1
Bond Basics
 Bonds are simply long-term IOUs that represent
claims against a firm’s assets.
 Bonds are a form of debt
 Bonds are often referred to as fixed-income
investments.
2
Key Features of a Bond
 Debt instrument issued by a corp. or government.
3
Key Features of a Bond
 Par value = face amount of the bond, which is paid at
maturity (assume $1,000).
=
4
Key Features of a Bond
 Coupon rate – stated interest rate (generally fixed)
paid by the issuer. Multiply by par to get dollar
payment of interest.
5
Key Features of a Bond
 Maturity date – when the bond must be repaid.
 Yield to maturity - rate of return earned on a bond
held until maturity.
6
What is interest rate risk?
 Interest rate risk is the concern that interest rates will
change, and therefore, a reduction in the value/price
of a security.
7
Interest rate risk example
Suppose you just inherited $500,000. You intend to
invest the money and live off the interest.
8
Interest rate risk example
 You may invest in either a:
 10-year bond
 series of ten 1-year bonds
 Both bonds currently yield 5%.
9
 If you choose the 1-year bond strategy:
 After year 1, you receive $25,000 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 5% interest rate, and
$25,000 annual income.
10
Interest Rate Risk
 Price Risk
 Change in price due to changes in interest
rates
 Long-term bonds have more price risk
than short-term bonds
 Low coupon rate bonds have more price
risk than high coupon rate bonds
11
12
Bond Value
 Bond Value = PV(coupons) + PV(par)
 Bond Value = PV(annuity) + PV(lump sum)
 Remember:
 As interest rates increase present values decrease
 ( r → PV  )
 As interest rates increase, bond prices decrease
and vice versa
13
Bond Valuation
Compute the value for an IBM Bond with a
6.375% coupon that will mature in 5 years
given that you require an 8% return on your
investment.
What are the annual interest payments ($)?
14
IBM Bond Timeline:
2009
0
2010
2011
1
2
63.75
63.75
2012
3
63.75
2013
4
63.75
5
63.75
1,000.00
15
IBM Bond Timeline:
2009
0
2010
2011
1
2
63.75
63.75
$63.75 Annuity for 5 years
2012
3
2013
4
63.75
63.75
5
63.75
1000.00
$1000 Lump Sum in 5 years
16
IBM Bond Timeline:
2009
0
2010
2011
1
2
63.75
63.75
$63.75 Annuity for 5 years
2012
3
2013
4
63.75
5
63.75
63.75
1000.00
$1000 Lump Sum in 5 years
= 63.75 PMT 1000 FV 8% I
5N
= PV = 935.12
17
Most Bonds Pay Interest Semi-Annually:
What is the value of a bond with a semi-annual
coupon with 5 years to maturity, 9% (nominal)
coupon rate if an investor desires a 10% (nominal)
return?
18
Most Bonds Pay Interest Semi-Annually:
e.g. semiannual coupon bond with 5 years
to maturity, 9% annual coupon rate.
Instead of 5 annual payments of $90, the bondholder
receives 10 semiannual payments of $45.
2013
0
2014
1
45
45
2015
2
45
45
2016
3
45
45
2017
4
45
45
5
45
45.00
1000.00
19
Most Bonds Pay Interest Semi-Annually:
2013
0
2014
1
45
45
2015
2
45
45
2016
3
45
45
2017
4
45
45
5
45
45.00
1000.00
Compute the value of the bond given that you
require a 10% s-a. return on your investment.
Since interest is received every 6 months, we need to use
semiannual compounding
VB =
45 - PMT
1000 - FV
5% - I
10 - N
20
Most Bonds Pay Interest Semi-Annually:
2013
0
2014
1
45
45
2015
2
45
45
2016
3
45
45
2017
4
45
45
5
45
45
1,000
Compute the value of the bond given that you
require a 10% s-a. return on your investment.
Since interest is received every 6 months, we need to use
semiannual compounding
= PV = 961.39
21
Semiannual Bonds




Coupon rate = 14% - Semiannual
YTM = 16% (APR)
Maturity = 7 years
Value of bond?
 Number of coupon payments? (2t or N)

14 = 2 x 7 years
 Semiannual coupon payment? (C/2 or PMT)

$70 = (14% x Face Value)/2
 Semiannual yield?

(YTM/2 or I/Y)
8% = 16%/2
22
Semiannual Bonds
 Semiannual coupon = $70
 Semiannual yield = 8%
 Periods to maturity = 14
1

2t
1 1  YTM

2
Bond Value  C 
2
YTM

2


 Bond value =
 70[1 – 1/(1.08)14] / .08 + 1000
/ (1.08)14 = 917.56
1


1


1000
(1.08)14 


B  70

14
0
.
08
(
1
.
08
)








F

2t

 1  YTM 2




Using the calculator:
14
N
8
I/Y
70
PMT
1000
FV
CPT PV = -917.56
Using Excel: =PV(0.08, 14, 70, 1000, 0)
23
Yield to Maturity
2013
0
-1,000
2014
1
80
2015
2
80
2016
2017
3
4
80
80
5
80
1,000
 If bond Sells at a DISCOUNT (less than
$1,000) then YTM > Coupon Rate
 If bond Sells at a PREMIUM (more than
$1,000) then YTM < Coupon Rate
24
Valuing a Discount Bond
with Annual Coupons






Coupon rate = 10%
Annual coupons
Par = $1,000
Maturity = 5 years
YTM = 11%
Price= ?
25
Valuing a Discount Bond
with Annual Coupons





Coupon rate = 10%
Annual coupons
Par = $1,000
Maturity = 5 years
YTM = 11%
Using the formula:
B = PV(annuity) + PV(lump sum)
B = 369.59 + 593.45 = 963.04
Using the calculator:
5
N
11
I/Y
100
PMT
1000 FV
CPT PV = -963.04
1

1


(1.11)5
B  100 
0.11




1000

5
 (1.11)

Using Excel: =PV(0.11, 5, 100, 1000, 0)
Note: When YTM > Coupon rate  Price < Par = “Discount Bond”
26
Valuing a Premium Bond
with Annual Coupons






Coupon rate = 10%
Annual coupons
Par = $1,000
Maturity = 20 years
YTM = 8%
Price = ?
27
Valuing a Premium Bond
with Annual Coupons





Coupon rate = 10%
Annual coupons
Par = $1,000
Maturity = 20 years
YTM = 8%
Using the formula:
B = PV(annuity) + PV(lump sum)
B = 981.81 + 214.55 = 1196.36
Using the calculator:
20
N
8
I/Y
100
PMT
1000 FV
CPT PV = -1196.36
1


1

 (1.08) 20 
1000

B  100
20
0
.
08

 (1.08)


Using Excel: =PV(0.08, 20, 100, 1000, 0)
Note: When YTM < Coupon rate  Price > Par = “Premium Bond”
28
Yield to Maturity
 If an investor purchases a 6.375% annual
coupon bond today for $900 and holds it until
maturity (5 years), what is the expected annual
rate of return (YTM)?
2013
0
-900
??
+ ??
2014
2015
1
2
63.75
63.75
2016
3
63.75
2017
4
63.75
5
63.75
1000.00
900
29
Yield to Maturity
• If an investor purchases a 6.375% annual coupon
bond today for $900 and holds it until maturity (5
years), what is the expected annual rate of return ?
Will it be >< than 6.375%?
2013
0
-900
??
+ ??
900
2014
2015
1
2
63.75
63.75
2016
3
63.75
2017
4
5
63.75
63.75
1000.00
YTMB = 63.75 PMT
1000 FV
5N
-900 PV
I=?
30
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”!
31
INPUTS
OUTPUT
10
N
I/YR
10.91
-887
PV
90
PMT
1000
FV
32
Types of Bonds
 Vanilla – fixed coupons, repaid at maturity
 Zero Coupon – pay no explicit interest but instead, sell
at a deep discount
 Convertible – can be converted into to stock
33
Types of Bonds
 Junk Bonds – below investment grade
34
Government Bonds
 Treasury Securities = Federal government debt
 Treasury Bills (T-bills)
 Pure discount bonds
 Original maturity of one year or less
 Treasury notes (T-notes)
 Coupon debt
 Original maturity between one and ten years
 Treasury bonds (T-bonds)
 Coupon debt

Original maturity greater than ten years
35
Tax Consequences
A taxable bond has a yield of 8% and a
municipal bond has a yield of 6%
 If you are in a 40% tax bracket, which bond do
you prefer?
 8%(1 - .4) = 4.8%
 The after-tax return on the corporate bond is 4.8%,
compared to a 6% return on the municipal
 At what tax rate would you be indifferent
between the two bonds?
 8%(1 – T) = 6%
 T = 25%
36
Bond Ratings
 Moody’s , Standard & Poor’s and Fitch regularly
monitor issuer’s financial condition and assign a
rating to the debt
Investment
Grade
Below
Investment
Grade
(Junk)
AAA
AA
A
BBB
BB
B
CCC
CC
C
D
Best Quality
High Quality
Upper Medium Grade
Medium Grade
Speculative
Very Speculative
Very Very Speculative
No Interest Being Paid
Currently in Default
37
Bond Ratings –
Investment Quality
 High Grade
 Moody’s Aaa and S&P AAA – capacity to pay is extremely
strong
 Moody’s Aa and S&P AA – capacity to pay is very strong
 Medium Grade
 Moody’s A and S&P A – capacity to pay is strong, but
more susceptible to changes in circumstances
 Moody’s Baa and S&P BBB – capacity to pay is adequate,
adverse conditions will have more impact on the firm’s
ability to pay
38
Bond Ratings - Speculative
 Low Grade
 Moody’s Ba, B, Caa and Ca
 S&P BB, B, CCC, CC
 Considered speculative with respect to capacity
to pay. The “B” ratings are the lowest degree
of speculation.
 Very Low Grade
 Moody’s C and S&P C – income bonds with no
interest being paid
 Moody’s D and S&P D – in default with principal
and interest in arrears
39
What affects Bond prices?
 Risk
 Interest rates
40
What is the “term structure of interest rates”?
What is a “yield curve”?
 Term structure: the relationship between
interest rates (or yields) and maturities.
 A graph of the term structure is called the yield
curve.
41
Draw a normal yield curve
42
Hypothetical Treasury Yield Curve
Interest
Rate (%)
15
Maturity risk premium
10
Inflation premium
1 yr
10 yr
20 yr
8.0%
11.4%
12.65%
5
Real risk-free rate
Years to Maturity
0
1
10
20
43
What factors can explain the shape of this
yield curve?
 This constructed yield curve is upward
sloping.
 This is due to increasing expected inflation
and an increasing maturity risk premium.
44
Current Yield Curve
 Bloomberg
45
Default risk
 If an issuer defaults, investors receive less than
the promised return.
 Influenced by the issuer’s financial strength and
the terms of the bond contract.
46