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```									                       Valuing Bonds

Professor Dr. Rainer Stachuletz
Corporate Finance

Berlin School of Economics

Berlin, 04.01.2006                Fußzeile             1
Valuation Fundamentals

Present Value of Future Cash Flows

Expected Return
on Assets

Valuation

Berlin, 04.01.2006                 Fußzeile               2
The Basic Valuation Model
CF 1     CF 2              CF n
P0 =        1
+      2
+ . . .+
(1+ r ) (1+ r )            (1+ r )n

•    P0 = Price of asset at time 0 (today)
•    CFt = Cash flow expected at time t
•    r = Discount rate (reflecting asset’s risk)
•    n = Number of discounting periods (usually years)

This model can express the price of any asset at
t = 0 mathematically.
Marginal benefit of owning the asset: right to
Marginal cost: opportunity cost of owning the
Berlin, 04.01.2006
assetFußzeile                    3
Valuation Fundamentals: Example

Company issues a 5% coupon interest rate, 10-year
instrument with a \$1,000 par value
Assume annual interest payments

 Investors in company’s financial instrument
- \$50 coupon interest paid at the end of each
year
- \$1,000 principal at the end of the 10th year

P = \$1,000
Berlin, 04.01.2006           Fußzeile                  4
Yield to Maturity (YTM)

Estimate of return investors earn if they buy
the bond at P0 and hold it until maturity

The YTM on a bond selling at par will always equal
the coupon rate.

YTM is the discount rate that equates the
PV of a bond’s cash flows with its price.

Berlin, 04.01.2006          Fußzeile                 5

What happens to bond values if required return is not
equal to the coupon rate?

The bond's price will differ from its par value

r > Coupon Interest Rate                P0 < par value
=   DISCOUNT

r < Coupon Interest Rate                P0 > par value

Berlin, 04.01.2006                          Fußzeile                                   6
Semi-Annual Interest Payments
C       C         C             C
F
Price      2     2         2     .... 2
r 1    r 2        r 3            r 2n
(1  ) (1  )     (1  )          (1  )
2      2          2              2

Value a T-Bond                   \$40          \$40        \$40      \$40
 1,000
P0        2           2         2      2
Par value = \$1,000                      1          2          3               4
    0.044   0.044   0.044   0.044 
1         1       1       1          
Maturity = 2 years                2          2        2          2 

Coupon rate = 4%             \$20      =
\$20 \$992.43 \$1,020
\$20
               2
     3
      4

(1.022) (1.022) (1.022) (1.022)
r = 4.4% per year
Berlin, 04.01.2006                  Fußzeile                                  7
Factors that Affect Bond Prices

Time to maturity: bond prices converge to par
value (plus final coupon) with passage of time.

Interest rates: bond prices and interest rates move
in opposite directions.

Changes in interest rates have larger impact on long-
term bonds than on short-term bonds.

Berlin, 04.01.2006        Fußzeile                      8
Interest Rate Risk

\$1,500
\$1,300
\$1,100
\$900
\$700
\$500
1   2   3   4   5    6     7         8    9    10   11   12   13   14   15

Yield to maturity, %
2-year bond              10-year bond

What does this tell you about the relationship
between bond prices and yields for bonds with
different maturities?
Berlin, 04.01.2006                                  Fußzeile                                           9
Primary vs. Secondary Markets

Primary market: the initial sale of bonds by issuers
to large investors or syndicates

Secondary market: the market in which investors

Trades in the secondary market do not raise
any capital for issuing firms.

Berlin, 04.01.2006                  Fußzeile                   10
Bonds by Issuer

• Usually with par \$1000 and semi-
Corporate         annual coupon
Bonds          • Bonds if maturity > 10 years; notes if
maturity < 10 years

Municipal      • Issued by local and state government
Bonds         • Interest on municipal bonds tax-free
• If maturity < 1 year: Treasury Bills
• If 1 year < maturity < 10 years:
Treasury     Treasury Notes
Bonds     • Maturity > 10 years: Treasury Bonds
• Used to fund budget deficits

Agency     • Issued by government agencies:
FHLB, FNMA (Fannie Mae), GNMA
Berlin, 04.01.2006
Bonds        (Ginnie Mae), FHLMC (Freddie Mac)
Fußzeile                          11
Bonds by Features

• Floating-rate bonds: coupon tied to
Fixed vs.     prime rate, LIBOR, Treasury rate or
other interest rate
Floating    • Floating rate = benchmark rate +
• Floating rate can also be tied to the
inflation rate: TIPS, for example
• Unsecured bonds (debentures) are
backed only by general faith and
Secured vs.           credit of issuer
Unsecured           • Secured bonds are backed by specific
assets (collateral)
Bonds             • Mortgage bonds, collateral trust
bonds, equipment trust certificates

Berlin, 04.01.2006                  Fußzeile                          12
Bonds by Features (Continued)

• Discount bonds or pure discount
Zero-Coupon          bonds
• Sell below par value
Bonds           • Treasury Bills (Tbills)
• Treasury STRIPs

• Convertible bonds, in addition to
Convertible         paying coupon, offers the right to
and              convert the bond into common stock
of the issuer of the bond
Exchangeable       • Exchangeable bonds are convertible
Bonds             in shares of a company other than
the issuer’s
Berlin, 04.01.2006              Fußzeile                         13
Bonds by Features (Continued)

• Callable bonds: bond issuer has the
right to repurchase the bonds at a
Callable and         specified price (call price).
• Firms could retire and reissue debt if
Putable            interest rates fall.
Bonds           • Putable bonds: the investors have
the right to sell the bonds to the
issuer at the put price.

• Sinking fund provisions: the issuer is
outstanding bonds.
from Default      • Protective covenants: requirements
Risk           the bond issuer must meet
• Positive and negative covenants
Berlin, 04.01.2006               Fußzeile                          14
Bond Markets

The U.S bond market has grown from \$250 billion
in 1950 to \$22 trillion in 2004
Amount Oustanding in 2004
\$1.900
\$3.900

\$3.700

Municipal Bonds
Treasury Bonds
Corporate Bonds
Federal Agency Bonds
Mortgage-related debt
\$5.300
Other

\$4.500

\$2.700
Berlin, 04.01.2006                                  Fußzeile                                     15
U.S. Treasury Bond Quotations

MO/YR                                                   YLD

Government Bonds & Notes
5.500            May 09n    107:13                 107:14    3           3.83

Rate                                     Coupon rate of 5.5%

sell a bond to the dealer. Quoted in
Bid prices                          increments of 32nds of a dollar
(percentage of
par value)
and bid prices.

Berlin, 04.01.2006                                   Fußzeile                                16
Corporate Bond Quotations

Company                                                             Estimated         Est \$ Vol
Coupon   Maturity      Last Price           Last Yield               UST

SBC Comm
5.875    Aug 15,2012   107.161              4.836        80          10    73,867
(SBC)

Corporate prices are quoted as percentage of par,
without the 32nds of a dollar quoting convention

Yield spread: the difference in yield-to-maturities
between a corporate bond and a Treasury bond with
same maturity

The greater the default risk, the higher
Berlin, 04.01.2006                                     Fußzeile                                              17
Bond Ratings

Bond ratings: grades assigned to bond issues based
on degree of default risk

Investment-          • Moody’s Aaa to Baa3 ratings
grade bonds          • S&P and Fitch AAA to BBB-
ratings

Junk bonds         • Moody’s Ba1 to Caa1 or
lower
• S&P and Fitch BB to CCC+
Berlin, 04.01.2006
or lower
Fußzeile                   18
Term Structure of Interest Rates

 Relationship between yield and maturity is called the Term Structure
of Interest Rates
- Graphical depiction called a Yield Curve
- Usually, yields on long-term securities are higher than on short-term
securities.
- Generally look at risk-free Treasury debt securities
 Yield curves normally upwards-sloping
- Long yields > short yields
- Can be flat or even inverted during times of financial stress

What do you think a Yield Curve would look like
graphically?
Berlin, 04.01.2006                                  Fußzeile                                   19
Yield Curves U.S. Treasury Securities

16

14                                                May 1981

12
Interest Rate %

10

8                                              January 1995

6                                                   August 1996
October 1993
4

2

1   3   5   10             15        20                  30

Years to Maturity

Berlin, 04.01.2006                                         Fußzeile                                  20
Bond Valuation

 Bond price equals present value of its coupons and principal.

     Bond prices are inversely related to interest rates.

     Bonds could have a number of features: such as convertibility,
callability.

Berlin, 04.01.2006                          Fußzeile                       21

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