Chapter 4 Valuing Bonds

Professor ThomsonFin 3013

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Quote from Gyourko (UPenn)• "Basically we've been growing rich people

in the U.S.," he said. In 1940, less than 1% of families earned $100,000 in today's dollars. By 1970 that income level applied to about 5% of families. By 2000 it applied to about 12% of families.

From Knowledge at Whartonhttp://knowledge.wharton.upenn.edu/article/

1498.cfm

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Bonds

• Bonds are debt instruments (i.e. loans)

• Government Bonds include:– US Treasury– Federal Agency– Municipal (Government bonds issued by

non Federal entities such as States and Local Governments

• Corporate Bonds – are private Bonds

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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

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Bonds

• Bonds typically make “interest only” payments, and repay the amount borrowed at maturity. – New bonds may be issue to repay an

issue that is maturing.

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Par Value or Face Value

• The Par or Face Value is the amount that will be refunded at the maturity date.

• The par value is usually $1000 (especially for corporate bonds).

• Assume $1000 par value unless another value is provided.

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Coupon Rate

• The coupon rate is the annual rate of interest (APR) paid on the bonds par value. E.g. 6.125% or 6 1/8

• Bond coupons historically were in 1/8% increments, but that is becoming less common

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Coupon Payment

• The coupon payment is the periodic interest payment made to bond holders.

• Payments per year, P/YR, is the number of coupon payments per year

• P/YR = 2 for a typical (semiannual) bond• If P/YR not stated, assume P/YR=2

earymentsPerYNumberOfPa

FaceValueCouponRateCouponPmt

*

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Show bond quote from WSJ

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Example 4.1: Semi Annual Coupon Bond

• A 6% semi annual coupon bond has 10 years until maturity. The market (discount) rate is 5%. What is its price?

• What would be the price of a similar annual coupon bond?

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Example 4.2:

• Consider a 7% semiannual coupon bond with 28 years until maturity. The market rate = 8%. What is the price of the bond?

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Bond Price depends on the Market rate (or discount rate or YTM)Example 4.3: Consider 2 Bonds

A: 7% Bond with 28 years to maturityB: 7% Bond with 4 years to maturity

Compute the market price of these bonds as the market rate changes from 3-10%

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Example 4.4: What is the YTM of the Wachovia Bond?

• The Wachovia Capital trust bond with a 5.800 coupon which matures Mar 15, 2011 has a price quote of 97.748. What is its YTM? (Assume today is March 16, 2006)

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Example 4.5 Bond Prices

• You purchased a 5% semi annual coupon bond, with 10 years until maturity, one year ago when the market rate was 7%. The market rate is now 6%. What price did you pay for your bond, and what could you sell it for today?

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Inflation

• What matters is not how many $ you have, but what you can purchase with the $ you have.

• Measures of inflation compute how many $ it takes over time to purchase the same basket of goods

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Inflation: Some Notation

• NR = Nominal Rate, which is the quoted rate or yield on a bond

• RR = Real Rate, which measures your increase in purchasing power over time

• IN = INflation rate, which is the rate at which the cost of goods goes up

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Fisher Effect

• The Fisher effect shows the relationship among the nominal rate [NR], the inflation rate, [IN], and the real rate [RR].

• Exact relationship is:(1+NR) = (1+IN)*(1+RR)

• Approximate relationship (works best if inflation rate is low) is:

NR = IN+RR

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Example 4.5: Calculating the real rate of return on a Treasury Bill

• If Treasury bills are currently paying 5 percent and the inflation rate is 3.4 percent, what is the approximate real rate of interest? The exact real rate?

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What affects Bond Yields?

• Inflation – the higher the inflation rate, the higher the bond yield (bond yields were much higher in early 1980’s than today because inflation was higher)

• Default risk – Riskier bonds have higher yields (Thus, Treasury bonds have lower yields than corporate bonds, and investment grade bonds have lower yields than “junk bonds”

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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

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Bond Yields (continued)

• Liquidity – highly liquid bonds such as Treasuries have lower yields than safe, but less traded bonds.

• Taxes – Bonds that are tax free (most Municipal Bonds) have lower yields than taxable bonds

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Bond Yields (continued)

• Maturity – Other things equal, bonds with a longer time until maturity usually have a higher yield than bonds near their maturity date (when this is not true, we say we have an inverted yield curve)

• The Treasury Yield Curve plots the yield on Treasury Bonds versus their maturity, and it is typically upward sloping. (see Wall Street Journal)

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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?

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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

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See Smart Animation

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Example 4.7

• Example 4.7. Zero coupon Treasury strips with 3 years until maturity have a yield of 5%, while similar 2-year strips yield 6%. According to the expectations theory, what yield will one year strips have two years from now?

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Bond Indenture

• Are “the rules” I.e. is the bond contract

• It states the provisions of the bond including the coupon rate and maturity date

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Possible Bond Provisions

• Call Provision– Allows bond to be refunded (I.e. called)

prior to its maturity date

• Put Provision– Allows the bond purchaser to sell the

bond back to the issuer prior to its maturity date

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Possible Bond Provisions

• Convertible Bond– Allows the bond to be swapped for stock– This is an “option” as it gives you the

right but not the obligation to do the swap

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Covenants to Protect Bondholders• May have a limit on the dividends the

firm is allowed to pay, to keep cash in the firm for paying bondholders coupons

• Seniority Rule– Most senior (I.e. first issued) have their

coupon paid before junior issues, and has first claim on firm assets in default

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Covenants to Protect Bondholders

• Sinking Fund – various ways to ensure that the bond will be repaid at maturity, such as making deposits into a dedicated account for this purpose, or repurchasing some bonds over time

• Collateral – may be required to pledge certain assets of the firm as surity

• Debenture – a bond where no collateral is pledged. Most bonds are debentures

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Zero Coupon Bonds

• These bonds are bought at a deep discount and redeemed for par

• A disadvantage is the you must pay taxes each year on the imputed interest earned, even though no coupon interest is paid to you.

• More popular for tax sheltered investments such as IRA or insurance

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Other Bond Types

• Variable Coupon – The coupon paid each period depends on an interest rate index– For example, the coupon on Series EE

savings bond is set to 90% of the yield on 5 year Treasury Bonds

• TIPS (Treasury Inflation Protected Securities)– These Treasury Bonds pay a real coupon

rate, on a Face Value that adjusts with inflation thus providing a real rate of return for investors

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End of lecture notes

• The slides which follow are alternate ways to state what has been covered thus far, and some additional information for those that may be interested.

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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

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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

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Valuation Fundamentals

Present Value of Future Cash Flows

Link Risk & Return

Expected Return on Assets

Valuation

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The Basic Valuation Model

)r +(1CF + . . . +

)r +(1

CF +

)r +(1

CF = P n

n2

21

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• 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

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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

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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.

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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 =

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Semi-Annual Interest Payments

An example....

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....)

21(

2

)2

1(

2

)2

1(

2Price

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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.

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Interest Rate Risk

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

different maturities?

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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.

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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)

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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

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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

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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

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.

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