2011 6-1
McGraw-Hill/Irwin
Copyright by the McGraw-Hill Companies, Inc. All rights reserved.
Bond Definitions
Bond
Debt contract
Interest-only loan
Par value (face value) ~ $1,000
Coupon rate
Coupon payment
Maturity date
Yield to maturity
6-2
Key Features of a Bond
Par value:
Face amount
Re-paid at maturity
Assume $1,000 for corporate bonds
Coupon interest rate:
Stated interest rate
Usually = YTM at issue
Multiply by par value to get coupon
payment
6-3
Key Features of a Bond
Maturity:
Years until bond must be repaid
Yield to maturity (YTM):
The market required rate of return for bonds of
similar risk and maturity
The discount rate used to value a bond
Return if bond held to maturity
Usually = coupon rate at issue
Quoted as an APR
6-4
Bond Value
What is the value of a $1,000 bond that
pays 10% interest and matures in 5
years?
0
1
$100
2
$100
3
$100
Why the
additional
$1,000?
4
$100
5
$100
+$1,000
$1,100
6-5
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
6-6
The Bond-Pricing Equation
1
1 (1 + YTM) t
Bond Value = C
YTM
F
+
(1 + YTM) t
PV(Annuity)
PV(lump sum)
C = Coupon payment; F = Face value
6-7
Texas Instruments BA-II Plus
= number of periods to maturity
= period interest rate = YTM
= present value = bond value
= coupon payment
= future value = face value = par value
6-8
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
11
100
1000
-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
6-9
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
8
100
1000
-1,196.36
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
6-10
Bond Prices:
Relationship Between Coupon and Yield
Coupon rate = YTM Price = Par
Coupon rate < YTM Price < Par
Discount bond Why?
Coupon rate > YTM Price > Par
Premium bond Why?
6-11
The Bond-Pricing Equation
Adjusted for Semi-annual Coupons
1
1 - (1 + YTM/2) 2t
C
Bond Value =
2
YTM/2
C = Annual coupon payment
F
+
(1 + YTM/2) 2t
C/2 = Semi-annual coupon
YTM = Annual YTM (as an APR) YTM/2 = Semi-annual YTM
t = Years to maturity
2t = Number of 6-month
periods to maturity
6-12
Semiannual Bonds
Example 6.1
Coupon rate = 14% - Semiannual
YTM = 16% (APR)
Maturity = 7 years
Number of coupon payments?
14 = 2 x 7 years
Semiannual coupon payment?
$70 = (14% x Face Value)/2
Semiannual yield?
8% = 16%/2
(t or )
(C or )
(YTM or )
6-13
Example 6.1
Semiannual coupon = $70
Semiannual YTM = 8%
Periods to maturity = 14
1
1- (1 + YTM) t
Bond Value = C
YTM
Bond value =
70[1 1/(1.08)14] / .08 +
1000 / (1.08)14 = 917.56
1
1
(1.08)14
B = 70
0.08
1000
+
(1.08)14
F
+
t
(1 + YTM)
Using the calculator:
14
8
70
1000
-917.56
Using Excel: =PV(0.08, 14, 70, 1000, 0)
6-14
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
6-15
Interest Rate Risk
Reinvestment Rate Risk
Uncertainty concerning rates at which
cash flows can be reinvested
Short-term bonds have more reinvestment
rate risk than long-term bonds
High coupon rate bonds have more
reinvestment rate risk than low coupon
rate bonds
6-16
Excel example of interest rate
risk
6-17
Computing Yield-to-Maturity YTM
Yield-to-maturity (YTM) = the market
required rate of return implied by the
current bond price
With a financial calculator,
Enter , , , and
Remember the sign convention
and need to have the same sign (+)
the opposite sign (-)
6-18
YTM with Annual Coupons
Consider a bond with a 10% annual
coupon rate, 15 years to maturity and a
par value of $1000. The current price is
$928.09.
Will the yield be more or less than 10%?
15
928.09
1000
100
= 11% Result = YTM
Using Excel: =RATE(15, 100, -928.09, 1000, 0)
6-19
YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate
and semiannual coupons, has a face value
of $1000, 20 years to maturity and is
selling for $1197.93.
Is the YTM more or less than 10%?
What is the semiannual coupon payment?
How many periods are there?
6-20
YTM with Semiannual Coupons
Suppose a bond with a 10% coupon rate and
semiannual coupons, has a face value of $1,000,
20 years to maturity and is selling for $1,197.93.
40
NOTE: Solving a semi1197.93
annual payer for YTM
results in a 6-month YTM.
1000
The calculator & Excel
50
solve what you enter.
4%
YTM = 4%*2 = 8%
Result = YTM
Using Excel: =RATE(40, 50, -1197.93, 1000, 0) = 4%
6-21
Debt versus Equity
Debt
Not an ownership interest
No voting rights
Interest is tax-deductible
Creditors have legal
recourse if interest or
principal payments are
missed
Excess debt can lead to
financial distress and
bankruptcy
Equity
Ownership interest
Common stockholders
vote to elect the board of
directors and on other
issues
Dividends are not tax
deductible
Dividends are not a
liability of the firm until
declared. Stockholders
have no legal recourse if
dividends are not
declared
An all-equity firm cannot
go bankrupt
6-22
The Bond Indenture
Deed of Trust
Contract between issuing company and
bondholders includes:
Basic terms of the bonds
Total amount of bonds issued
Secured versus Unsecured
Sinking fund Call provisions
provisions
Deferred call
Call premium
Details of protective covenants
Return 6-23
to Quiz
Bond Provisions
Convertible bonds
Callable bonds
Many types of provisions can be added to
a bond
Important to recognize how these provisions
affect required returns
Who does the provision benefit?
6-24
Bond Classifications
Registered vs. Bearer Bonds
Security
Collateral secured by financial securities
Mortgage secured by real property,
normally land or buildings
Debentures unsecured
Notes unsecured debt with original
maturity less than 10 years
Seniority
Senior versus Junior, Subordinated
6-25
Bond Characteristics and
Required Returns
Coupon rate
(risk characteristics of the bond when issued)
Usually yield at issue
Which bonds will have the higher coupon,
all else equal?
Secured debt versus a debenture
Subordinated debenture versus senior debt
A bond with a sinking fund versus one without
A callable bond versus a non-callable bond
6-26
Bond Ratings Investment
Quality
High Grade
Moodys Aaa and S&P AAA capacity to pay is
extremely strong
Moodys Aa and S&P AA capacity to pay is very
strong
Medium Grade
Moodys A and S&P A capacity to pay is strong,
but more susceptible to changes in
circumstances
Moodys Baa and S&P BBB capacity to pay is
adequate, adverse conditions will have more
Return
impact on the firms ability to pay
to Quiz
6-27
Bond Ratings - Speculative
Low Grade
Moodys 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
Moodys C and S&P C income bonds with no
interest being paid
Moodys D and S&P D in default with
principal and interest in arrears
6-28
Government Bonds
Municipal Securities
Debt of state and local governments
Varying degrees of default risk, rated similar
to corporate debt
Interest received is tax-exempt at the federal
level
Interest usually exempt from state tax in
issuing state
6-29
Government Bonds
Treasury Securities = Federal government debt
Treasury Bills (T-bills)
Pure discount bonds
Original maturity of one year or less
Treasury notes
Coupon debt
Original maturity between one and ten years
Treasury bonds
Coupon debt
Original maturity greater than ten years
6-30
Example 6.4
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%
6-31
Zero Coupon Bonds
Make no periodic interest payments
(coupon rate = 0%)
Entire yield-to-maturity comes from the
difference between the purchase price
and the par value (capital gains)
Cannot sell for more than par value
Sometimes called zeroes, or deep
discount bonds
Treasury Bills and U.S. Savings bonds are
good examples of zeroes
6-32
Inflation and Interest Rates
Real rate of interest
=Change in purchasing power
Nominal rate of interest
= Quoted rate of interest,
= Change in purchasing power and inflation
The ex ante nominal rate of interest
includes our desired real rate of return
plus an adjustment for expected inflation
6-33
The Fisher Effect
The Fisher Effect defines the relationship
between real rates, nominal rates and
inflation
(1 + R) = (1 + r)(1 + h)
R = nominal rate (Quoted rate)
r = real rate
h = expected inflation rate
Approximation: R = r + h
6-34
Example 6.6
If we require a 10% real return and we
expect inflation to be 8%, what is the
nominal rate?
R = (1.1)(1.08) 1 = .188 = 18.8%
Approximation: R = 10% + 8% = 18%
Because the real return and expected
inflation are relatively high, there is
significant difference between the actual
Fisher Effect and the approximation.
6-35
Term Structure of Interest Rates
Term structure: The relationship between
time to maturity and yields, all else equal
The effect of default risk, different coupons,
etc. has been removed.
Yield curve: Graphical representation of
the term structure
Normal = upward-sloping L/T > S/T
Inverted = downward-sloping L/T < S/T
6-36
Figure 6.5 A Upward-Sloping
Yield Curve
REPLACE with FIGURE 6.5 A
6-37
Figure 6.5 B DownwardSloping Yield Curve
6-38
Factors Affecting Required
Return
Default risk premium bond ratings
Taxability premium municipal versus taxable
Liquidity premium bonds that have more
frequent trading will generally have lower
required returns
Maturity premium longer term bonds will tend
to have higher required returns.
Anything else that affects the risk of the cash flows to
the bondholders will affect the required returns
6-39
Quick Quiz
How do you find the value of a bond and why
do bond prices change?
What is a bond indenture and what are some
of the important features?
What are bond ratings and why are they
important?
How does inflation affect interest rates?
What is the term structure of interest rates?
What factors determine the required return on
bonds?
6-40
Practice Problems Ch. 6
1.
A 6 percent bond has a yield to maturity of 6.5 percent. The bond
matures in 7 years, has a face value of $1,000, and pays
semiannual interest payments. What is the amount of each coupon
payment?
2.
A 5.5 percent $1,000 bond matures in 7 years, pays interest
semiannually, and has a yield to maturity of 6.23 percent. What is
the current market price of the bond?
6-41
Practice Problems Ch. 6
3.
One year ago, Alpha Supply issued 15-year bonds at par. The
bonds have a coupon rate of 6.5 percent and pay interest
annually. Today, the market rate of interest on these bonds is 7.2
percent. How does the price of these bonds today compare to the
issue price?
4.
A corporate bond pays 7 percent interest. How much would a
municipal bond have to pay to be equivalent to this on an after-tax
basis if you are in the 28 percent tax bracket?
6-42
Chapter 6
END
6-43