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Chapter 4 Valuing Bonds . Professor Thomson Fin 3013. Quote from Gyourko (UPenn).

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### Bond Valuation

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 Wharton

http://knowledge.wharton.upenn.edu/article/1498.cfm

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

Bond Markets

The U.S bond market has grown from $250 billion in 1950 to $22 trillion in 2004

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.

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.

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

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

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?

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?

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 maturity

B: 7% Bond with 4 years to maturity

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

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)

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?

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

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

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

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?

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”

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

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

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

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)

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?

May 1981

January 1995

August 1996

October 1993

Yield Curves U.S. Treasury Securities16

14

12

10

Interest Rate %

8

6

4

2

1

3

5

10

15

20

30

Years to Maturity

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?

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

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

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

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

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

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

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

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.

Corporate Bond Quotations

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

Rate

Ask Yield

Coupon rate of 5.5%

Yield to maturity on the ask price

Bid price:the price traders receive if they sell a bond to the dealer. Quoted in increments of 32nds of a dollar

Bid prices

Ask prices

(percentage of par value)

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

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

U.S. Treasury Bond QuotationsPresent Value of Future Cash Flows

Link Risk & Return

Expected Return

on Assets

Valuation

Valuation FundamentalsThe Basic Valuation Model

- 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

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

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.

r > Coupon Interest Rate

P0 < par value

DISCOUNT

=

r < Coupon Interest Rate

P0> par value

PREMIUM

=

Bond Premiums and DiscountsWhat happens to bond values if required return is not equal to the coupon rate?

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

An example....

Value a T-Bond

Par value = $1,000

Maturity = 2 years

Coupon rate = 4%

r = 4.4% per year

= $992.43

Semi-Annual Interest PaymentsFactors 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.

Interest Rate Risk

What does this tell you about the relationship

between bond prices and yields for bonds with

different maturities?

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.

Usually with par $1000 and semi-annual coupon

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

Corporate Bonds

Municipal Bonds

- 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

Treasury Bonds

Agency Bonds

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

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

Fixed vs. Floating Rates

- 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

Secured vs. Unsecured Bonds

Bonds by FeaturesDiscount bonds or pure discount bonds

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

Zero-Coupon Bonds

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

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.

Callable and Putable Bonds

- Sinking fund provisions: the issuer is required to gradually repurchase outstanding bonds.
- Protective covenants: requirements the bond issuer must meet
- Positive and negative covenants

Protection from Default Risk

Bonds by Features (Continued)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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