1
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?
2
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
3
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”
4
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
5
Term loansBank 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)
Types of Debt—Long-Term
6
Common Bonds
Government bondsTreasury—notes and bondsState and local governments (municipals)
• Revenue bonds• General obligation bonds
Corporate bondsMortgage bonds—backed by fixed assetsDebenture—unsecured bondSubordinated debenture—low priority
7
Other Types of BondsIncome bond—pays interest when the firm’s income is sufficient Putable bond—can be redeemed at the bondholder’s optionIndexed (purchasing power) bond—interest payments are based on an inflation indexFloating-rate bond—bond’s interest is based on market interest ratesZero (or very low) coupon bond—little or no interest is paid (discounted)Junk bond—high-risk, high-yield bond (low rating)
8
Bond Contract FeaturesIndenture—bond contractMaturity, coupon, etc. are set in the contractCoupon rate of interest—set at prevailing rate when the
bond is issuedTrustee—represents bondholders’ interestsRestrictive covenant—restricts borrower’s a actions
Sinking fund—a required annual paymentCall provision—issuer can redeem the bonds prior to maturityRefunding—retire (repay) existing debt with proceeds
of new debt—that is, refinancing debt
Convertible feature—conversion in to stock
9
Bond RatingsMoody’s S&P Aaa AAA Aa AA A A Baa BBB Ba BB B B Caa CCC C D
High qualityInvestmen
t grade
Substandard
Speculative
Ba BB B B Caa CCC C D
Junk Bonds
10
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
11
Foreign Debt Instruments
Foreign debt—sold by a foreign borrower; denominated in the currency of the country in which it is sold
EurodebtDebt sold in a country other than the one
in whose currency the debt is denominated
LIBOR: London InterBank Offer Rate
12
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.
13
Basic Valuation
n
1tt
t
nn
22
11
)r1(
CF
)r1(
CF
)r1(
CF
)r1(
CF
Value
Asset
r = required rate of return
t Period inflow cash expected CFt
14
Valuation of Bonds
1…
0 2 3 N
INT
PV of INTPV of M
Bond Value = Vd
INT INT INT
M
INT = $ interest paid each period
M = maturity, or face, value
rd
rd = investors’ required rate of return
15
Valuation of Bonds
Nd
Nd
2d
1d
d )r (1M
)r (1INT
)r (1INT
)r (1INT
V Value
Bond
d
)r (11
r
- 1 INT
Nd
Nd)r (1
1 M
16
Bond Valuation—Example
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50 = $1,000 x
0.05Years to maturity, N 8Market rate, rd 6%
Ndd
)r (11
d )r (11
M r
- 1 INT V
N d
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50 = $1,000 x
0.05Years to maturity, N 8Market rate, rd 6%
1,000
= 50(6.20979) + 1,000(0.62741) = 937.90
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50 = $1,000 x
0.05Years to maturity, N 8Market rate, rd 6%
50 1,000
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50 = $1,000 x
0.05Years to maturity, N 8Market rate, rd 6%
50 (1 + rd)8
(1+rd)8
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50 = $1,000 x
0.05Years to maturity, N 8Market rate, rd 6%
(1.06)8
(1.06)8
Ndd
)r (11
d )r (11
M r
- 1 INT V
N d 1,00050 1,00050 (1 + rd)8
(1+rd)8
(1.06)8
(1.06)8
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50 = $1,000 x
0.05Years to maturity, N 8Market rate, rd 6%
17
Bond ValuationFinancial Calculator Solution
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50Years to maturity, N 8Market rate, rd 6%
N I/Y PV PMT FV
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50Years to maturity, N 8Market rate, rd 6%
1,000
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50Years to maturity, N 8Market rate, rd 6%
1,00050
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50Years to maturity, N 8Market rate, rd 6%
1,000508
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50Years to maturity, N 8Market rate, rd 6%
1,000508 6
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 5%Annual interest payment, INT $50Years to maturity, N 8Market rate, rd 6%
1,000508 6 ?
-937.90
18
Bond Valuation—Yield to Maturity, rd
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100 = $1,000 x
0.10Years to maturity, N 5Market price, Vd $1,123
Ndd
)r (11
d )r (11
M r
- 1 INT V
Nd
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100 = $1,000 x
0.10Years to maturity, N 5Market price, Vd $1,123
1,000
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100 = $1,000 x
0.10Years to maturity, N 5Market price, Vd $1,123
100
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100 = $1,000 x
0.10Years to maturity, N 5Market price, Vd $1,123
5
5
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100 = $1,000 x
0.10Years to maturity, N 5Market price, Vd $1,123
rd = Yield to maturity, YTM
1,123
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100 = $1,000 x
0.10Years to maturity, N 5Market price, Vd $1,123
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100 = $1,000 x
0.10Years to maturity, N 5Market price, Vd $1,123
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Bond Valuation—Yield to Maturity, rd , Approximation
3
M )2(V
N V- M
d
d INT
ionApproximat
YTM
Example: M = $1,000, INT = $100, N = 5, Vd= $1,123
31,000 2(1,123)
51,123 - 1,000 100
ionApproximat
YTM
7.0% 0.0699
1,08275.40
=Adj interest
Avg investment
20
Bond Valuation—YTMFinancial Calculator Solution
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100Years to maturity, N 5Market price, Vd $1,123
N I/Y PV PMT FV
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100Years to maturity, N 5Market price, Vd $1,123
1,000
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100Years to maturity, N 5Market price, Vd $1,123
1,000100
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100Years to maturity, N 5Market price, Vd $1,123
1,0001005
7.0
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100Years to maturity, N 5Market price, Vd $1,123
1,0001005 -1,123?
Bond Characteristics:Face (maturity) value, M $1,000Coupon rate of interest, C 10%Annual interest payment, INT $100Years to maturity, N 5Market price, Vd $1,123
1,0001005 -1,123
21
Bond Valuation—Yield to CallBond Characteristics:Face (maturity) value, M $1,000Call price $1,060Coupon rate of interest, C 10%Annual interest payment, INT $100Years to maturity, N 5Date to first call 3Market price, Vd $1,123
N I/Y PV PMT FV
3 ? -1,123 1001,060
7.44
22
Bond ValuationSemiannual Payment of Interest
Most bonds pay interest semiannually Adjustments to computationsN = # years x m; m = # of interest payments per yearr = rd/m
INT = interest payment per period = Annual INT/m
Example: M = $1,000, C = 5%, Yrs to maturity = 8, rd = 6%
N I/Y PV PMT FV
1616 3.016 3.0 2516 3.0 25 1,000?16 3.0 25 1,000
-931.23
23
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.
24
Bond ValuationRelationship of YTM, Coupon, and Price
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
Market rate, kd
=Coupon rate, C
par;
Vd = M
Market rate, kd
>Coupon rate, C
discount;
Vd < M
Market rate, kd
<Coupon rate, C
premium
Vd > M
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
Market rate, rd
=Coupon rate, C
par;
Vd = M
Market rate, rd
>Coupon rate, C
discount;
Vd < M
Market rate, rd
<Coupon rate, C
premium
Vd > M
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
If rd = Vd =
Market rate, rd
=Coupon rate, C
par;
Vd = M
Market rate, rd
>Coupon rate, C
discount;
Vd < M
Market rate, rd
<Coupon rate, C
premium
Vd > M
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
If rd = Vd =
Market rate, rd
=Coupon rate, C
par;
Vd = M6%
Market rate, rd
>Coupon rate, C
discount;
Vd < M
Market rate, rd
<Coupon rate, C
premium
Vd > M
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
If rd = Vd =
Market rate, rd
=Coupon rate, C
par;
Vd = M6% $1,000.00
Market rate, rd
>Coupon rate, C
discount;
Vd < M
Market rate, rd
<Coupon rate, C
premium
Vd > M
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
If rd = Vd =
Market rate, rd
=Coupon rate, C
par;
Vd = M6% $1,000.00
Market rate, rd
>Coupon rate, C
discount;
Vd < M
Market rate, rd
<Coupon rate, C
premium
Vd > M
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
If rd = Vd =
Market rate, rd
=Coupon rate, C
par;
Vd = M6% $1,000.00
Market rate, rd
>Coupon rate, C
discount;
Vd < M10%
Market rate, rd
<Coupon rate, C
premium
Vd > M
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
If rd = Vd =
Market rate, rd
=Coupon rate, C
par;
Vd = M6% $1,000.00
Market rate, rd
>Coupon rate, C
discount;
Vd < M10% $754.22
Market rate, rd
<Coupon rate, C
premium
Vd > M
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
If rd = Vd =
Market rate, rd
=Coupon rate, C
par;
Vd = M6% $1,000.00
Market rate, rd
>Coupon rate, C
discount;
Vd < M10% $754.22
Market rate, rd
<Coupon rate, C
premium
Vd > M
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
If rd = Vd =
Market rate, rd
=Coupon rate, C
par;
Vd = M6% $1,000.00
Market rate, rd
>Coupon rate, C
discount;
Vd < M10% $754.22
Market rate, rd
<Coupon rate, C
premium
Vd > M4%
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
If rd = Vd =
Market rate, rd
=Coupon rate, C
par;
Vd = M6% $1,000.00
Market rate, rd
>Coupon rate, C
discount;
Vd < M10% $754.22
Market rate, rd
<Coupon rate, C
premium
Vd > M4% $1,162.22
Example: N = 10 yrs;
C = 6%; M = 1,000
Relationship of ratesMarket
Price, Vd
If rd = Vd =
Market rate, rd
=Coupon rate, C
par;
Vd = M6% $1,000.00
Market rate, rd
>Coupon rate, C
discount;
Vd < M10% $754.22
Market rate, rd
<Coupon rate, C
premium
Vd > M4% $1,162.22
25
Interest-Rate Risk
Bond Characteristics: M = $1,000.00INT = $60.00N = 5 yrs
Annual Interest
Rate, rd Value, Vd
4% $1,089.04
6
8
10
12
Rate, rd Value, Vd
4% $1,089.04
6 1,000.00
8
10
12
Rate, rd Value, Vd
4% $1,089.04
6 1,000.00
8 920.15
10
12
Rate, rd Value, Vd
4% $1,089.04
6 1,000.00
8 920.15
10 848.37
12
Rate, rd Value, Vd
4% $1,089.04
6 1,000.00
8 920.15
10 848.37
12 783.71
Rate, rd Value, Vd
4% $1,089.04
6 1,000.00
8 920.15
10 848.37
12 783.71
Rate, rd Value, Vd
4% $1,089.04
6 1,000.00
8 920.15
10 848.37
12 783.71
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
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
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
Rate, rd Value, Vd
4% $1,089.04
6 1,000.00
8 920.15
10 848.37
12 783.71
26
Bond Return
+=
Rate ofreturn
Current yield
= +Capital
gains yield
rd Vd0
INT Vd1 – Vd0
Vd0
Return oninvestment
Income yield
= +Capital
gains yield
27
Bond Valuation—Change in Value Over Time
Bond Characteristics: M = $1,000.00, INT = $60.00, rd
= 8%Years to Maturity
End of Year
Value, Vd
Capital Gain = (Vd1-Vd0)/Vd0
Current Yield = INT/Vd0
Total Return
5
4
3
2
1
0
920.15
933.76
948.46
964.33
981.48
1,000.00
1.48% 6.52% 8.00%933.76
920.15
933.76 1.48% 6.52% 8.00%
1.57 6.43 8.00%
1.67 6.33 8.00%
1.78 6.22 8.00%
1.89 6.11 8.00%
28
Bond Valuation—Change in Value Over Time
800.00
850.00
900.00
950.00
1,000.00
1,050.00
1,100.00
5 4 3 2 1 0
Years toMaturity
Market Value ($), Vd
920.15 if rd = 8% > C = 6%
M = 1,000
Discount bond, Vd < M
Par bond, Vd = M; rd = C = 6%
Premium bond, Vd > M
1,089.04 if rd = 4% < C = 6%
INT = $60 (C = 6%) N = 5 yrs
29
Long-Term versus Short-Term Bonds
$1,037.74
1,018.52
1,000.00
982.14
964.91
948.28
6%8
10121416
bondbond
Interest rate rd
15-year1-year
Current market
Value ofCoupon = 10%
$1,388.49
1,171.19
1,000.00
863.78
754.31
665.47
30
Long-Term versus Short-Term Bonds
400
600
800
1,000
1,200
1,400
1,600
6 8 10 12 14 16
Interest Rate, rd (%)
Bond Value, Vd
($)
1-Year Bond
14-Year Bond 15-Year Bond
31
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
Bonds (Debt)Characteristics and Valuation
32
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
Bonds (Debt)Characteristics and Valuation