© 2009 Cengage Learning/South-Western

Valuing Bonds

Chapter 4

2

Valuation Basics

Present Value of Future Cash Flows

Link Risk & Return

Expected Return on Assets

Valuation

3

The Fundamental 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 flows

Marginal cost: opportunity cost of owning the asset

4

Bond Vocabulary

Principal • The amount of money on which interest is paid.

Maturity date

• The date when a bond’s life ends and the borrower must make the final interest payment and repay the principal.

Par value • The face value of a bond, which the borrower repays at maturity.

Coupon • A fixed amount of interest that a bond promises to pay investors.

Indenture • A legal document stating the conditions under which a bond has been issued.

5

Bond Vocabulary

Coupon rate • The rate derived by dividing the bond’s annual coupon payment by its par value.

Coupon yield

• The amount obtained by dividing the bond’s coupon by its current market price (which does not always equal its par value). Also called current yield.

6

Bond Valuation: The Basic Equation

• Bond Price = PV of coupons + PV of principal

Assuming annual interest:

)r +(1

M+

)r +(1

C + . . . +

)r +(1

C +

)r +(1

C = P nn210

)r +(1

M+

rr

C = n

n

1

11

7

Time Line for Bond Valuation(Annual Interest Payments)

Worldwide United9-1/8% Coupon,$1,000 Par ValueBond, Maturing atEnd of 2019;Required ReturnAssumed To Be 8%

8

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.

9

YTM

An approximation formula for yield-to-maturity gives a reasonably close approximation of yield to maturity for low yields. It is not as accurate for very high-yielding bonds. The formula states:

YTM = I + (F-P)/N (F+P)/2

I = dollar amount of interest F = face value of bond P = price of bond N = number of years to maturity

10

YTM

Suppose a $1,000 face value bond is selling for $1,100. The bond has 10 years left to maturity. The bond has an 8% coupon rate. Using the approximation formula, the YTM is: 80 + (1000 – 1100)/10 = 70/1050 = 6.7% (1000 + 1100)/2 Solving for YTM using a financial calculator, the solution is: N = 10 PMT = 80 FV = 1,000 PV = -1,100 Solve for I = 6.6%

11

YTM

Now suppose you have a deeply discounted bond, which could result if a company were financially distressed and investors were reluctant to buy the bonds for fear that they would not receive future payments. A $1,000 face value bond is selling for only $200. The bond has 10 years to maturity and a coupon payment of $80. Using the approximation formula, the YTM is: 80 + (1000 – 200)/10 = 160/600 = 26.7% (1000 + 200)/2 Calculating YTM using a financial calculator yields: N = 10 PMT = 80 FV = 1,000 PV = -200 Solve for I = 44.6% However, it is very rare for a bond to have such a high yield; this would only occur with a very deeply discounted bond. Note also that this is a way to compute IRR without using a financial calculator.

12

What happens to bond values if the 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=

Bond Premiums and Discounts

13

On Discount Rates

• Generally,

• the greater the uncertainty about an asset’s future benefits,

• the higher the discount rate investors will apply

• when discounting those benefits to the present.

14

Semiannual Compounding

An example....Value a T-Bond Par value = $1,000 Maturity = 2 yearsCoupon rate = 4% r = 4.4% per year

= $992.43

nr

FC

r

C

r

C

r

C

2321 )2

1(

2....)

21(

2

)2

1(

2

)2

1(

2Price

15

Economic Forces Affecting 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.

16

The Relationship BetweenBond Prices and Required Returns

6% coupon rate for both

17

Interest Rate Risk

Interest Rate Risk

• The risk that changes in market interest rates will cause fluctuations in a bond’s price. Also, the risk of suffering losses as a result of unanticipated changes in market interest rates.

Real return• Approximately, the difference

between an investment’s stated or nominal return and the inflation rate.

Nominal return

• The stated return offered by an investment unadjusted for the effects of inflation.

18

Treasury Bond Yields and Inflation Rates

19

Primary versus 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.

20

Types of 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 deficits

Agency Bonds

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

21

Types of 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

22

Types of Bonds: By Features

Zero-Coupon Bonds

• Zero-coupon bonds pay no interest• Also known as 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

23

Table 4.1 Zero-Coupon Bond Prices and Taxable Income

24

Types of Bonds: By Features

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

25

Types of Bonds: By Features

Treasury Inflation-Protected Securities(TIPS)

• Notes and bonds issued by the federal government that make coupon payments that vary with the inflation rate.

26

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

$3,700

$4,500

$2,700

$5,300

$3,900

Municipal Bonds

Treasury Bonds

Corporate Bonds

Federal Agency Bonds

Mortgage-related debt

Other

27

U.S. Treasury Bond Quotations

RATEMATURITY

MO/YRBID ASKED CHG

ASK

YLD

Government Bonds & Notes5.500 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

28

Corporate Bond Quotations

Company

(Ticker)Coupon Maturity Last Price Last Yield

Estimated Spread

USTEst $ Vol (000s)

SBC Comm

(SBC)5.875

Aug 15,2012

107.161 4.836 80 10 73,867

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 the yield spread

29

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

30

Figure 4.2 Bond Ratings

31

Table 4.3 The Relationship Between Bond Ratings and Spreads at Different Maturities at a Point in Time

32

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?

33

Fig. 4-5 Yield Curves for U.S. Government Bonds

34

The Expectations Hypothesis

35

Advanced Bond Valuation

Liquidity Preference

Theory

• States that the slope of the yield curve is influenced not only by expected interest rate changes, but also by the liquidity premium that investors require on long-term bonds.

Preferred Habitat Theory

• A theory that recognizes that the shape of the yield curve may be influenced by investors who prefer to purchase bonds having a particular maturity regardless of the returns those bonds offer compared to returns available at other maturities.

36

Valuing Bonds

• Bond price = present value of coupons + present value of principal

• Bond prices are inversely related to interest rates.

• Bonds can have features like convertibility and callability.

37

Bond Markets

P4-23. A corporate bond’s price is quoted as 102.312. If the bond’s par value is $1,000, what is its market price?

A4-23. $1,023.12 P4-24. A corporate bond’s price is quoted as 98.110. What is the price of the bond if its par value

is $1,000? A4-24. 98.110% of par value, or $981.10.

38

Advanced Bond Valuation– The Term Structure of Interest Rates

P4-25. A one-year Treasury bill offers a 6 percent yield to maturity. The market’s consensus forecast is that one-year T-bills will offer 6.25 percent next year. What is the current yield on a two-year Treasury security if the expectations hypothesis holds?

A4-25. (1+r)2 = (1.06)(1.0625), so r = 0.06125, or 6.125% P4-26. A one-year Treasury security offers a 4 percent yield to maturity (YTM). A two-year

Treasury security offers a 4.25 percent YTM. According to the expectations hypothesis, what is the expected interest rate on a one-year security next year?

A4-26. (1.0425)2 = (1.04)(1+r), so r = 0.045, or 4.5%

39

Valuation Fundamentals

P4-1. An oil well produces 20,000 barrels of oil per year. Suppose the price of oil is $50 per barrel. You want to purchase the right to the oil produced by this well for the next five years. At a discount rate of 10 percent, what is the value of the oil rights? (You can assume that the cash flows from selling oil arrive at annual intervals).

A4-1. 787,790,3$10.1

000,000,1$

10.1

000,000,1$

10.1

000,000,1$

10.1

000,000,1$

10.1

000,000,1$P

54321

P4-2. A best-selling author decides to cash in on her latest novel by selling the rights to the

book’s royalties for the next four years to an investor. Royalty payments arrive once per year, starting one year from now. In the first year the author expects $400,000 in royalties, followed by $300,000, then $100,000, and then $10,000 in the three subsequent years. If the investor purchasing the rights to royalties requires a return of 7 percent per year, what should the investor pay?

A4-2. 13.122,725$07.1

000,10$

07.1

000,100$

07.1

000,300$

07.1

000,400$P

4321

40

Bond ValuationP4-3. A bond sells for $900 and offers a coupon yield of 7.2 percent. What is the bond’s annual

coupon payment?

A4-3. $X/$900 = 0.072 so X = $64.80 P4-4. A bond offers a coupon rate of 5 percent. If the par value is $1,000 and the bond sells for

$1,250, what is the coupon yield?

A4-4. $50/$1,250 = 0.04 or 4%. P4-5. A $1,000 par value bond has a coupon rate of 8 percent and a coupon yield of 9 percent.

What is the bond’s market price? A4-5. The annual coupon is $80. To find the price, solve 0.09 = $80/P, P = $888.89 P4-6. A bond makes two $45 interest payments each year. Given that the bond’s par value is

$1,000 and its price is $1,050, calculate the bond’s coupon rate and coupon yield. A4-6. Coupon yield is $90/$1,050 = 0.0857 or 8.57%. Coupon rate = $90/$1,000 = 0.09, or 9%. P4-7. A $1,000 par value bond makes two interest payments each year of $45 each. What is the

bond’s coupon rate?

A4-7. 9% = 45(2)/1,000