Transcript Document
Bond Valuation
Corporate Finance
Dr. A. DeMaskey
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Learning Objectives
Questions to be answered:
What is a bond?
Who issues bonds?
What are the key characteristics of bonds?
How are bonds valued?
What is the rate of return on a bond?
What types of risk are bondholders exposed to?
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Types of Bonds
Treasury Bonds
Corporate Bonds
Municipal Bonds
Foreign Bonds
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Basic Terminology
Bond
Par Value
Coupon Interest Payment
Coupon Interest Rate
Maturity Date
Bond’s Market Rate of Interest, kd
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Financial Asset Valuation
0
1
2
k
...
Value
PV =
n
CF1
CF1
1+ k
1
+
CF2
CF2
1+ k
2
+ ... +
CFn
CFn
1+ k
n
.
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Required Rate of Return
The discount rate (ki) is the opportunity cost
of capital, i.e., the rate that could be earned
on alternative investments of equal risk.
ki = k* + IP + LP + MRP + DRP
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Default Risk
Risk that issuer will not make interest
or principal payments.
Increases required rate of return
Bond ratings provide one measure of
default risk
Defaulting on bonds may result in
bankruptcy and/or reorganization
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Value of Bond
0
1
2
10%
...
V=?
VB
10
100
$100
1 + k d
1
+ . . . +
= $90.91 +
= $1,000.
100 + 1,000
100
$100
1 + k d
10
+
$1,000
1+ k d
10
. . . + $38.55 + $385.54
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Annual Coupon Bonds
N
INT
M
VB
t
N
1 kd
t 1 1 kd
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Semiannual Coupon Bonds
Multiply years by 2 to get periods = 2n.
Divide nominal rate by 2 to get periodic
rate = kd/2.
Divide annual INT by 2 to get PMT = INT/2.
2N
INT / 2
M
VB
t
2N
1 kd / 2
t 1 1 k d / 2
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General Observations About
Bond Values
If coupon rate < kd, bond sells at a discount.
If coupon rate > kd, bond sells at a premium.
If coupon rate = kd, bond sells at its par
value.
If kd rises, price falls; if kd falls, price rises.
At maturity, the value of a bond equals par.
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Changes in Bond Values Over
Time
At maturity, the value of any bond must
equal its par value.
The value of a premium bond would
decrease to $1,000.
The value of a discount bond would increase
to $1,000.
A par bond stays at $1,000 if kd remains
constant.
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Time Path of Bond Value
Bond Value ($)
kd = 7%.
1,372
1,211
kd = 10%.
1,000
M
837
kd = 13%.
775
30
25
20
15
10
5
0
Years remaining to Maturity
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Bond Yields
Yield-to-Maturity (YTM)
Effective Annual Return on Bond
Yield-to-Call
Current Yield
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Yield-to-Maturity
YTM is the rate of return earned on a bond
held to maturity, also called “promised
yield.”
It is the discount rate that equates the present
value of the interest and principal payments
to the price of the bond.
Annualized YTM = 2 x six-month yield
Effective YTM = (1 + six-month yield)2 - 1
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Total Return or Yield on Bond
The effective annual return on a bond is
equal to its current yield and capital gains
yield.
Current yield
Capital gains yield
YTM = Current yield + Capital gains yield
Effective annual yield
(1 + semiannual return)2 -1
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Yield-to-Call
Call Provision
Callable bonds
Call premium
Refunding operation
YTC is the average annual return an investor
will receive if the bond is held until its
expected call date.
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Current Yield
Annual interest payment/Current value of
bond
Provides information about cash income on
bond.
Does not provide accurate measure of total
expected return on bond.
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Interest Rate Risk
Rising interest rates have an adverse effect on bond
values.
The longer the maturity of a bond, the greater the
exposure to interest rate risk.
kd
1-year
Change 10-year Change
5%
$1,048
$1,386
10%
1,000
4.8%
15%
956
4.4%
1,000
38.6%
749
25.1%
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Interest Rate Risk
Value
1,500
10-year
1-year
1,000
500
0
0%
5%
10%
kd
15%
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Reinvestment Rate Risk
The risk that CFs will have to be
reinvested in the future at lower rates,
reducing income.
The shorter the maturity of the bond,
the greater the risk of a decrease in
interest rates.
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