2 100
PV
PMT
1050
FV
5 - 52
Yield to Call
A callable bond allows the issuer to
buy back the bond at a specified call
price anytime after an initial call
protection period, until the bond
matures.
5 - 53
How does adding a call provision
affect a bond?
Issuer can refund if rates decline.
That helps the issuer but hurts the
investor.
Therefore, borrowers are willing to
pay more, and lenders require more,
on callable bonds.
5 - 54
If you bought bonds, would you be
more likely to earn YTM or YTC?
Coupon rate = 10% vs. YTC = rd =
7.54%. Could raise money by selling
new bonds which pay 7.54%.
Could thus replace bonds which pay
$100/year with bonds that pay only
$75.40/year.
Investors should expect a call, hence
YTC = 7.54%, not YTM = 8%.
5 - 55
In general, if a bond sells at a
premium, then (1) coupon > rd, so
(2) a call is likely.
So, expect to earn:
YTC on premium bonds.
YTM on par & discount bonds.
5 - 56
Bond Indentures or Provisions
 Secured versus unsecured debt
Debenture: Unsecured bond
 Senior versus subordinated debt
 Guarantee provisions
 Sinking fund provisions
 Restrictive covenants
5 - 57
Bankruptcy
Two main chapters of Federal
Bankruptcy Act:
Chapter 11, Reorganization
Chapter 7, Liquidation
Typically, company wants Chapter
11, creditors may prefer Chapter 7.
5 - 58
5 - 59
Summary
 A bond is a debt security.
 YTM = Rate of return to be earned if holding until
maturity
 YTM = Current yield + Capital gains (loss) yield
 Price and yield are negatively correlated.
 At maturity, price = par value
 A premium bond is not necessary “better”
investment opportunity than a discount bond.
 Default risk, reinvestment risk, and price risk are
three most important risk factors in trading bonds.
 Reinvestment risk and price risk can move in
opposite direction for a given bond.
 Callable bond carries a higher reinvestment risk than
a straight bond, from the buyer’s perspective.
5 - 60
Bonds Quotation at
www.bondpage.com
5 - 61
Quiz
You could buy, for $1,000, either a
10%, 10-year, annual payment
bond or an equally risky 10%, 10year semiannual bond. Which
would you prefer?
The semiannual bond’s EFF% is:
m
iNom 

EFF%   1 
 1

m
2
 1  0.10  1  10.25%

2 