Transcript Document

Bond Valuation
Corporate Finance
Dr. A. DeMaskey
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Learning Objectives
 Questions to be answered:
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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.
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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.
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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.
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Current yield
Capital gains yield
YTM = Current yield + Capital gains yield
 Effective annual yield
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(1 + semiannual return)2 -1
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Yield-to-Call
 Call Provision
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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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