FIN 300

Bonds
Lecture 6

Topics Covered



  • Bonds
  • Bond Valuation
  • Yield to Maturity
  • Current Yield
  • Zero Coupon Bonds
  • Additional Features of Bonds
  • Term Structure of Interest Rates

Bonds


  • Debt securities
  • Large sums of money raised
  • Promise to pay specified amounts at specified times
  • Maturity describes the lifetime of the bond
  • Asset that entitles the owner to specified cash flows at specified times
    •     Coupon Payments
    •     Face Value

  • Coupon Rate

$\text{Coupon Rate}= \dfrac{\text{Annual Coupon}}{\text{Face Value}}$

Bond Valuation


A bond is made up of its coupons and its face value:


$\text{Bond Value} = \text{Value of Coupons} + \text{Face Value}$

                                            Annuity                            Future Cash Flow




$\text{Bond Value}= \text{Coupon} \times \left\lbrace \dfrac{1-[1/(1+r)^t]}{R} \right\rbrace + \dfrac{\text{Face Value}}{(1+R)^t}$

Example

A bond matures in 8 years with annual payments of $\$100$. If the interest rate is $5\%$, how much is the bond worth?

$\text{Bond Value}= \text{\$100} \times \left\lbrace \dfrac{1-[1/(1+0.05)^8]}{0.05} \right\rbrace \\ \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space + \dfrac{\text{1,000}}{(1+0.05)^8}$

$= \$1,323.16$
Example 2

A bond matures in 8 years with annual payments of $\$100$ PAID SEMIANNUALLY. If the interest rate is $5\%$, how much is the bond worth?

Step 1: get semi-annual $R = (1.05)^{1/2}-1 =0.0247$ $\text{Bond Value}= \text{\$50} \times \left\lbrace \dfrac{1-[1/(1+0.0247)^{16}]}{0.0247} \right\rbrace \\ \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space \space + \dfrac{\text{1,000}}{(1+0.0247)^{16}}$

$= \$1,331.64$

Yield to Maturity

  • We can observe the bond's price
  • The cash flows are predetermined
  • We can infer a rate of return

Yield to Maturity (YTM)

$\text{Price}= \text{Coupon} \times \left\lbrace \dfrac{1-[1/(1+YTM)^t]}{YTM} \right\rbrace + \dfrac{\text{Face Value}}{(1+YTM)^t}$


We need a financial calculator to find YTM

Current Yield

  • Not to be confused with YTM

  • $Current \space Yield = \dfrac{Coupon \space Payment}{Current \space Price}$

  • Example: $Price=\$980$ and $Coupon=\$50$ $Current \space Yield= \space ?$
$Current \space Yield = \dfrac{\$50}{\$980}$ $=5.1\%$

Zero Coupon Bonds

  • Coupon payment size varies
  • Some bonds even have adjustable rate coupons
  • Zero Coupon Bonds have no coupon

$Value_{Zero\ Coupon}= \dfrac{\text{Face Value}}{(1+R)^t}$

$YTM= \left( \dfrac{\text{Face Value}}{Price_{Zero\ Coupon}}\right)^{1/t}-1$

Additional Features of Bonds

Callable Bonds

  • Can be redeemed before maturity [issuer's option]
      Call Premium: Call Price - Stated Value
  • Call provision not always active
  • Deferred Call provision temporarily gives call protection
Debt Covenants

  • There is an agency problem with debt
      Who bears this cost?
  • Covenants limit this problem
    • Explicitely prohibit activity
    • Leverage
    • Dividend Increases
  • Not always good -- this could limit opportunities
Default Risk
  • Default is a possibility with debt
  • Ratings agencies monitor the quality of debt
    • S&P, Moody's
  • A Credit Default SWAP
    • Traded asset in another market
    • Pays owner in event of a default
Other Factors

  • Default risk premium
  • Liquidity premium
  • Taxability premium
      Municipal bonds exempt [conditions apply]
  • Term structure of interest rates

Term Structure of Interest Rates



  • The relation between interest rates and debt maturity
  • Real rate of interest
  • Inflation premium
  • Interest rate risk premium


See WSJ's "Understanding the Yield Curve"
RECAP:

Determinants Bond Yields and Interest Rates


  • Real rate of interest
  • Inflation
  • Interest rate risk
  • Default risk
  • Taxability
  • Illiquidity

Summary



  • Bonds
  • Bond Valuation
  • Yield to Maturity
  • Current Yield
  • Zero Coupon Bonds
  • Additional Features of Bonds
  • Term Structure of Interest Rates