Description
This is a presentation explaining about the bond valuation.
Bond Valuation
Corporate Finance
1
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?
2
Types of Bonds
? Treasury Bonds ? Corporate Bonds ? Municipal Bonds ? Foreign Bonds
3
Basic Terminology
? Bond ? Par Value ? Coupon Interest Payment ? Coupon Interest Rate ? Maturity Date ? Bond’s Market Rate of Interest, kd
4
Financial Asset Valuation
0
k Value CF1 CF2
1
2
n
...
CFn
PV =
?1 + k?
CF1
1
+
?1+ k?
CF2
2
+ ... +
?1 + k?
CFn
n
.
5
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
6
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
7
Value of Bond
0 10% V=? 100 100 1 2 10
...
100 + 1,000
VB ?
$100
?1 + k d ?
1
+ . . . +
$100
?1 + k d ?
10
+
$1,000
?1+ k d ?
10
= $90.91 + = $1,000.
. . . + $38.55 + $385.54
8
Annual Coupon Bonds
INT M VB ? ? ? t N ?1 ? kd ? 1 t ?1 ? ? k d ?
N
9
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.
INT / 2 M VB ? ? ? t 2N ?1 ? kd / 2? 1 t ?1 ? ? k d / 2?
10
2N
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.
11
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 $1,000 if kd remains constant.
12
Time Path of Bond Value
Bond Value ($)
1,372 1,211
kd = 7%.
1,000
kd = 10%.
M
837
775
30 25 20 15 10
kd = 13%.
5
0
Years remaining to Maturity
13
Bond Yields
? Yield-to-Maturity (YTM) ? Effective Annual Return on Bond ? Yield-to-Call ? Current Yield
14
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
15
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
16
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.
17
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.
18
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% 10% 15%
$1,048 1,000 956 4.8%
4.4%
$1,386 1,000 749 38.6%
25.1%
19
Interest Rate Risk
Value
1,500 1,000 500
10-year 1-year
0 0%
5%
10%
15%
kd
20
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.
21
doc_347605490.ppt
This is a presentation explaining about the bond valuation.
Bond Valuation
Corporate Finance
1
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?
2
Types of Bonds
? Treasury Bonds ? Corporate Bonds ? Municipal Bonds ? Foreign Bonds
3
Basic Terminology
? Bond ? Par Value ? Coupon Interest Payment ? Coupon Interest Rate ? Maturity Date ? Bond’s Market Rate of Interest, kd
4
Financial Asset Valuation
0
k Value CF1 CF2
1
2
n
...
CFn
PV =
?1 + k?
CF1
1
+
?1+ k?
CF2
2
+ ... +
?1 + k?
CFn
n
.
5
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
6
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
7
Value of Bond
0 10% V=? 100 100 1 2 10
...
100 + 1,000
VB ?
$100
?1 + k d ?
1
+ . . . +
$100
?1 + k d ?
10
+
$1,000
?1+ k d ?
10
= $90.91 + = $1,000.
. . . + $38.55 + $385.54
8
Annual Coupon Bonds
INT M VB ? ? ? t N ?1 ? kd ? 1 t ?1 ? ? k d ?
N
9
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.
INT / 2 M VB ? ? ? t 2N ?1 ? kd / 2? 1 t ?1 ? ? k d / 2?
10
2N
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.
11
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 $1,000 if kd remains constant.
12
Time Path of Bond Value
Bond Value ($)
1,372 1,211
kd = 7%.
1,000
kd = 10%.
M
837
775
30 25 20 15 10
kd = 13%.
5
0
Years remaining to Maturity
13
Bond Yields
? Yield-to-Maturity (YTM) ? Effective Annual Return on Bond ? Yield-to-Call ? Current Yield
14
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
15
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
16
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.
17
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.
18
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% 10% 15%
$1,048 1,000 956 4.8%
4.4%
$1,386 1,000 749 38.6%
25.1%
19
Interest Rate Risk
Value
1,500 1,000 500
10-year 1-year
0 0%
5%
10%
15%
kd
20
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.
21
doc_347605490.ppt