Chapter 7 Bond Valuation
May 06
1
2
Bonds
™Debt Instrument
™Bondholders are lending the corporation money for
some stated period of time.
™Liquid Asset
™Corporate Bonds can be traded in the secondary
market.
™Price at which a given bond trades is determined by
market conditions and terms of the bond.
Interest Rates
and
Bond Valuation
Bond Terminology
™Par Value
™Usually $1,000 also called Face Value
™Coupon Interest Rate
™Borrowers (firms) typically make periodic interest
payments to the bondholders.
™Maturity
™Time at which the original principal (Par Value) is
repaid to the bondholder.
3
™Moody’s and Standard & Poors regularly monitor
corporate financial statements and assign a rating to
the corporation’s debt
™similar to a personal credit report
Investment
Grade
™Indenture
™Document which details the legal obligation of the
corporation to the bondholders.
4
Bond Ratings
Speculative
AAA
Top Quality
AA+/- system
Lower Ratings are somewhat more
A
susceptible to adverse effects of
BBB changes in circumstances and
conditions than debt in
BB economic
higher rated categories.
B
CCC
CC
Low Quality
C
No interest being paid
D
Currently in Default
Chapter 7 Bond Valuation
May 06
5
Bond Ratings
6
Bond Quotes
™Bond Ratings can change due to many factors.
Cur
Yld
Bonds
AMR6¼27
ATT 8.35s28
IBM 63/8 11
Kroger 9s10
Corporate Bond Ratings
McDonalds
AA
ATT
AACaterpillar Corp
A+
3 Com
BBB
Delta Air Lines
BBBAOL
BBPlanet Hollywood
CCC+
TWA
CCC
Golden Books Family Entmt D
Vol
6.8
6
8.1 110
6.6 228
8.8
74
Close
Net
Chg
91¼
102¾
965/8
1017/8
-1½
+¼
-1/8
-¼
Source: Wall Street Journal
Company Issuing the Bond
S&P Research Insight
7
Bond Quotes
Bonds
AMR6¼27
ATT 8.35s28
IBM 63/8 11
Kroger 9s10
Cur
Yld
Vol
6.8
6
8.1 110
6.6 228
8.8
74
Close
Net
Chg
91¼
102¾
965/8
1017/8
-1½
+¼
-1/8
-¼
Source: Wall Street Journal
Coupon Interest Rate
Determines the Investor’s Periodic Cash Flow
Cash Flow = Interest Payment = Coupon Rate x Par
For IBM:
.06375 x 1000 = $63.75/Year
8
Bond Quotes
Cur
Yld
Bonds
AMR6¼27
ATT 8.35s28
IBM 63/8 11
Kroger 9s10
Vol
6.8
6
8.1 110
6.6 228
8.8
74
Close
Net
Chg
91¼
102¾
965/8
1017/8
-1½
+¼
-1/8
-¼
Source: Wall Street Journal
Year of Maturity
Determines the Time frame for the Investment
IBM Bond:
11 = year 2011, therefore in 2006 this is a 5 year investment
Chapter 7 Bond Valuation
May 06
9
Bond Quotes
Bonds
AMR6¼27
ATT 8.35s28
IBM 63/8 11
Kroger 9s10
Cur
Yld
Vol
6.8
6
8.1 110
6.6 228
8.8
74
Close
Net
Chg
91¼
102¾
965/8
1017/8
-1½
+¼
-1/8
-¼
10
Bond Quotes
Bonds
AMR6¼27
ATT 8.35s28
IBM 63/8 11
Kroger 9s10
Cur
Yld
Source: Wall Street Journal
-1½
+¼
-1/8
-¼
Coupon Rate = 6.375
= .066 = 6.6%
Market Price
96.625
11
AMR6¼27
ATT 8.35s28
IBM 63/8 11
Kroger 9s10
Net
Chg
91¼
102¾
965/8
1017/8
Daily Trading Volume (,000)
Bond Quotes
Bonds
Close
Source: Wall Street Journal
Current Yield (%)
Current Yield =
Vol
6.8
6
8.1 110
6.6 228
8.8
74
Cur
Yld
Vol
6.8
6
8.1 110
6.6 228
8.8
74
Close
Net
Chg
91¼
102¾
965/8
1017/8
-1½
+¼
-1/8
-¼
Source: Wall Street Journal
Daily Closing Market Price as a % of Par
IBM Bond
$Price = 965/8 % x 1000 = $966.25
= $966.25
= 965/8 x 10
12
Bond Quotes
Bonds
AMR6¼27
ATT 8.35s28
IBM 63/8 11
Kroger 9s10
Cur
Yld
Vol
6.8
6
8.1 110
6.6 228
8.8
74
Close
Net
Chg
91¼
102¾
965/8
1017/8
-1½
+¼
-1/8
-¼
Source: Wall Street Journal
Change in from Previous Day’s Close
Chapter 7 Bond Valuation
Valuation: An Overview
May 06
13
14
Basic Factors Determining Value
Investor Attributes
Asset Characteristics
Investor’s assessment of
the riskiness of the asset’s
cash flows
Expected level of cash flow
The value of an asset is its intrinsic value or the
present value of its expected future cash flows,
where these cash flows are discounted back to the
present using the investor’s required rate of return.
Value is impacted by
Timing of cash flow
Investor’s willingness to
bear risk
Riskiness of cash flow
™Asset characteristics
™Investor attributes
™These two areas determine the investor’s required
rate of return
Investor’s required rate of return
Asset value = Present value of
expected cash flows discounted
using investor’s required rate
Bond Valuation Model
15
™3 Cash Flows
IBM Bond Timeline:
™Amount that is paid to purchase the bond (PV)
™Periodic Interest Payments made to the bondholders
(PMT)
™Repayment of Par value at end of Bond’s life (FV)
Cur
Yld
Bonds
AMR6¼27
ATT 8.35s28
IBM 63/8 11
Kroger 9s10
™Other Terminology
™Time frame for cash flows (N) = Bond’s Maturity
™ Interest Rate for Time Value is the rate at which
future cash flows are being discounted to present.
(I/YR)
16
Bond Valuation Model
Vol
6.8
6
8.1 110
6.6 228
8.8
74
Close
Net
Chg
91¼
102¾
965/8
1017/8
-1½
+¼
-1/8
-¼
Source: Wall Street Journal
Investor that purchases bond today for $966.25 will receive 5 annual
interest payments of $63.75 and a $1,000 payment in 5 years.
2006
0
2007
1
63.75
2008
2
63.75
2009
3
63.75
2010
2011
4
5
63.75
63.75
1000.00
Chapter 7 Bond Valuation
May 06
17
Bond Valuation Model
Compute Bond’s Intrinsic Value
18
Bond Valuation Model
Compute Bond’s Intrinsic Value
2006
2007
2008
2009
2010
2011
2006
2007
2008
2009
2010
2011
0
1
2
3
4
5
0
1
2
3
4
5
63.75
63.75
63.75
63.75
$59.03
$54.66
$50.61
$46.86
$43.39
63.75
1000.00
63.75
63.75
63.75
$63.75 Annuity for 5 years
-254.54
$1000
(1.08) 5
$680.58
$935.12
N
I/YR
5
8
xP/YR
Compute the Intrinsic Value for the IBM Bond given that
you require a 8% return on your investment.
19
Bond Valuation Model
Compute Bond’s Intrinsic Value
2006
2007
2008
2009
0
1
2
3
63.75
63.75
$63.75 Annuity for 5 years
4
63.75
?
P/YR
FV
254.54
+680.58
935.12
63.75
2011
Cur
Yld
Bonds
5
AMR6¼27
ATT 8.35s28
IBM 63/8 11
Kroger 9s10
63.75
1000.00
N
I/YR
5
8
NOM
%
PV
EFF%
?
1
45
P/YR
N
I/YR
5
8
xP/YR
NOM
%
PV
EFF%
PMT
FV
P/YR
?
1000
FV
63.75 1000
Vol
Close
Net
Chg
91¼
102¾
965/8
1017/8
-1½
+¼
-1/8
-¼
Source: Wall Street Journal
2007
0
PMT
-680.58
20
6.8
6
8.1 110
6.6 228
8.8
74
$1000 Lump Sum in 5 years
-935.12
xP/YR
PMT
$1000 Lump Sum in 5 years
Bond Valuation Model
2006
Compute PV
of annuity and
PV of Lump
Sum in ONE
Step
PV
EFF%
63.75
1000.00
Bonds that Pay Interest Semi-Annually:
2010
63.75
NOM
%
63.75
45
45
2008
2009
20010
2
3
4
45
45
45
45
2011
5
45.00
1000.00
Rather than receiving 4 annual payments of $90, the
bondholder will receive 4x2 = 8 semiannual payments
of 90÷2=$45.
Chapter 7 Bond Valuation
May 06
21
Bond Valuation Model
Bonds that Pay Interest Semi-Annually:
2006
2007
0
45
45
Bonds that Pay Interest Semi-Annually:
2008
2009
2010
2011
2006
2
3
4
5
0
1
45
45
45
45
45
45.00
1000.00
2007
45
2010
2011
3
4
5
45
45
45
45
45
45.00
1000.00
-967.68
# of Semi-Annual
Periods 4 years x 2
™Bondholder’s Expected Rate of Return.
2009
2
Compute the Intrinsic Value for the Kroger Bond given
that you require a 10% return on your investment.
Since interest is received every 6 months, need to use
semi-annual compounding
Yield to Maturity
2008
1
45
Compute the Intrinsic Value for the Kroger Bond given
that you require a 10% return on your investment.
Semi-Annual
10%
Compounded Rate 2
22
Bond Valuation Model
N
I/YR
8
5
xP/YR
23
NOM
%
PV
EFF%
?
PMT
FV
45
1000
P/YR
24
Yield to Maturity
™Relationship between YTM and Intrinsic Value
™If an investor purchases bond at today’s price and
hold it until maturity, what is the annual rate of return
that is earned?
Given
Required Rate of
Return
Market Price
Compute
Intrinsic Value
YTM
Compare
Intrinsic Value to
Market Price
YTM to Required
Rate
Chapter 7 Bond Valuation
May 06
29
Yield to Maturity
™Bond Prices fluctuate over Time
IBM Corporate Bond:
2006
2007
0
2008
2009
2010
2011
2
3
4
5
63.75
63.75
63.75
1
-966.25
63.75
966.25 < 1000
7.2% > 6.375%
7.203%
N
xP/YR
5
I/YR
NOM
%
PV
EFF%
PMT
P/YR
FV
? -966.25 63.75 1000
™As interest rates in the economy change, required
rates on bonds will also change resulting in investor’s
intrinsic values changing and market prices changing.
63.75
1000.00
Interest
Rates
• If Price < 1000 bond sells at a
Discount (YTM > Coupon Rate)
• If Price > 1000 bond sells at a
Premium (YTM < Coupon Rate)
Vb
Vb
Interest
Rates
• If Price = 1000 bond sells at Par
(YTM = Coupon Rate)
32
Interest Rate Risk
™When bonds are originally issued, the coupon rate is
set to match current prevailing rates.
™Over time, the prevailing rates may change, but the
coupon rate is fixed.
™Results in the market price of the bond changing.
33
Interest Rate Risk
2006
™Bond Prices fluctuate over Time
2006
31
Interest Rate Risk
AAA Bonds are currently yielding 6%
Purchase ATT 6s26 Bond for $1000.00
2009
AAA Bonds are currently yielding 9%
If you want to sell the the ATT 6s26 Bond, it must be priced to
earn the purchaser a competitive rate (required rate = 9%)
AAA Bonds are currently yielding 6%
Purchase ATT 6s23 Bond for $1000.00
-743.69
-1000
N
I/YR
17
6
xP/YR
NOM
%
N
I/YR
17
9
xP/YR
PV
PMT
FV
?
60
1000
EFF%
P/YR
NOM
%
PV
PMT
FV
?
60
1000
EFF%
P/YR
Chapter 7 Bond Valuation
May 06
34
Interest Rate Risk
2006
2006
AAA Bonds are currently yielding 6%
Purchase ATT 6s26 Bond for $1000.00
2009
2009
AAA Bonds are currently yielding 9%
Market Price for ATT6s26 is now $743.69
2008
2012
AAA Bonds are currently yielding 5%
-1,098.99
N
I/YR
14
5
xP/YR
NOM
%
PV
PMT
FV
?
60
1000
EFF%
P/YR
AAA Bonds are currently yielding 5%
If you want to sell the the ATT 6s26
6s22
Bond, it must be priced to earn the
purchaser a competitive rate (required
rate = 5%)
36
Interest Rates
AAA Bonds are currently yielding 9%
If you want to sell the the ATT 6s26 Bond, it must be priced to
earn the purchaser a competitive rate (required rate = 9%)
Market Price for ATT6s26 is now $743.69
If you want to sell the the ATT 6s26
Bond, it must be priced to earn the
purchaser a competitive rate (required
rate = 5%)
AAA Bonds are currently yielding 6%
Purchase ATT 6s26 Bond for $1000.00
If you want to sell the the ATT 6s26 Bond, it must be priced to
earn the purchaser a competitive rate (required rate = 9%)
2012
35
Interest Rate Risk
Market Price for ATT6s26 is now
$1,098.99
Bond Prices fall during
periods of rising interest
rates and rise during
periods of falling interest
rates.
Interest Rates
Interest Rates Determined by
™Real Rate of Interest
™Expected Inflation
™Default Risk
™Interest Rate Risk Interest
™Liquidity Risk
Rates
Real Rate of Interest
™Compensates for the lender’s lost opportunity to
consume.
37
Chapter 7 Bond Valuation
May 06
39
Interest Rates
Default Risk
42
Interest Rates
Expected Inflation
™For most securities, there is some risk that the
borrower will not repay the interest and/or principal on
time, or at all.
™The greater the chance of default, the greater the
interest rate the investor demands and the issuer
must pay.
™Savers are hurt by inflation since the money that is
saved will purchase fewer good and services
™Example: Joe saves $100 for one year in an account
earning 7% interest. During the year prices go up by
10%.
$100
$107
™In REAL TERMS, the $107 at the end of the year
will only purchase $97.27 worth of constant goods
and services.
107
= 97.27
1.10
1+ Inflation Rate
43
Interest Rates
Interest Rates
44
Interest Rate Risk
Expected Inflation
™Savers are hurt by inflation since the money that is
saved will purchase fewer good and services
™Example: Joe saves $100 for one year in an account
earning 7% interest. During the year prices go up by
10%.
$100
$107
™In REAL TERMS, the $107 at the end of the year
will only purchase $97.27 worth of constant goods
and services.
™Conclusion: Savers will demand to be compensated
for expected inflation so as not to be hurt by the
effects of inflation.
™If interest rates rise, lenders may find that their loans
are earning rates that are lower than what they could
get on new loans.
™The risk of this occurring is higher for longer maturity
loans.
™Lenders will adjust the premium they charge for this
risk depending on whether they believe rates will go up
or down.
Chapter 7 Bond Valuation
Interest Rates
May 06
45
46
Interest Rates
Determination of Rates
Liquidity
k = k* + IP + DRP + IRP + LP
™Investments that are easy to sell without losing value
are more liquid.
™Illiquid securities have a higher interest rate to
compensate the lender for the inconvenience of being
“stuck.”
k
=
k* =
IP =
DRP =
LP =
the nominal, or observed rate on security
real, risk free rate of interest
Inflation Premium
Default Risk Premium
Liquidity Premium - Reflects the ability to sell security
easily.
IRP = Interest Rate Risk Premium - Reflects interest rate risk
long term securities are more sensitive to changes in interest
rates
Interest Rates
Determination of Rates EXAMPLE
Find the Nominal Interest Rates for 1 year and 4 year
Government Bonds and 1 and 4 year BBB Corporate
Bonds using the following information:
• The Real risk-free is currently 2.5%;
• Inflation is expected to be 3% in the next year, 4% in
the year after that, and 5% for each year thereafter
• All bonds currently include a 0.1% Interest Rate Risk
Premium for each year remaining to maturity
• The Default Risk Premium for BBB rated bonds is
currently 1.0%.
• The Liquidity Premium is 0% for these bonds
47
50
Interest Rates
Determination of Rates EXAMPLE
0%
k = k* + IP + DRP + IRP + LP
Real Risk Free Rate = 2.5%
Expected Inflation Rates
1
2
3
3%
Purchase
Date
Maturity
Date
Holding Period
1 yr Gov’t
2.5%
4
∞
Chapter 7 Bond Valuation
May 06
53
Interest Rates
Determination of Rates EXAMPLE
Determination of Rates EXAMPLE
0%
k = k* + IP + DRP + IRP + LP
4
∞
3.0%
3%
Interest Rate Risk Prem.= 0.10% for each year of maturity 0.1%
0.0%
5.6%
Default Risk Premium = 0% for Gov’t Bonds
57
Interest Rates
Determination of Rates EXAMPLE
0%
3%
4%
5%
Purchase
Date
5%
Maturity
Date
∞
∞
3.0%
3%
Interest Rate Risk Prem.= 0.10% for each year of maturity 0.1%
1.0%
6.6%
Default Risk Premium = 1.0% for BBB Rated Bonds
58
Interest Rates
Determination of Rates EXAMPLE
0%
4 yr Gov’t
2.5%
Real Risk Free Rate = 2.5%
Expected Inflation Rates
1
2
3
3%
4%
5%
4
5%
IP = Average Inflation Rate over Term
=
Holding Period
4
k = k* + IP + DRP + IRP + LP
4 yr Gov’t
2.5%
4
1 yr BBB
2.5%
Real Risk Free Rate = 2.5%
Expected Inflation Rates
1
2
3
k = k* + IP + DRP + IRP + LP
Real Risk Free Rate = 2.5%
Expected Inflation Rates
1
2
3
0%
k = k* + IP + DRP + IRP + LP
1 yr Gov’t
2.5%
Real Risk Free Rate = 2.5%
Expected Inflation Rates
1
2
3
55
Interest Rates
3%+ 4%+ 5%+ 5%
4 years
∞
4.25%
Chapter 7 Bond Valuation
May 06
60
Interest Rates
Determination of Rates EXAMPLE
Determination of Rates EXAMPLE
0%
k = k* + IP + DRP + IRP + LP
3%
4%
5%
∞
4
4.25%
5%
0%
k = k* + IP + DRP + IRP + LP
4 yr Gov’t
2.5%
Real Risk Free Rate = 2.5%
Expected Inflation Rates
1
2
3
62
Interest Rates
Interest Rate Risk Prem.= 0.10% for each year of maturity 0.4%
0.0%
7.15%
Default Risk Premium = 0% for Gov’t Bonds
63
Term Structure of Interest Rates
Relationship between short term rates on a particular
security (Typically Treasury Securities) and long term
rates
4 yr BBB
2.5%
Real Risk Free Rate = 2.5%
Expected Inflation Rates
1
2
3
3%
4%
5%
4
∞
5%
Interest Rate Risk Prem.= 0.10% for each year of maturity 0.4%
1.0%
8.15%
Default Risk Premium = 1.0% for BBB Rated Bonds
Interest Rates
Yield Curve on the Web
Rate (%)
Possible
YIELD CURVES
7.15
http://stockcharts.com/charts/YieldCurve.html
5.6
1
4
Maturity
4.25%
http://www.smartmoney.com/onebond/index.cfm?story=yieldcurve
64
Chapter 7 Bond Valuation
May 06
65
Comprehensive Interest Rate Problem
Interest Rate Data:
Corporate
DRP
Bond Rating
A
1.2%
IRP
LP
0.2% per year of maturity
0%
B
1.8%
0.2% per year of maturity
0%
C
2.9%
0.2% per year of maturity
0%
Expected Annual Inflation Rates for the next 6 years:
0
1
6%
2
5%
3
4%
4
2%
5
3%
6
4%
3 year C rated corporate bonds currently pay 10.25%
interest annually. What is the real rate of interest for
this economy?