bonds and valuing bonds

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Berlin, 04.01.2006 Fußzeile 1 Bonds and Valuing Bonds Professor Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics

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Bonds and Valuing Bonds. Professor Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics. The Basic Valuation Model. P 0 = Price of asset at time 0 (today) CF t = Cash flow expected at time t r = Discount rate (reflecting asset’s risk) - PowerPoint PPT Presentation

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Page 1: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 1

Bonds and Valuing Bonds

Professor Dr. Rainer Stachuletz

Corporate Finance

Berlin School of Economics

Page 2: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 2

The Basic Valuation Model

)r +(1CF + . . . +

)r +(1

CF +

)r +(1

CF = P n

n2

21

10

• 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 receive the cash flowsMarginal cost: opportunity cost of owning

the asset

Page 3: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 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 receive the contractual rights- $50 coupon interest paid at the end of each

year - $1,000 principal at the end of the 10th year

000,1$ = P

Page 4: Bonds and Valuing Bonds

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.

Page 5: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 5

Bond Premiums and Discounts

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

P0 < par valuer > Coupon Interest Rate DISCOUNT =

P0 > par valuer < Coupon Interest Rate PREMIUM =

Page 6: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 6

Semi-Annual Interest Payments

Value a T-Bond

Par value = $1,000

Maturity = 2 years

Coupon rate = 4%

r = 4.4% per year

= $992.43

nr

FC

r

C

r

C

r

C

2321 )2

1(

2....)2

1(

2

)2

1(

2

)2

1(

2Price

Page 7: Bonds and Valuing Bonds

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.

Page 8: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 8

Interest Rate Risk

What does this tell you about the relationship between bond prices and yields for bonds with

different maturities?

Page 9: Bonds and Valuing Bonds

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 trade with each other

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

Page 10: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 10

Bonds by Issuer

Corporate Bonds

• Usually with par $1000 and semi-annual coupon

• Bonds if maturity > 10 years; notes if maturity < 10 years

Municipal Bonds

• Issued by local and state government

• Interest on municipal bonds tax-free

Treasury Bonds

• If maturity < 1 year: Treasury Bills

• If 1 year < maturity < 10 years: Treasury Notes

• Maturity > 10 years: Treasury Bonds

• Used to fund budget deficitsAgency Bonds

• Issued by government agencies: FHLB, FNMA (Fannie Mae), GNMA (Ginnie Mae), FHLMC (Freddie Mac)

Page 11: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 11

Bonds by Features

Fixed vs. Floating Rates

• Floating-rate bonds: coupon tied to prime rate, LIBOR, Treasury rate or other interest rate

• Floating rate = benchmark rate + spread

• Floating rate can also be tied to the inflation rate: TIPS, for example

Secured vs.

Unsecured Bonds

• Unsecured bonds (debentures) are backed only by general faith and credit of issuer

• Secured bonds are backed by specific assets (collateral)

• Mortgage bonds, collateral trust bonds, equipment trust certificates

Page 12: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 12

Bonds by Features (Continued)

Zero-Coupon Bonds

• Discount bonds or pure discount bonds

• Sell below par value• Treasury Bills (Tbills) • Treasury STRIPs

Convertible and

Exchangeable Bonds

• Convertible bonds, in addition to paying coupon, offers the right to convert the bond into common stock of the issuer of the bond

• Exchangeable bonds are convertible in shares of a company other than the issuer’s

Page 13: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 13

Bonds by Features (Continued)

Callable and

Putable Bonds

• Callable bonds: bond issuer has the right to repurchase the bonds at a specified price (call price).

• Firms could retire and reissue debt if interest rates fall.

• Putable bonds: the investors have the right to sell the bonds to the issuer at the put price.

Protection from

Default Risk

• Sinking fund provisions: the issuer is required to gradually repurchase outstanding bonds.

• Protective covenants: requirements the bond issuer must meet

• Positive and negative covenants

Page 14: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 14

U.S. Treasury Bond Quotations

RATEMATURITY

MO/YRBID ASKED CHG

ASK

YLD

Government Bonds & Notes

5.500 May 09n 107:13 107:14 3 3.83

Rate Coupon rate of 5.5%

Bid pricesAsk prices

(percentage of par value)

Bid price: the price traders receive if they sell a bond to the dealer.

Quoted in increments of 32nds of a dollar

Ask price: the price traders pay to the dealer to buy a bond

Bid-ask spread: difference between ask and bid prices.

Ask Yield Yield to maturity on the ask price

Page 15: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 15

Bond Ratings

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

Investment-grade bonds

• Moody’s Aaa to Baa3 ratings

• S&P and Fitch AAA to BBB- ratings

Junk bonds • Moody’s Ba1 to Caa1 or lower

• S&P and Fitch BB to CCC+ or lower

Page 16: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 16

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?

Page 17: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 17

Yield Curves U.S. Treasury Securities

2

4

6

8

10

12

14

16

5 10 15 20 30

Years to Maturity

Inte

res

t R

ate

%

August 1996

October 1993

May 1981

January 1995

1 3

Page 18: Bonds and Valuing Bonds

Berlin, 04.01.2006 Fußzeile 18

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.