Bonds (Debt)
Characteristics and Valuation
What is debt?
What are bond ratings?
How are bond prices determined?
How are bond yields determined?
What is the relationship between
bond prices and interest rates?
1
Debt Characteristics
Principal value, face value, maturity
value, and par value
Interest payments—coupon rate of
interest
Maturity date
Priority to assets and earnings
Control of the firm
2
Types of Debt—Short-Term
Treasury bills—U.S. government
securities
Repurchase agreement—repo
Federal funds—loans from one bank to
another
Banker’s acceptance—a “postdated
check”
3
Types of Debt—Short-Term
Commercial Paper (CP)—promissory note
Certificate of Deposit (CD)—time deposit
Eurodollar deposit—dollar-denominated
deposits
Money market mutual funds—short-term
investments
4
Types of Debt—Long-Term
Term loans
 Bank or insurance company
 Amortized—payment includes principal and
interest
Bonds
 Borrower agrees to make payments of interest
and principal on specific dates to the bondholder
(investor)
5
Common Bonds
Government bonds
 Treasury—notes and bonds
 State and local governments (municipals)
• Revenue bonds
• General obligation bonds
Corporate bonds
Mortgage bonds—backed by fixed assets
Debenture—unsecured bond
Subordinated debenture—low priority
6
Other Types of Bonds
Income bond—pays interest when the firm’s income
is sufficient
Putable bond—can be redeemed at the
bondholder’s option
Indexed (purchasing power) bond—interest
payments are based on an inflation index
Floating-rate bond—bond’s interest is based on
market interest rates
Zero (or very low) coupon bond—little or no
interest is paid (discounted)
Junk bond—high-risk, high-yield bond (low rating)
7
Bond Contract Features
Indenture—bond contract
 Maturity, coupon, etc. are set in the contract
 Coupon rate of interest—set at prevailing rate when the bond
is issued
 Trustee—represents bondholders’ interests
 Restrictive covenant—restricts borrower’s a actions
Sinking fund—a required annual payment
Call provision—issuer can redeem the bonds prior to
maturity
 Refunding—retire (repay) existing debt with proceeds of new
debt—that is, refinancing debt
Convertible feature—conversion in to stock
8
Bond Ratings
High quality
Investment
grade
Substandard
Junk Bonds
Speculative
Moody’s
Aaa
Aa
A
Baa
Ba
B
Caa
C
S&P
AAA
AA
A
BBB
BB
B
CCC
D
9
Importance of Bond Ratings
Indication of default risk
Institutional investors are restricted to
investment-grade securities
Ratings changes—affect a firm’s ability
to borrow and the cost of borrowing
10
Foreign Debt Instruments
Foreign debt—sold by a foreign
borrower; denominated in the currency
of the country in which it is sold
Eurodebt
 Debt sold in a country other than the one
in whose currency the debt is denominated
LIBOR: London InterBank Offer Rate
11
Basic Valuation
From “The Time Value of Money” we
know that the value of an asset is
based on the present value of the cash
flows the asset is expected to produce
in the future.
12
Basic Valuation
Asset
Value





CF1
CF2
CFn
(1  r )
1
n

(1  r )
2

(1  r )
n

 (1  r) t
CFt
t 1

CFt  expected cash flow in Period t
r = required rate of return
13
Valuation of Bonds
0
1
2
3
INT
INT
INT
rd
PV of INT
PV of M
…
N
INT
M
Bond Value = Vd
INT = $ interest paid each period
M = maturity, or face, value
rd = investors’ required rate of return
14
Valuation of Bonds
Bond
INT
INT
INT
M
 Vd 



1
2
N
Value
(1  rd ) (1  rd )
(1  rd )
(1  rd )N
1 - (1 1rd )N 


1
 INT 
  M
N
(1

r
)
r
d


d


15
Bond Valuation—Example
Bond Characteristics:
Face (maturity) value, M
$1,000
Coupon rate of interest, C
5%
Annual interest payment, INT
$50 = $1,000 x 0.05
Years to maturity, N
8
Market rate, rd
6%
1
1 - (1(1.06)



1
 rrdd))88N
+
50
1,000
Vd  INT 
M
 
8N 
(1+r
)
rd
 rdd ) 
(1.06)


 (1
= 50(6.20979) + 1,000(0.62741) = 937.90
16
Bond Valuation
Financial Calculator Solution
Bond Characteristics:
Face (maturity) value, M
$1,000
Coupon rate of interest, C
5%
Annual interest payment, INT
$50
Years to maturity, N
8
Market rate, rd
6%
8
N
6
?
50
I/Y
PV
PMT
1,000
FV
-937.90
17
Bond Valuation—Yield to Maturity, rd
Bond Characteristics:
Face (maturity) value, M
Coupon rate of interest, C
Annual interest payment, INT
Years to maturity, N
Market price, Vd
$1,000
10%
$100 = $1,000 x 0.10
5
$1,123
1 - (1 1rd )N 


1
100
1,000
1,123
Vd  INT 
M
 
5N 
r
(1

r
)
d
d




5
rd = Yield to maturity, YTM
18
Bond Valuation—Yield to Maturity, rd ,
Approximation

M - Vd
N
INT
YTM

Approximation
2(Vd )  M

3


=
Adj interest
Avg investment
Example: M = $1,000, INT = $100, N = 5, Vd= $1,123
YTM

Approximation
100  1,000 5- 1,123 

2(1,123)  1,000
3


75.40
 0.0699  7.0%
1,082
19
Bond Valuation—YTM
Financial Calculator Solution
Bond Characteristics:
Face (maturity) value, M
$1,000
Coupon rate of interest, C
10%
Annual interest payment, INT
$100
Years to maturity, N
5
Market price, Vd
$1,123
5
?
-1,123
N
I/Y
PV
100
PMT
1,000
FV
7.0
20
Bond Valuation—Yield to Call
Bond Characteristics:
Face (maturity) value, M
Call price
Coupon rate of interest, C
Annual interest payment, INT
Years to maturity, N
Date to first call
Market price, Vd
$1,000
$1,060
10%
$100
5
3
$1,123
3
?
-1,123
100
1,060
N
I/Y
PV
PMT
FV
7.44
21
Bond Valuation
Semiannual Payment of Interest
Most bonds pay interest semiannually
Adjustments to computations
 N = # years x m; m = # of interest payments per year
 r = rd/m
 INT = interest payment per period = Annual INT/m
Example: M = $1,000, C = 5%, Yrs to maturity = 8, rd = 6%
16
3.0
?
25
1,000
N
I/Y
PV
PMT
FV
-931.23
22
Changes in Bond Values Over Time
Whenever the going rate of interest, rd, equals
the coupon rate, a bond will sell at its par value
An increase (decrease) in interest rates will cause
the price of an outstanding bond to fall (rise).
The market value of a bond will always approach
its par value as its maturity date approaches,
provided the firm does not go bankrupt.
23
Bond Valuation
Relationship of YTM, Coupon, and Price
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of rates
Market rate, rkdd = Coupon rate, C
Market rate, rkdd > Coupon rate, C
Market rate, rkdd < Coupon rate, C
Market
Price, Vd
par;
Vd = M
discount;
Vd < M
premium
Vd > M
If rd =
Vd =
6%
$1,000.00
10%
$754.22
4%
$1,162.22
24
Interest-Rate Risk
When market rates change, bondholders are affected in two
ways:
 bond prices change in an opposite direction—price risk
 the rates investors earn change—reinvestment risk
Bond Characteristics:
M = $1,000.00
INT =
$60.00
N =
5 yrs
Annual Interest
Rate, rd
4%
Value, Vd
$1,089.04
6
1,000.00
8
920.15
10
848.37
12
783.71
25
Bond Return
Return on
=
investment
rd
Rate of
return
Income
yield
=
INT
Vd0
=
Current
yield
+
Capital
gains yield
+
Vd1 – Vd0
Vd0
+
Capital
gains yield
26
Bond Valuation—Change in Value Over Time
Bond Characteristics: M = $1,000.00, INT = $60.00, rd = 8%
Years to
Maturity
End of Year
Value, Vd
Capital Gain =
(Vd1-Vd0)/Vd0
Current Yield
= INT/Vd0
Total
Return
5
920.15
4
933.76
1.48%
6.52%
8.00%
3
948.46
1.57
6.43
8.00%
2
964.33
1.67
6.33
8.00%
1
981.48
1.78
6.22
8.00%
0
1,000.00
1.89
6.11
8.00%
27
Bond Valuation—Change in Value Over Time
INT = $60 (C = 6%)
N = 5 yrs
Market Value ($), Vd
1,100.00
1,089.04 if rd = 4% < C = 6%
Premium bond, Vd > M
1,050.00
1,000.00
Par bond, Vd = M; rd = C = 6%
950.00
M = 1,000
Discount bond, Vd < M
900.00
920.15 if rd = 8% > C = 6%
850.00
800.00
5
4
3
2
1
0
Years to
Maturity
28
Long-Term versus Short-Term Bonds
Coupon = 10%
Current market
Interest rate rd
6%
8
10
12
14
16
Value of
1-year
15-year
bond
bond
$1,037.74 $1,388.49
1,018.52
1,171.19
1,000.00
1,000.00
982.14
863.78
964.91
754.31
948.28
665.47
29
Long-Term versus Short-Term Bonds
Bond Value, Vd
($)
1,600
1,400
1,200
1-Year Bond
1,000
800
15-Year Bond
14-Year
Bond
600
Interest Rate,
rd (%)
400
6
8
10
12
14
16
30
Bonds (Debt)
Characteristics and Valuation
What is debt?
 Debt represents a loan
What are bond ratings?
 Ratings give an indication of the default risk
associated with a bond
How are bond prices determined?
 Value = PV of the cash flows the bond is
expected to pay during its life
31
Bonds (Debt)
Characteristics and Valuation
How are bond yields determined?
 YTM is the average annual rate of return that an investor will
earn if he or she buys the bond at the current market price and
holds it until it matures
 YTC is the average annual rate of return that an investor will
earn if he or she buys the bond at the current market price and
holds it until the first date the bond can be called
What is the relationship between bond prices and
interest rates?
 When interest rates increase, bond prices decrease, and vice
versa
32