Chapter 4 Valuing Bonds

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Chapter 4 Valuing Bonds

• Fin 401

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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 Wharton
• http//knowledge.wharton.upenn.edu/article/1498.cf
  m

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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
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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/YR2

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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 maturity
• B 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
• (1NR) (1IN)(1RR)
• Approximate relationship (works best if inflation
  rate is low) is
• NR INRR

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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 1980s 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
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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 gt 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
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12
10
Interest Rate
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6
4
2
5
10
15
20
30
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Years to Maturity
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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 UST Est 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
RATE MATURITY MO/YR BID ASKED CHG ASK YLD
Government Bonds Notes Government Bonds Notes Government Bonds Notes Government Bonds Notes Government Bonds Notes Government Bonds Notes
5.500 May 09n 10713 10714 3 3.83
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Valuation Fundamentals
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The Basic Valuation Model

• P0 Price of asset at time 0 (today)
• CFt Cash flow expected at time t
• r Discount rate (reflecting assets 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 companys 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

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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 bonds 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
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Semi-Annual Interest Payments
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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
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Bonds by Features
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Bonds by Features (Continued)
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Bonds by Features (Continued)
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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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