Valuing Bonds

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Valuation Basics

Present Value of Future Cash Flows Link Risk & Return Expected Return on Assets Valuation

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The Fundamental Valuation Model

P 0 = (1 CF + r 1 ) 1 + (1 CF + r 2 ) 2 + .

.

.

+ (1 CF + r n ) n

P 0 CF t = Price of asset at time 0 (today) = 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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Bond Vocabulary

Principal Maturity date Par value Coupon Indenture • The amount of money on which interest is paid.

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

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

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

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

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Bond Vocabulary

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

• 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.

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Bond Valuation: The Basic Equation

• Bond Price = PV of coupons + PV of principal Assuming annual interest:

C P 0 = (1 + r C ) 1 + (1 + r ) 2 + .

.

C .

+ (1 + r ) n M + (1 + r ) n = C

      1   1  1

r



n r

    

+ M (1 + r ) n

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Time Line for Bond Valuation

(Annual Interest Payments)

Worldwide United 9-1/8% Coupon, $1,000 Par Value Bond, Maturing at End of 2019; Required Return Assumed To Be 8%

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Yield to Maturity (YTM)

Estimate of return investors earn if they buy the bond at P 0 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 the required return is not equal to the coupon rate?

The bond's price will differ from its par value.

r > Coupon Interest Rate r < Coupon Interest Rate P 0 < par value

=

DISCOUNT P 0 > par value

=

PREMIUM

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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.

Semiannual Compounding

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C C

Price  ( 1  2

r

2 ) 1  ( 1  2

r

2 ) 2

C

 ( 1  2

r

2 ) 3

C

 ....

 2 ( 1  

F r

2 ) 2

n

An example....

Value a T-Bond Par value = $1,000 Maturity = 2 years Coupon rate = 4% r = 4.4% per year

P

0    1 $ 40 2 0 .

044 2    1    1 $ 40 2 0 .

044 2    2    1 $ 40 2 0 .

044 2    3    $ 40  1 , 000 2 1 0 .

044 2    4 = $992.43

 $ 20  ( 1 .

022 ) ( 1 $ 20 .

022 ) 2  $ 20 ( 1 .

022 ) 3  $ 1 , 020 ( 1 .

022 ) 4   $ 19 .

57  $ 19 .

15  $ 18 .

74  $ 934 .

97  $ 992 .

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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.

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The Relationship Between Bond Prices and Required Returns

6% coupon rate for both

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Interest Rate Risk

Interest Rate Risk Real return • 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.

• 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.

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Treasury Bond Yields and Inflation Rates

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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.

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Types of Bonds: By Issuer

Corporate Bonds Municipal Bonds Treasury Bonds Agency Bonds • Usually with par $1000 and semi-annual coupon • Bonds if maturity > 10 years; notes if maturity < 10 years • Issued by local and state government • Interest on municipal bonds tax-free • If maturity < 1 year: Treasury Bills • If 1 year < maturity < 10 years: Treasury Notes • Maturity > 10 years: Treasury Bonds • Used to fund budget deficits • Issued by government agencies: FHLB, FNMA (Fannie Mae), GNMA (Ginnie Mae), FHLMC (Freddie Mac)

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Types of Bonds: By Features

Fixed vs. Floating Rates Secured vs. Unsecured Bonds • 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 • 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

Types of Bonds: By Features

Zero-Coupon Bonds

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Convertible and Exchangeable 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 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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Types of Bonds: By Features

Callable and Putable Bonds Protection from Default Risk • 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.

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

• Protective covenants: requirements the bond issuer must meet • Positive and negative covenants

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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.

U.S. Treasury Bond Quotations

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RATE 5.500

Rate

MATURITY MO/YR May 09n BID ASKED CHG

Government Bonds & Notes

107:13 107:14 3

Coupon rate of 5.5%

ASK YLD 3.83

Bid prices Ask prices (percentage of par value) Ask Yield Bid price: the price traders receive if they sell a bond to the dealer. Quoted in increments of 32 nds 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.

Yield to maturity on the ask price

Corporate Bond Quotations

Company (Ticker) Coupon SBC Comm (SBC) 5.875

Maturity Aug 15,2012 Last Price 107.161

Last Yield 4.836

Estimated Spread 80 UST 10 Est $ Vol (000s) 73,867 Corporate prices are quoted as percentage of par, without the 32 nds of a dollar quoting convention

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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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Bond Ratings

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

Investment grade bonds Junk bonds • Moody’s Aaa to Baa3 ratings • S&P and Fitch AAA to BBB ratings • Moody’s Ba1 to Caa1 or lower • S&P and Fitch BB to CCC+ or lower

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Figure 4.2 Bond Ratings

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

Term Structure of Interest Rates

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

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The Expectations Hypothesis

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Advanced Bond Valuation

Liquidity Preference Theory Preferred Habitat 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.

• 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.

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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.