Fundamentals of corporate finance,
BMM
Chapter 6 Valuing bond
Finansiell ekonomi höst 2012

• 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
2

The Structure of Corporate Governance
Equity Markets
Analysts and other market agents evaluate the performance of the firm on a daily basis
Entities with capital at risk in the corporation, but can also reap gains or returns from activities with the corporation
Debt Markets
Ratings agencies and other analysts review the ability of the firm to service debt
The Marketplace
(external)
The Corporation (internal)
Board of Directors
Chairman of the Board and members are accountable for the organization
Management
Chief Executive Officer (CEO) and his team run the company
Regulators
SEC, the OMX, or other regulatory bodies by country
Auditors
External opinion as to the fairness of presentation and conformity to stds of financial statements
Entities whose services are purchased by the corporation
Legal Counsel
Provides legal opinions and recommendations on legality of corporate activities 3

• 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.
4

• 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.
5

• 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.
6

Kopior av aktiebrev och obligation från Bofors-
Gullspång Aktiebolag
7

Premium bond issued by British
National savings association
8

Government bond issued by the State of South Carolina 2011
9

10

Pris
130
125
120
115
110
105
100
Statsobligation RGKB 1041, löptid: 2014,05,05, Kupong 6,750 köpränta 109,737%
Högsta kurs Lägsta kurs Average price
11

• RGKB 1047, säljränta 128,48%, kupong 5kr, slutvärde 100, löptid 8 år + 96/360=8,267 år.
• Yielden blir 1,338 %.
12

• 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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• 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
14

• 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%.
15

PV

( 1
C
1
 r )
1

( 1
C
2
 r )
2

...

1 , 000
( 1


C r )
N
N
16

Example
 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 Flows
Sept 11 12 13 14 15
115 115 115 115 1115
17

Example 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%)
PV

115
1 .
075


115
1 .
075
 
115
1 .
075
 
115
1 .
075
 
1 , 115
1 .
075

5

$ 1 , 161 .
84
18

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?
PV

8.5
1.03


8.5
1.03
 
8.5
1.03
 
108.5
1.03

4
 120.44 €
19

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)
20

Another 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?
PV

16
1 .
045


16
1 .
045
 
1
16
.
045
 
1
16
.
045
 
216
1 .
045

5

230 .
73 Yen
Note the value is
230.73. corrected!
21

Example - 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?
Present value of c/2 coupon payment over 2 t period. Apply Annuity formula. Halva kupong och dubbel löptid! Samt relevant yielden!
PV

C
2
1 r
2





1



1
1 r
2
2 t








1
FV r
2
2 t or
PV

24 .
375
1 .
006003

24 .
375

1 .
006003
24 .
375
1 .
006003
24 .
375
1 .
006003
24 .
375 1024 .
375
1 .
006003
 
1 .
006003

6

$ 1 , 107 .
95
22

Example 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?
PV

24 .
375

1 .
04

24 .
375
1 .
04
 
24 .
375
1 .
04
 
24 .
375
1 .
04
 
24 .
375
1 .
04

5

1024 .
375

1 .
04

6

$ 918 .
09
23

16
10
8
6
4
14
12
2
0
Year
24

110,00
105,00
100,00
95,00
90,00
85,00
80,00
Bond Prices and Yields (inverse relationship)
115,00
Interest Rates, %
25

Time to Maturity and Prices: increase interest rate, the price of longer term bonds decrease more, all else konstant!
3 000
2 500
30 yr bond
2 000
1 500
1 000
When the interest rate equals the 5% coupon, both bonds sell for face value
3 yr bond
500
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Interest Rates, %
26

Figure 1: Yield Curve January 2008: changing term structure
Source: Bloomberg.com
27

The recent term structure of interest
Rate: upward sloping
YieldCurve.com
UK Gilt
US Treasury
August 22, 2011
August 15, 2011
August 8, 2011
August 1, 2011
Yield Curve figures updated weekly since October 2003
To select historical yield curve data use drop-down menu
6 Month
3 Month
1 Year
6 Month
2 Year
2 Year
5 Year
5 Year
10 Year
10 Year
30 Year
30 Year
0.58
0.01
0.62
0.01
0.58
0.01
0.60
0.09
0.53
0.02
0.57
0.07
0.47
0.04
0.49
0.15
0.61
0.20
0.65
0.19
0.55
0.29
0.63
0.36
1.26
0.93
1.30
0.96
1.42
1.25
1.58
1.36
2.41
2.12
2.53
2.25
2.69
2.56
2.86
2.80
4.12
3.78
3.42
3.95
3.73
3.87
3.85
4.02
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UK gilt and US treasury yield vs. Time to maturity (2011 aug 22.)
4
3,5
3
2,5
2
1,5
1
0,5
0
0
UK gilt
US Treasury
5 10 15 20
29

• 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.
30

YTM (r)
1981
1987 & Normal
1976
Year
1 5 10 20 30
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
31

U.S. Treasury Strip Spot Rates as of February 2009: the yield curve
1,0
0,5
0,0
2,5
2,0
1,5
4,5
4,0
3,5
3,0
Maturity
The yield curve depicts the term structure of interest rate.
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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
-1078.80
105
C1
105
C2
105
C3
105
C4
1105
C5
Calculate IRR = 8.5%
Obs: använd Ränta= som argument I excel program svenska version.
33

34

Annual rates of inflation in the United States from 1900–2008.
15
10
5
25
20
-10
-15
0
-5
35

Global Inflation Rates
Averages from 1900-2006
12,00
10,00
8,00
6,00
4,00
2,00
0,00
36

Debt & Interest Rates
Nominal r = Real r + expected inflation
(approximation)
Actual formula
1
 r nominal

( 1
 r real
)

( 1
 i )

UK Bond Yields
20
18
16
14
12
10
8
6
4
2
0
10 year nominal interest rate
10 year real interest rate
38

United Kingdom
15,00
10,00
5,00
0,00
30,00
25,00
20,00
Inflation
T-Bill Returns
39

United States
16,00
14,00
12,00
10,00
8,00
6,00
4,00
2,00
0,00
-2,00
Inflation
T-Bill Returns
40

Germany
12,00
10,00
8,00
6,00
4,00
2,00
0,00
-2,00
-4,00
Inflation
T-Bill Returns
41

• 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.
42

Yield Spread: credit risk
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!
7
6
5
4
3
2
1
0
-1
Spread on Baa bonds
Spread on Aaa bonds
Years
43

• 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
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