Valuing bond

Fundamentals of corporate finance, BMMChapter 6 Valuing bond

Finansiell ekonomi höst 2012

2

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

3

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

4

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.

5

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.

6

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.

7

Kopior av aktiebrev och obligation från Bofors-Gullspång Aktiebolag

8

Premium bond issued by British National savings association

9

Government bond issued by the State of South Carolina 2011

10

(SOX) Obligationer Sverige

11

Exempel: statsobligation

1/4/2010

1/27/2

010

2/19/2

010

3/14/2

010

4/6/2010

4/29/2

010

5/22/2010

6/14/2

010

7/7/2010

7/30/2

010

8/22/2

010

9/14/2

010

10/7/2010

10/30/2010

11/22/2010

12/15/2010

1/7/2011

1/30/2

011

2/22/2011

3/17/2

011

4/9/2011

5/2/2011

5/25/2

011

6/17/2

011

7/10/2011

8/2/2011

8/25/2011

9/17/2

011

10/10/2011

11/2/2011

11/25/2011

12/18/2011

1/10/2

012

2/2/2012

2/25/2

012

3/19/2

012

4/11/2

012

5/4/2012

5/27/2

012

6/19/2

012

7/12/2

012

8/4/2012

100

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

12

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 %.

13

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.

14

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

15

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

rC

rC

rC

PV)1(

000,1...

)1()1( 22

11

17

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

18

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$

075.1115,1

075.1115

075.1115

075.1115

075.1115

5432

PV

19

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 8.5 108.51.03 1.03 1.03 1.03

120.44 €

PV

20

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)

21

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

045.1216

045.116

045.116

045.116

045.116

5432

PV

Note the value is 230.73. corrected!

22

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$

006003.1375.1024

006003.1375.24

006003.1375.24

006003.1375.24

006003.1375.24

006003.1375.24

21

21

1112CPV

65432

222

PV

orrFV

r ttr

Present value of c/2 coupon payment over 2 t period. Apply Annuity formula. Halva kupong och dubbel löptid! Samt relevant yielden!

23

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$

04.1375.1024

04.1375.24

04.1375.24

04.1375.24

04.1375.24

04.1375.24

65432

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 , %

25

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

26

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

27

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

29

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

30

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.

31

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

520

10 A

ug 1

520

11 A

ug 1

520

12 A

ug 1

520

13 A

ug 1

520

14 A

ug 1

520

15 A

ug 1

520

16 A

ug 1

520

17 A

ug 1

520

18 A

ug 1

520

19 A

ug 1

520

20 A

ug 1

520

21 A

ug 1

520

22 A

ug 1

520

23 A

ug 1

520

24 A

ug 1

520

25 A

ug 1

520

26 A

ug 1

520

27 A

ug 1

520

28 A

ug 1

520

29 A

ug 1

520

30 A

ug 1

520

31 A

ug 1

520

32 A

ug 1

520

33 A

ug 1

520

34 A

ug 1

520

35 A

ug 1

520

36 A

ug 1

520

37 A

ug 1

5

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.

33

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.

34

35

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

(%)

36

Global Inflation Rates

0,00

2,00

4,00

6,00

8,00

10,00

12,00

Aver

age

Infla

tion,

%

Averages from 1900-2006

Debt & Interest Rates

Nominal r = Real r + expected inflation (approximation)

Actual formula

)1()1(1 realnominal irr

38

02468

101214161820

1-Ja

n-84

1-Ap

r-85

1-Ju

l-86

1-O

ct-8

7

1-Ja

n-89

1-Ap

r-90

1-Ju

l-91

1-O

ct-9

2

1-Ja

n-94

1-Ap

r-95

1-Ju

l-96

1-O

ct-9

7

1-Ja

n-99

1-Ap

r-00

1-Ju

l-01

1-O

ct-0

2

1-Ja

n-04

1-Ap

r-05

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

(%)

39

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

.000.00

5.00

10.00

15.00

20.00

25.00

30.00

Inflation

T-Bill Returns

40

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

41

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

42

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.

43

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

44

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