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Valuing bond
Fundamentals of corporate finance, BMMChapter 6 Valuing bond
Finansiell ekonomi höst 2012
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Topics Covered
• Using The Present Value Formula to Value Bonds
• How Bond Prices Vary With Interest Rates• The Term Structure of Interest Rates• Real and Nominal Rates of Interest• Corporate Bonds and the Risk of Default
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Board of DirectorsChairman of the Board andmembers are accountable
for the organization
ManagementChief Executive Officer (CEO)and his team run the company
The Corporation (internal)
The Marketplace (external)
Equity MarketsAnalysts and other market agents
evaluate the performanceof the firm on a daily basis
Debt MarketsRatings agencies and otheranalysts review the abilityof the firm to service debt
AuditorsExternal opinion as to the fairness
of presentation and conformity to stds of financial statements
RegulatorsSEC, the OMX, or other
regulatory bodies by country
Legal CounselProvides legal opinions and
recommendations on legalityof corporate activities
Entities with capital at risk in the corporation, but can also reap gains or returns from
activities with the corporation
Entities whose services arepurchased by the corporation
The Structure of Corporate Governance
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Why companies issue bonds?• To finance their investment project.• Issuing bond does not have the loss of ownership
as issuing stocks do, since bond is a debt certificate.
• Bondholders have a role in monitoring the firm´s activities due to the periodic payment feature of the bond.
• Bonds provide a fixed rate of return for investors!• The required rate of return on bond is lower than
the stocks. Since stocks are inherently riskier.
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Definitions
• A bond is a debt security. It is a formal contract promising to repay borrowed money with interest at fixed intervals. (Obligation)
• Maturity date — the date on which the issuer has to repay the nominal amount. (löptid)
• Yield to maturity is internal rate of return (IRR, overall interest rate) earned by an investor who buys the bond today at the market price.
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Zero Coupon Bond (nollkupongare)
• A zero coupon bond pay no regular interest. It is issued at a substantial discount to par value (face value). Sensitive to interest rate changes.
t.ex. SSVX Statsskuldsväxlar är nollkupongare.
• Current yield: annual coupon payments divided by bond price.
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Kopior av aktiebrev och obligation från Bofors-Gullspång Aktiebolag
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Premium bond issued by British National savings association
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Government bond issued by the State of South Carolina 2011
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(SOX) Obligationer Sverige
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Exempel: statsobligation
1/4/2
010
1/27/2
010
2/19/2
010
3/14/2
010
4/6/2
010
4/29/2
010
5/22/2
010
6/14/2
010
7/7/2
010
7/30/2
010
8/22/2
010
9/14/2
010
10/7/2
010
10/30/2
010
11/22/2
010
12/15/2
010
1/7/2
011
1/30/2
011
2/22/2
011
3/17/2
011
4/9/2
011
5/2/2
011
5/25/2
011
6/17/2
011
7/10/2
011
8/2/2
011
8/25/2
011
9/17/2
011
10/10/2
011
11/2/2
011
11/25/2
011
12/18/2
011
1/10/2
012
2/2/2
012
2/25/2
012
3/19/2
012
4/11/2
012
5/4/2
012
5/27/2
012
6/19/2
012
7/12/2
012
8/4/2
012100
105
110
115
120
125
130
Statsobligation RGKB 1041, löptid: 2014,05,05, Kupong 6,750 köpränta 109,737%
Högsta kurs Lägsta kurs Average price
Pris
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Räkna ut ränta (Yield to maturity)• RGKB 1047, säljränta 128,48%, kupong 5kr,
slutvärde 100, löptid 8 år + 96/360=8,267 år.• Yielden blir 1,338 %.
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Exempel (yield to maturity)• RGKB 1046, löptid 44 dagar/360 år.• Kupong 5,5 säljränta 100,486, slutvärde 100, • Yielden blir 1,49%.• Du märkte att yielden är lite högre än 8 års
yield.
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The pricing of bonds
• Any bond can be valued as an annuity plus a single payment.
• It is the present value of the interest payments and the principal payment (face value) discounted at the yield to maturity of the bond.
• Bond dealers earn a spread by selling higher than its bid price. Bid price –ask price= spread
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Zero coupon bond (discount bond)
• Consider a 30-year zero-coupon bond with a face value of $100. If the bond is priced at an annual YTM of 10%, what is the price of the bond today?
Price = PV (cash flow)=100/(1,1)30 = 5,73 $ the discount amount is your interest payment. 5,73 $ is the price you pay for the bond. At the maturity date, you will be paid 100 $ face value, the effective annualized return or Yield to Maturity is 10%.
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Valuing a Coupon Bond
NN
r
C
r
C
r
CPV
)1(
000,1...
)1()1( 22
11
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Valuing a BondExample If today is October 1, 2010, what is the value of the following bond? An IBM
Bond pays $115 every September 30 for 5 years. In September 2015 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)
Cash FlowsSept 1112 13 14 15115 115 115 115 1115
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Valuing a BondExample continued If today is October 1, 2010, what is the value of the following bond? An
IBM Bond pays $115 every September 30 for 5 years. In September 2015 it pays an additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA YTM is 7.5%)
84.161,1$
075.1
115,1
075.1
115
075.1
115
075.1
115
075.1
1155432
PV
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Valuing a BondExample - France In December 2008 you purchase 100 Euros of bonds in France which
pay a 8.5% coupon every year. If the bond matures in 2012 and the YTM is 3.0%, what is the value of the bond?
2 3 4
8.5 8.5 8.5 108.5
1.03 1.03 1.03 1.03
120.44 €
PV
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Kalkyler i excel Example - France In December 2008 you purchase 100 Euros of bonds in France which
pay a 8.5% coupon every year. If the bond matures in 2012 and the YTM is 3.0%, what is the value of the bond? (obs! På engelska version använder vi NPV I stäälet för Netnuvärde)
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Valuing a BondAnother Example - Japan In July 2010 you purchase 200 Yen of bonds in Japan which pay a 8%
coupon every year. If the bond matures in 2015 and the YTM is 4.5%, what is the value of the bond?
Yen 73.230
045.1
216
045.1
16
045.1
16
045.1
16
045.1
165432
PV
Note the value is 230.73. corrected!
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Valuing a BondExample - USA In February 2009 you purchase a 3 year US Government bond. The
bond has an annual coupon rate of 4.875%, paid semi-annually. If investors demand a 0.006003% semiannual return, what is the price of the bond?
95.107,1$
006003.1
375.1024
006003.1
375.24
006003.1
375.24
006003.1
375.24
006003.1
375.24
006003.1
375.24
21
21
11
1
2
CPV
65432
222
PV
orr
FV
rttr
Present value of c/2 coupon payment over 2 t period. Apply Annuity formula. Halva kupong och dubbel löptid! Samt relevant yielden!
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Valuing a BondExample continued - USA Take the same 3 year US Government bond. If investors demand a 4.0%
semiannual return, what is the new price of the bond?
09.918$
04.1
375.1024
04.1
375.24
04.1
375.24
04.1
375.24
04.1
375.24
04.1
375.2465432
PV
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Interest Rate on 10yr Treasuries19
0019
0319
0619
0919
1219
1519
1819
2119
2419
2719
3019
3319
3619
3919
4219
4519
4819
5119
5419
5719
6019
6319
6619
6919
7219
7519
7819
8119
8419
8719
9019
9319
9619
9920
0220
0520
08
0
2
4
6
8
10
12
14
16
Year
Yiel
d , %
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Bond Prices and Yields (inverse relationship)
Interest Rates, %
Bond
Pric
e
80,00
85,00
90,00
95,00
100,00
105,00
110,00
115,00
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Time to Maturity and Prices: increase interest rate, the price of longer term bonds decrease more, all else konstant!
Interest Rates, %
Bond
Pric
e, ($
)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 140
500
1,000
1,500
2,000
2,500
3,000
30 yr bond
3 yr bond
When the interest rateequals the 5% coupon,both bonds sell forface value
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Source: Bloomberg.com
Figure 1: Yield Curve January 2008: changing term structure
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The recent term structure of interest Rate: upward sloping
YieldCurve.com Yield Curve figures updated weekly since October 2003To select historical yield curve data use drop-down menu
UK GiltUS Treasury
6 Month3 Month
1 Year6 Month
2 Year2 Year
5 Year5 Year
10 Year10 Year
30 Year30 Year
August 22, 2011 0.58 0.53 0.61 1.26 2.41 3.780.01 0.02 0.20 0.93 2.12 3.42
August 15, 2011 0.62 0.57 0.65 1.30 2.53 3.950.01 0.07 0.19 0.96 2.25 3.73
August 8, 2011 0.58 0.47 0.55 1.42 2.69 3.870.01 0.04 0.29 1.25 2.56 3.85
August 1, 2011 0.60 0.49 0.63 1.58 2.86 4.020.09 0.15 0.36 1.36 2.80
4.12
2011 ratesaugustshow rates
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UK gilt and US treasury yield vs. Time to maturity (2011 aug 22.)
0 2 4 6 8 10 12 14 16 18 200
0.5
1
1.5
2
2.5
3
3.5
4
UK giltUS Treasury
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Interest Rates• Short- and long-term interest rates do not always move in parallel.
Between September 1992 and April 2000 U.S. short-term rates rose sharply while long term rates declined. A indication of recession in 2000.
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Term Structure of Interest Rates
The relationship between short term and long term interest rate is called the term structure of interest rate.
Spot Rate - The actual interest rate today (t=0)Forward Rate - The interest rate, fixed today, on a loan made in
the future at a fixed time.Future Rate - The spot rate that is expected in the future
YTM (r)
Year
19811987 & Normal
1976
1 5 10 20 30
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Maturity
U.S. Treasury Strip Spot Rates as of February 2009: the yield curve20
09 A
ug 1
5
2010
Aug
15
2011
Aug
15
2012
Aug
15
2013
Aug
15
2014
Aug
15
2015
Aug
15
2016
Aug
15
2017
Aug
15
2018
Aug
15
2019
Aug
15
2020
Aug
15
2021
Aug
15
2022
Aug
15
2023
Aug
15
2024
Aug
15
2025
Aug
15
2026
Aug
15
2027
Aug
15
2028
Aug
15
2029
Aug
15
2030
Aug
15
2031
Aug
15
2032
Aug
15
2033
Aug
15
2034
Aug
15
2035
Aug
15
2036
Aug
15
2037
Aug
15
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Spot
rate
s (%
)
The yield curve depicts the term structure of interest rate.
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Yield to Maturity
Example• A $1000 treasury bond expires in 5 years. It pays a
coupon rate of 10.5%. If the market price of this bond is 1078.8, what is the YTM?
C0 C1 C2 C3 C4 C5
-1078.80 105 105 105 105 1105
Calculate IRR = 8.5%
Obs: använd Ränta= som argument I excel program svenska version.
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Inflation Rates
1900
.00
1903
.00
1906
.00
1909
.00
1912
.00
1915
.00
1918
.00
1921
.00
1924
.00
1927
.00
1930
.00
1933
.00
1936
.00
1939
.00
1942
.00
1945
.00
1948
.00
1951
.00
1954
.00
1957
.00
1960
.00
1963
.00
1966
.00
1969
.00
1972
.00
1975
.00
1978
.00
1981
.00
1984
.00
1987
.00
1990
.00
1993
.00
1996
.00
1999
.00
2002
.00
2005
.00
2008
.00
-15
-10
-5
0
5
10
15
20
25
Annual rates of inflation in the United States from 1900–2008.An
nual
Infla
tion
(%)
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Global Inflation Rates
0,00
2,00
4,00
6,00
8,00
10,00
12,00
Ave
rag
e In
flat
ion
, %
Averages from 1900-2006
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Debt & Interest Rates
Nominal r = Real r + expected inflation (approximation)
Actual formula
)1()1(1 realnominal irr
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38
02468
101214161820
1-Ja
n-84
1-A
pr-8
5
1-Ju
l-86
1-O
ct-8
7
1-Ja
n-89
1-A
pr-9
0
1-Ju
l-91
1-O
ct-9
2
1-Ja
n-94
1-A
pr-9
5
1-Ju
l-96
1-O
ct-9
7
1-Ja
n-99
1-A
pr-0
0
1-Ju
l-01
1-O
ct-0
2
1-Ja
n-04
1-A
pr-0
5
1-Ju
l-06
1-O
ct-0
7
1-Ja
n-09
UK Bond Yields
10 year nominal interest rate
10 year real interest rate
Inte
rest
rate
(%)
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Govt. Bills vs. Inflation (’53-’08)%
United Kingdom
1953
.00
1956
.00
1959
.00
1962
.00
1965
.00
1968
.00
1971
.00
1974
.00
1977
.00
1980
.00
1983
.00
1986
.00
1989
.00
1992
.00
1995
.00
1998
.00
2001
.00
2004
.00
2007
.00
0.00
5.00
10.00
15.00
20.00
25.00
30.00
Inflation
T-Bill Returns
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1953
.00
1956
.00
1959
.00
1962
.00
1965
.00
1968
.00
1971
.00
1974
.00
1977
.00
1980
.00
1983
.00
1986
.00
1989
.00
1992
.00
1995
.00
1998
.00
2001
.00
2004
.00
2007
.00
-2.00
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
Govt. Bills vs. Inflation (’53-’08)%
United States
Inflation
T-Bill Returns
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1953
.00
1956
.00
1959
.00
1962
.00
1965
.00
1968
.00
1971
.00
1974
.00
1977
.00
1980
.00
1983
.00
1986
.00
1989
.00
1992
.00
1995
.00
1998
.00
2001
.00
2004
.00
2007
.00
-4.00
-2.00
0.00
2.00
4.00
6.00
8.00
10.00
12.00
Govt. Bills vs. Inflation (’53-’08)%
Germany
Inflation
T-Bill Returns
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Bond Ratings• Key to bond ratings. The highest-quality bonds are rated triple A. Bonds
rated triple B or above are investment grade. Lower-rated bonds are called high-yield, or junk, bonds.
Check the course book BMM for more details.
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Yield Spread: credit riskYi
eld
spre
ad b
etw
een
corp
orat
e an
d go
vern
men
t bon
ds, %
Yield spreads between corporate and 10-year Treasury bonds. Obs: the spread indicates the credit risk of Baa related corporate bond over riskfree
treasury bond!
0.4
0.26
0.19
0.11
0.47
0.24
0.23
0.52
0...
0.72
1.42
0.59
0.72
0.67
0.20
0...
0.20
0...
1.11
0.80
0...
0.83
0...
0.61
0.82
0...
1.49
0.97
0.84
0...
1.46
2.06
1.78
0.99
0.78
2.46
-1
0
1
2
3
4
5
6
7
Spread on Baa bonds bonds
Spread on Aaa bonds
Years
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Prices and Yields
• Prices and yields of a sample of corporate bonds, December 2008. (jämför yield to maturity! Kapitalkostnad för företag!)
Source: Bond transactions reported on FINRA’s TRACE service: http://cxa.marketwatch.com/finra/BondCenter