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Pricing of Bonds. Chapter 2. Time of Value. Future Value where: n = number of periods P n = future value n periods from now (in dollars) P o = original principal (in dollars) r = interest rate per period (in decimal form) Future Value of on Ordinary Annuity.

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time of value
Time of Value
  • Future Value

where:

n = number of periods

Pn = future value n periods from now (in dollars)

Po = original principal (in dollars)

r = interest rate per period (in decimal form)

  • Future Value of on Ordinary Annuity
time value of money
Time Value of Money
  • Present Value
  • Present Value of a Series of Future Values
time value of money4
Time Value of Money
  • Present Value of an Ordinary Annuity
bond pricing
Bond Pricing
  • price = PV of all future cash flows
  • to find price, you need
    • expected CFs
      • coupon payments
      • par value
    • yield
bond pricing6
Bond Pricing
  • price – yield relationship
    • inverse because as yield falls, PV of CFs increases and price of bond increases
    • price-yield curve is convex for noncallable bonds
  • discount / premium to par when coupon rate < / > required yield
  • market price changes when
    • yield changes due to credit quality of issuer
    • change in price of bond selling at discount/premium because getting closer to maturity
    • change in yield required by market for bonds of similar risk
bond pricing7
Bond Pricing
  • floater – security that has coupon rate that changes when market rates change
    • coupon = reference rate plus spread
    • reset periodically
    • cap / floor
  • inverse floater
    • created using a fixed rate bond (collateral)
    • create floater and inverse floater so that
      • total coupon interest paid to two bonds in each period is less than or equal to collateral’s coupon interest in each period
      • total par value of two bonds is less than or equal to collateral’s total par value
      • ie., two securities created so that CFs from collateral can satisfy obligation of floater and inverse floater