7-1

A long-term debt instrument in which a
borrower agrees to make payments of
principal and interest, on specific dates,
to the holders of the bond.
7-2

Treasury/Government Bonds
 No default risk, price falls as interest rises so its
not free of all risks.

Corporate Bonds
 Issued by corporations exposed to default risk, its
level depends on characteristics of co’s securities.
 Default risk is also named as credit risk.
7-3

Municipal Bonds
 They do have default risk but the advantage is
that they are free of federal & state taxes. So it
has lower interest rate then corporate bonds

Foreign Bonds
 Issued by foreign government or corporations.
Exposed to default risk and exchange rate risk.
7-4
Primarily traded in the over-the-counter (OTC)
market.
 Most bonds are owned by and traded among large
financial institutions.
 Full information on bond trades in the OTC market
is not published, but a representative group of
bonds is listed and traded on the bond division of
the NYSE.

7-5
Although bonds have some features in common, but
they do not always have same contractual features,
for instance call provisions.
 Par value – face amount of the bond, which
is paid at maturity (assume $1,000). Amount firm
borrows and promises to repay on maturity.
 Coupon interest rate – stated ANNUAL interest rate
(generally fixed) paid by the issuer. Multiply by par
to get dollar payment of interest.
Coupon payment is the specified number of dollars of
interest paid each period, generally six months.

7-6



This payment is fixed and remains in force
during the life of the bond. Typically, at the time
bond is issued its coupon payment is set at a
level that will enable bond to be issued at or near
its par.
Floating rate bonds also exist: A bond whose
interest rates fluctuate with shifts in general
level of interest rates.
Zero Coupon Bond: A bond that pays no annual
interest but is sold at a discount below par, thus
providing compensation to investors in form of
capital appreciation.
7-7



Maturity date – years until the bond must be
repaid. Date at which par value of bond must
be repaid.
Issue date – when the bond was issued.
Yield to maturity - rate of return earned on
a bond held until maturity (also called the
“promised yield”).
7-8

The Issuing company has the right to call
the bonds for redemption. The call
provision states that the company must
pay the bond holder an amount greater
than the par value if the bonds are called.
7-9

Suppose a company sold bonds when interest
rates were relatively high. Provided the bond
is callable, the company could sell a new issue
of low yielding securities if and when interest
rates drop. It could then use proceeds of the
new issue to retire the high rate issue and
then reduce its interest expense. This process
is called REFUNDING OPERATION.
7-10



Allows issuer to refund the bond issue if rates
decline (helps the issuer, but hurts the
investor).
Borrowers are willing to pay more, and
lenders require more, for callable bonds.
Most bonds have a deferred call and a
declining call premium.
7-11





Convertible bond – may be exchanged for common
stock of the firm, at the holder’s option.
Warrant – long-term option to buy a stated number
of shares of common stock at a specified price.
Putable bond – allows holder to sell the bond back
to the company prior to maturity.
Income bond – pays interest only when interest is
earned by the firm.
Indexed bond – interest rate paid is based upon the
rate of inflation.
7-14
0
1
2
k
...
Value
Value 
n
CF1
CF1
(1  k)1

CF2
(1  k)2
CF2
 ... 
CFn
CFn
(1  k)n
7-15

The discount rate (ki ) is the opportunity
cost of capital, and is the rate that could
be earned on alternative investments of
equal risk.
ki = k* + IP + MRP + DRP + LP
7-16
0
1
2
k
VB = ?
n
...
100
100
100 + 1,000
$100
$100
$1,000

...


(1.10)1
(1.10)10 (1.10)10
VB  $90.91  ...  $38.55  $385.54
VB  $1,000
VB 
7-17

This bond has a $1,000 lump sum due at t = 10, and
annual $100 coupon payments beginning at t = 1
and continuing through t = 10, the price of the bond
can be found by solving for the PV of these cash
flows.
INPUTS
OUTPUT
10
10
N
I/YR
PV
100
1000
PMT
FV
-1000
7-18

Suppose inflation rises by 3%, causing kd = 13%.
When kd rises above the coupon rate, the bond’s
value falls below par, and sells at a discount.
INPUTS
OUTPUT
10
13
N
I/YR
PV
100
1000
PMT
FV
-837.21
7-19

Suppose inflation falls by 3%, causing kd = 7%.
When kd falls below the coupon rate, the
bond’s value rises above par, and sells at a
premium.
INPUTS
OUTPUT
10
7
N
I/YR
PV
100
1000
PMT
FV
-1210.71
7-20



Whenever going interest rate is equal to
coupon rate, a fixed rate bond will sell at its
par value.
When going interest rate rises above coupon
interest rate, bond price will fall below its par
value. Such a bond is called a discount bond
Discount = Price – Par value
When going interest rate falls below coupon
interest rate, bond price will rise above its par
value. Such a bond is called a premium bond.
7-21

VB
What would happen to the value of this bond if its
required rate of return remained at 10%, or at 13%,
or at 7% until maturity?
1,372
1,211
kd = 7%.
kd = 10%.
1,000
837
775
kd = 13%.
30
25
20
15
10
5
0
Years
to Maturity
7-22
At maturity, the value of any bond must equal
its par value.
 If kd remains constant:
 The value of a premium bond would decrease
over time, until it reached $1,000.
 The value of a discount bond would increase
over time, until it reached $1,000.
 A value of a par bond stays at $1,000.

7-23

Must find the kd that solves this model.
INT
INT
M
VB 
 ... 

1
N
(1  k d )
(1  k d )
(1  k d )N
90
90
1,000
$887 
 ... 

1
10
(1  k d )
(1  k d )
(1  k d )10
7-24
Given years to maturity=10, Price of bond is $887,
Coupon interest rate is 9%. Solve for Interest?
 Solving for I/YR, the YTM of this bond is 10.91%. This
bond sells at a discount, because YTM > coupon rate.

INPUTS
10
N
OUTPUT
I/YR
- 887
90
1000
PV
PMT
FV
10.91
7-25

Solving for I/YR, the YTM of this bond is
7.08%. This bond sells at a premium, because
YTM < coupon rate.
INPUTS
10
N
OUTPUT
I/YR
-1134.2
90
1000
PV
PMT
FV
7.08
7-26



Yield to Maturity: The rate of return earned
on a bond if it is held till maturity.
Yield to Call: return earned on a bond if it is
called before its maturity. Call price is
different from par value.
Current Yield: The annual interest payment
on a bond divided by current price.
7-27
Annual coupon payment
Current yield (CY) 
Current price
Change in price
Capital gains yield (CGY) 
Beginning price
 Expected   Expected 
  

Expected total return  YTM  
CY
CGY

 

7-28

Find the current yield and the capital gains
yield for a 10-year, 9% annual coupon
bond that sells for $887, and has a face
value of $1,000.
Current yield
= $90 / $887
= 0.1015 = 10.15%
7-29
YTM = Current yield + Capital gains yield
CGY = YTM – CY
= 10.91% - 10.15%
= 0.76%
Could also find the expected price one year from now
and divide the change in price by the beginning price,
which gives the same answer.
7-30

Interest rate risk is the concern that rising kd will
cause the value of a bond to fall.
% change 1 yr
+4.8% $1,048
$1,000
-4.4%
$956
kd
5%
10%
15%
10yr
$1,386
$1,000
$749
% change
+38.6%
-25.1%
The 10-year bond is more sensitive to interest rate
changes, and hence has more interest rate risk.
7-31

Reinvestment rate risk is the concern that kd
will fall, and future CFs will have to be
reinvested at lower rates, hence reducing
income.
EXAMPLE: Suppose you just won
$500,000 playing the lottery. You
intend to invest the money and
live off the interest.
7-32
You may invest in either a 10-year bond or a series
of ten 1-year bonds. Both 10-year and 1-year
bonds currently yield 10%.
 If you choose the 1-year bond strategy:
 After Year 1, you receive $50,000 in income and
have $500,000 to reinvest. But, if 1-year rates
fall to 3%, your annual income would fall to
$15,000.
 If you choose the 10-year bond strategy:
 You can lock in a 10% interest rate, and $50,000
annual income.

7-33
Short-term AND/OR Long-term AND/OR
High coupon bonds Low coupon bonds
Interest
rate risk
Reinvestment
rate risk

Low
High
High
Low
CONCLUSION: Nothing is riskless!
7-34
1.
2.
3.
Multiply years by 2 : number of periods = 2n.
Divide nominal rate by 2 : periodic rate (I/YR) = kd / 2.
Divide annual coupon by 2 : PMT = ann cpn / 2.
INPUTS
2n
kd / 2
OK
cpn / 2
OK
N
I/YR
PV
PMT
FV
OUTPUT
7-35
1.
2.
3.
Multiply years by 2 : N = 2 * 10 = 20.
Divide nominal rate by 2 : I/YR = 13 / 2 = 6.5.
Divide annual coupon by 2 : PMT = 100 / 2 = 50.
INPUTS
OUTPUT
20
6.5
N
I/YR
PV
50
1000
PMT
FV
- 834.72
7-36
The semiannual bond’s effective rate is:
m
2
 iNom 
 0.10 
EFF%  1 
  1  1 
  1  10.25%
m 
2 


10.25% > 10% (the annual bond’s effective
rate), so you would prefer the semiannual
bond.
7-37

The semiannual coupon bond has an effective
rate of 10.25%, and the annual coupon bond
should earn the same EAR. At these prices, the
annual and semiannual coupon bonds are in
equilibrium, as they earn the same effective
return.
INPUTS
OUTPUT
10
10.25
N
I/YR
PV
100
1000
PMT
FV
- 984.80
7-38

The bond’s yield to maturity can be determined to
be 8%. Solving for the YTC is identical to solving
for YTM, except the time to call is used for N and
the call premium is FV.
INPUTS
8
N
OUTPUT
I/YR
- 1135.90
50
1050
PV
PMT
FV
3.568
7-39



3.568% represents the periodic semiannual
yield to call.
YTCNOM = kNOM = 3.568% x 2 = 7.137% is the
rate that a broker would quote.
The effective yield to call can be calculated
 YTCEFF = (1.03568)2 – 1 = 7.26%
7-40



The coupon rate = 10% compared to YTC =
7.137%. The firm could raise money by selling
new bonds which pay 7.137%.
Could replace bonds paying $100 per year
with bonds paying only $71.37 per year.
Investors should expect a call, and to earn the
YTC of 7.137%, rather than the YTM of 8%.
7-41


In general, if a bond sells at a premium, then
(1) coupon > kd, so (2) a call is more likely.
So, expect to earn:
 YTC on premium bonds.
 YTM on par & discount bonds.
7-42