Bond Prices and Yields

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Chapter 10

• Bond Prices and Yields

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Bond Characteristics

• Face or par value
• Coupon rate
• Zero coupon bond
• Compounding and payments
• Accrued Interest
• invoice price versus quoted price
• Indenture

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Provisions of Bonds

• Secured or unsecured (debenture)
• Call provision
• refunding
• call price
• deferred callable bond
• coupon rates and promised ytm at issuance

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Provisions of Bonds

• Convertible provision
• conversion ratio
• market conversion value
• conversion premium
• coupon rate ytm at issuance
• Convertible example
• conversion ratio 25
• market price of stock 42
• callable bond price 1150

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Provisions of Bonds

• Put provision (putable bonds)
• coupon rate ytm at issuance
• Floating rate bonds
• changing credit condition of issuer
• Sinking funds

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Other innovations

• Pay in kind bonds (pik)
• reverse floaters
• indexed bonds (TIPS -Treasury Inflation
  Protection bonds)

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Default Risk and Ratings

• Rating companies
• Moodys Investor Service
• Standard Poors
• Duff and Phelps
• Fitch
• Rating Categories
• Investment grade
• Speculative grade

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Factors Used by Rating Companies

• Coverage ratios
• Leverage ratios
• Liquidity ratios
• Profitability ratios
• Cash flow to debt

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Protection Against Default

• Sinking funds
• Subordination of future debt
• Dividend restrictions
• Collateral
• mortgage bond
• equipment obligation
• collateral trust

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Bond Pricing

• PB Price of the bond
• Ct interest or coupon payments
• T number of periods to maturity
• y semi-annual discount rate or the
  semi-annual yield to maturity

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Solving for Price 10-yr, 8 Coupon Bond, Face
1,000




PB 1,148.77
Ct 40 (SA) P 1000 T 20 periods r 3 (SA)
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Bond Prices and Yields

• Prices and Yields (required rates of return) have
  an inverse relationship
• When yields get very high the value of the bond
  will be very low
• When yields approach zero, the value of the bond
  approaches the sum of the cash flows

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Prices and Coupon Rates
Price
Yield
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Yield to Maturity

• YTM the discount rate that makes the present
  value of the bonds promised payments equal to
  its price.
• Bond is priced at 1067.95, it has a coupon rate
  of 9 paid semiannually, a par value of 1000,
  and 10 years to maturity. Find the bonds ytm.
• What is the current yield?
• Bond is priced at 945.40 , it has a coupon rate
  of 6 paid semiannually, a par value of 1000,
  and 14 years to maturity. Find the bonds ytm.
• What is the current yield?

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YTM versus current yield versus coupon rate

• Bond selling at par
• coupon YTM current yield
• Bond selling at a premium
• coupon gt current gt YTM
• Bond selling at a discount
• coupon lt current lt YTM

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Yield to call (YTC)

• Similar to YTM, but use time to first call date
  and call price as future value.
• Bond with 15 years to maturity, par of 1000, a
  coupon rate of 8 (paid semiannually), price of
  1025, callable in 5 years at 1080. Find YTC.

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Realized compound yield versus yield to maturity

• YTM will equal the realized return over the life
  of the bond if all payments are reinvested at an
  interest rate equal to the bonds yield.
• Consider a bond with 10 years to maturity, coupon
  rate of 9 percent paid annually, and a price of
  1067.10.

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Realized compound yield (RCY) versus yield to
maturity (YTM)

• Consider a bond with 10 years to maturity, coupon
  rate of 9 percent paid annually, and a price of
  1067.10.
• What is its ytm?
• Realized compound yield if you reinvest at ytm?
• RCY if you reinvest at 3 percent?

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Holding period return (HPR) versus YTM.

• Consider a bond with 10 years to maturity, coupon
  rate of 9 percent paid annually, and a price of
  1067.10. Note ytm 8
• Suppose you hold the bond one year and interest
  rates decline to 7 percent. Calculate your HPR.
• Suppose instead that rates had risen to 9
  percent. What is your HPR?

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Original Issue Discount (OID)

• Consider a 10 year Treasury strip with a yield of
  5 percent and face of 10,000.
• Price 6,139.13
• After one year (yield 5)
• P 6,446.09
• Difference implicit interest 306.96
• If you sold the strip for 6,500, then you would
  have interest income of 306.96 and capital gain
  of 53.91

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Term Structure of Interest Rates

• Relationship between yields to maturity and
  maturity
• Yield curve - a graph of the yields on bonds
  relative to the number of years to maturity
• Usually Treasury Bonds
• Have to be similar risk or other factors would be
  influencing yields

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Yield Curves
Yields
Upward Sloping
Downward Sloping
Maturity
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Theories of Term Structure

• Expectations
• Liquidity Preference
• Upward bias over expectations
• Market Segmentation
• Preferred Habitat